Webb, B (2001) Can robots make good models of biological behaviour? BEHAVIORAL AND BRAIN SCIENCES (2001) 24(6)

Can robots make good models of biological behaviour?

Barbara Webb
Centre for Computational and Cognitive Neuroscience
Department of Psychology
University of Stirling
Stirling FK9 4LA
Scotland, U.K.


How should biological behaviour be modelled? A relatively new approach is to investigate problems in neuroethology by building physical robot models of biological sensorimotor systems. The explication and justification of this approach are here placed within a framework for describing and comparing models in the behavioural and biological sciences. First, simulation models - the representation of a hypothesis about a target system - are distinguished from several other relationships also termed 'modelling' in discussions of scientific explanation. Seven dimensions on which simulation models can differ are defined and distinctions between them discussed:

  1. Relevance: whether the model tests and generates hypotheses applicable to biology.
  2. Level: the elemental units of the model in the hierarchy from atoms to societies.
  3. Generality: the range of biological systems the model can represent.
  4. Abstraction: the complexity, relative to the target, or amount of detail included in the model.
  5. Structural accuracy: how well the model represents the actual mechanisms underlying the behaviour.
  6. Performance match: to what extent the model behaviour matches the target behaviour
  7. Medium: the physical basis by which the model is implemented
No specific position in the space of models thus defined is the only correct one, but a good modelling methodology should be explicit about its position and the justification for that position. It is argued that in building robot models biological relevance is more effective than loose biological inspiration; multiple levels can be integrated; that generality cannot be assumed but might emerge from studying specific instances; abstraction is better done by simplification than idealisation; accuracy can be approached through iterations of complete systems; that the model should be able to match and predict target behaviour; and that a physical medium can have significant advantages. These arguments reflect the view that biological behaviour needs to be studied and modelled in context, that is in terms of the real problems faced by real animals in real environments.


models; simulation; animal behaviour; neuroethology; robotics; realism; levels.

Barbara Webb joined the Psychology Department at Stirling University in January 1999. Previously she lectured at the University of Nottingham (1995-1998) and the University of Edinburgh (1993-1995). She recieved her Ph.D. (in Artificial Intelligence) from the University of Edinburgh in 1993, and her B.Sc. (in Psychology) from the University of Sydney in 1988.

1. Introduction

'Biorobotics' can be defined as the intersection of biology and robotics. The common ground is that robots and animals are both moving, behaving systems; both have sensors and actuators and require an autonomous control system that enables them to successfully carry out various tasks in a complex, dynamic world. In other words "it was realised that the study of autonomous robots was analogous to the study of animal behaviour" p.60 (Dean, 1998), hence robots could be used as models of animals. As summarised by Lambrinos et al. (1997) et al "the goal of this approach is to develop an understanding of natural systems by building a robot that mimics some aspects of their sensory and nervous system and their behaviour" (p.185).

Dean (op. cit.) reviews some of this work, as do Meyer (1997), Beer et al. (1998), Bekey (1996), and Sharkey & Ziemke (1998), although the rapid growth and interdisciplinary nature of the work make it difficult to comprehensively review. Biorobotics will here be considered as new methodology in biological modelling, rather than as a new 'field' per se. It can then be discussed directly in relation to other forms of modelling. Rather than vague justification in terms of intuitive similarities between robots and animals, the tenets of the methodology can be more clearly stated and a basis for comparison to other approaches established. However, a difficulty that immediately arises is that a "wide divergence of opinion … exists concerning the proper role of models" p. 597 (Reeke & Sporns, 1993) in biological research.

For example, the level of mechanism that should be represented in the model is often disputed. Cognitivists criticise connectionism for being too low level (Fodor & Pylyshyn, 1988), while neurobiologists complain that connectionism abstracts too far from real neural processes (Crick, 1989). Other debates address the most appropriate means for implementing models. Purely computer-based simulations are criticised by advocates of sub-threshold transistor technology (Mead, 1989) and by supporters of ‘real-world’ robotic implementations (Brooks, 1986). Some worry about oversimplification (Segev, 1992) while others deplore overcomplexity (Maynard Smith, 1974; Koch, 1999). Some set out minimum criteria for ‘good’ models in their area (e.g. Pfeifer, 1996; Selverston, 1993); others suggest there are fundamental trade-offs between desirable model qualities (Levins, 1966).

The use of models at all is sometimes disputed, on the grounds that detailed models are premature and more basic research is needed. Croon & van de Vijver (1994) argue that "Developing formalised models for phenomena which are not even understood on an elementary level is a risky venture: what can be gained by casting some quite gratuitous assumptions about particular phenomena in a mathematical form?" p.4-5. Others argue that "the complexity of animal behaviour demands the application of powerful theoretical frameworks" (Barto, 1991, p.94) and "nervous systems are simply to complex to be understood without the quantitative approach that modelling provides" (Bower, 1992, p.411). More generally, the formalization involved in modelling is argued to be an invaluable aid in theorising - "important because biology is full of verbal assertions that some mechanism will generate some result, when in fact it won’t" (Maynard Smith, 1988, p.231).

Beyond the methodological debates, there are also ‘meta’-arguments regarding the role and status of models in both pure and applied sciences of behaviour. Are models essential to gaining knowledge or just convenient tools? Can we ever really validate a model (Oreskes, et al, 1994)? Is reification of models mistaken i.e. can a model of a process ever be a replica of that process (Pattee, 1989; Webb, 1991)? Do models really tell us anything we didn’t already know?

In what follows a framework for the description and comparison of models will be set out in an attempt to answer some of these points, and the position of biorobotics with regard to this framework will be made clear. Section 2 will explicate the function of models, in particular to clarify some of the current terminological confusion, and define 'biorobotic' modelling. Section 3 will describe different dimensions that can be used to characterise biological models, and discuss the relationships between them. Section 4 will lay out the position of robot models in relation to these dimensions, and discuss how this position reflects a particular perspective on the problems of explaining biological behaviour.

2. The process of modelling

2.1 The "model muddle" (Wartofsky, 1979)

Discussions of the meaning and process of modelling can be found: in the philosophy of science e.g. Hesse (1966), Harre (1970b), Leatherdale (1974), Bunge (1973), Wartofsky (1979), Black (1962) and further references throughout this paper; in cybernetic or systems theory, particularly Zeigler (1976); and in textbooks on methodology - recent examples include Haefner (1996), Giere (1997), and Doucet & Sloep (1992). It also arises as part of some specific debates about approaches in biology and cognition: in ecological modelling e.g. Levins (1966) and Orzack & Sober (1993); in cognitive simulation e.g. Fodor (1968), Colby (1981), Fodor & Pylyshyn (1988), Harnad (1989); in neural networks e.g. Sejnowski et al (1988), Crick (1989); and in Artificial Life e.g. Pattee (1989), Chan & Tidwell (1993). However the situation is accurately summed up by Leatherdale (1974): "the literature on ‘models’ displays a bewildering lack of agreement about what exactly is meant by the word ‘model’ in relation to science" (p.41). Not only ‘model’ but most of the associated terms - such as 'simulation', 'representation', 'realism', 'accuracy', 'validation' – have come to be used in a variety of ways by different authors. Several distinct frameworks for describing models can be found, some explicit and some implicit, most of which seem difficult to apply to real examples of model building. Moreover many authors seem to present their usage as the obvious or correct one and thus fail to spell out how it relates to previous or alternative approaches. Chao in 1960 noted 30 different, sometimes contradictory, definitions of 'model' and the situation has not improved.

There does seem to be general agreement that modelling involves the relationship of representation or correspondence between a (real) target system and something else(1). Thus "A model is a representation of reality" Lamb, 1987, p.91) or "all [models] provide representations of the world" (Hughes, 1997, p. 325). What might be thought uncontroversial examples are: a scale model of a building which corresponds in various respects to an actual building; and the ‘billiard-ball model’ of gases, suggesting a correspondence of behaviour in microscopic particle collisions to macroscopic object collisions. Already, however, we find some authors ready to dispute the use of the term ‘model’ for one or other of these examples. Thus Kaplan (1964) argues that purely ‘sentential’ descriptions like the billiard-ball example should not be called ‘models’; whereas Kacser (1960) maintains that only sentential descriptions should be called ‘models’ and physical constructions like scale buildings should be called ‘analogues’; and Achinstein (1968) denies that scale buildings are analogies while using ‘model’ for both verbal descriptions and some physical objects.

A large proportion of the discussion of models in the philosophy of science concerns the problem that reasoning by analogy is not logically valid. If A and A* correspond in factors x1,…,xn, it is not possible to deduce that they will therefore correspond in factor xn+1. ‘Underdetermination’ is a another aspect of essentially the same problem – if two systems behave the same, it is not logically valid to conclude the cause or mechanism of the behaviour is the same; so a model that behaves like its target is not necessarily an explanation of the target’s behaviour. These problems are sometimes raised in arguments about the practical application of models, e.g. Oreskes et al. (1994) use underdetermination to argue that validation of models is impossible. Weitzenfeld (1984) suggests that a defence against this problem can be made by arguing that if there is a true isomorphism between A and A*, the deduction is valid, and the problem is only to demonstrate the isomorphism. Similar reasoning perhaps explains the frequently encountered claim that a model is "what mathematicians call an ‘isomorphism’" (Black, 1962, p.222)a one to one mapping - of ‘relevant aspects’ (Schultz & Sullivan, 1972), or ‘essential structure’ (Kaplan, 1964). Within cybernetic theory one can find formal definitions of models (e.g. Klir & Valach, 1965) that require there to be a complete isomorphic or homomorphic mapping of all elements of a system, preserving all relationships.

However, this is not helpful when considering most actual examples of models (unless one allows there "to be as many definitions possible to isomorphism as to model" Conant & Ashby, 1991, p.516). In the vast majority of cases, models are not (mathematical) isomorphisms, nor are they intended to be. Klir and Valach (op. cit.) go on to include as examples of models "photos, sculptures, paintings, films…even literary works" (p.115). It would be interesting to know how they intend to demonstrate a strict homomorphism between Anna Karenina and "social, economic, ethical and other relations" (op. cit.) in 19th century Russia. In fact it is just as frequently (and often by the same authors) emphasised that a model necessarily fails to represent everything about a system. For example Black (1962) goes on to warn of "risks of fallacies of inference from inevitable irrelevancies or distortions in the model" (p.223) – but if there is a true isomorphism, how can there be such a risk? A ‘partial isomorphism’ is an oxymoron; and more to the point, cannot suffice for models to be used in valid deduction. Moreover this approach to modelling obscures the fact that the purpose in modelling is often to discover what are the 'relevant features' or 'essential structures', so model usage cannot depend on prior knowledge of what they are to establish the modelling relationship.

2.2 What use are models?

"There are things and models of things, the latter being also things, but used in a special way" (Chao, 1960, p.564)

Models are intended to help us deal in various ways with a system of interest. How do they fulfil this role? It is common to discuss how they offer a convenient/cost-effective/manageable/safe substitute for working on or building the real thing. But this doesn’t explain why working on the model has any relevance to the real system, or provide some basis by which relevance can be judged i.e. what makes a model a useful substitute? It is easier to approach this by casting the role of modelling as part of the process of explanation and prediction described in the following diagram:

Figure 1: Models and the process of explanation

This picture can be regarded as an elaboration of standard textbook illustrations of either the 'hypothetico-deductive' approach or the 'semantic' approach to science (see below). To make each part of the diagram clear, consider an example. Our target - selected from the world - might be the human cochlea and the human behaviour of pitch perception. Our hypothesis might be that particular physical properties of the basilar membrane enable differently positioned hair cells to respond to different sound frequencies. One source of this idea may be the Fourier transform, and associated notion of a bank of frequency filters as a way of processing sound. To see what is predicted by the physical properties of the basal membrane we might build a symbolic simulation of the physical properties we think perform the function, and run it using computer technology, with different simulated sounds to see if it produces the same output frequencies as the cochlea (in fact Bekesy first investigated this problem using rubber as the technology to represent the basilar membrane). We could interpret the dominant output frequency value as a ‘pitch percept’ and compare it to human pitch perception for the same waveforms: insofar as it fails to match we might conclude our hypothesis is not sufficient to explain human pitch perception. Or as Chan & Tidwell (1993) concisely summarise this process, we theorise that a system is of type T, and construct an analogous system to T, to see if it behaves like the target system.

I have purposely not used the term 'model' in the above description because it can be applied to different parts of this diagram. Generally, in this paper, I take 'modelling' to correspond to the function labelled 'simulation': models are something added to the 'hypothesis - prediction - observation' cycle merely as "prostheses for our brains" (Milinski, 1991). That is, modelling aims to make the process of producing predictions from hypotheses more effective by enlisting the aid of an analogical mechanism. A mathematical model such as the Hodgkin-Huxley equations sets up a correspondence between the processes in theorised mechanism – the ionic conductances involved in neural firing – and processes defined on numbers – such as integration. We can more easily manipulate the numbers than the chemicals so the results of a particular configuration can be more easily predicted. However limitations in the accuracy of the correspondence might compromise the validity of conclusions drawn.

However, under the 'semantic' approach to scientific explanation (Giere, 1997) the hypothesis itself is regarded as a ‘model’, i.e. it specifies a hypothetical system of which the target is supposed to be a type. The process of prediction is then described as ‘demonstration’ (Hughes, 1997) of how this hypothetical system should behave like the target. Demonstration of the consequences of the hypothesis may involve ‘another level’ of representation in which the hypothesis is represented by some other system, also called a model. This system may be something already 'found' - an analogical or source model - or something built - a simulation model (Morgan, 1997). Moreover the target itself can also be considered a 'model', in so far as it involves abstraction or simplification in selecting a system from the world (Cartwright, 1983). This idea perhaps underlies Gordon's (1969) definition of model: "we define a model as the body of information about a system gathered for the purpose of studying the system" (p.5).

2.3 Theories, models, simulations and sources

While the usage of 'model' to mean the target is relatively rare, it is common to find 'model' used interchangeably with ‘hypothesis’ and ‘theory' (2): even claims that "A model is a description of a system" (Haefner, 1996 p.4); or "A scientific model is, in effect, one or a set of statements about reality"(Ackoff, 1962, p.109). This usage of 'model' is often qualified, most commonly as the ‘theoretical model’, but also as the ‘conceptual model’ (Rykiel, 1996; Ulinski, 1999; Brooks & Tobias, 1996), ‘sentential model’ (Harre, 1970a), ‘abstract model’ (Spriet & Vansteenkiste, 1982), or, confusingly, the ‘real model’ (Maki & Thompson, 1973) or ‘base model’ (Zeigler, 1976). The tendency to call the hypothesis a ‘model’ seems to be linked to how formal or precise is the specification it provides (Braithwaite, 1960), as hypotheses can range from a vague qualitative predictions to Zeigler’s (1976) notion of a ‘well-described’ base model, which involves defining all input, output and state variables, and their transfer and output functions, as a necessary prior step to simulation. The common concept of the theoretical model is that of a hypothesis that describes the components and interactions thought sufficient to produce the behaviour: "the actual building of the model is a separate step" (Brooks & Tobias, 1996, p.2).

This separate step is implementation (3) as a simulation, which involves representing the hypothesis in some physical instantiation - taken here in its widest sense i.e. including carrying out mathematical calculations or running a computer program, as well as more obviously 'physical' models. But as Maki & Thompson (1973) note: "in many cases it is very difficult to decide where the real model [the hypothesis] ends and the mathematical model [the simulation] begins" (p.4). Producing a precise formulation may have already introduced a number of 'technological' factors that are not really part of the hypothesis, in the sense that they are there only to make the solution possible, not because they are really considered to be potential components or processes in the target system. Grice (cited in Cartwright, 1983) called these "properties of convenience" and Colby (1981) makes this a basis for distinguishing models from theories: all statements of a theory are intended to be taken as true whereas some statements in a model are not.

Simulation (4) is intended to augment our ability to deduce consequences from the assumptions expressed in the hypothesis: "a simulation program is ultimately only a high speed generator of the consequences that some theory assigns to various antecedent conditions" (Dennett, 1979, p.192); "models…help…by making predictions of unobvious consequences from given assumptions" (Reeke & Sporns, 1993, p.599). Ideally, a simulation should clearly and accurately represent the whole of the hypothesis and nothing but the hypothesis, so conclusions based on the simulation are in fact correct conclusions about the hypothesis. However, a simulation must also necessarily be precise in the sense used above, that is, all components and processes must be fully specified for it to run. The ‘formalization’ imposed by implementation usually involves elaborations or simplifications of the hypothesis to make it tractable, which may have no theoretical justification. In other words, as is generally recognised, any actual simulation contains a number of factors that are not part of the 'positive analogy' between the target and the model.

In the philosophy of science, discussion of 'simulation' models has been relatively neglected. Rather, as Redhead (1980) points out the extensive literature on models in science is mostly about modelling in the sense of using a ‘source’ analogy. A source (5)  is a pre-existing system used in devising the hypothesis. For example, Amit (1989) describes how concepts like 'energy' from physics can be used in an analogical sense to provide powerful analysis tools for neural networks, without any implication that a 'physics level' explanation of the brain is being attempted. Though traditionally the ‘source’ has been thought of as another physical system (e.g. a pump as the source of hypotheses for the functioning of the heart) it is plausible to consider mathematics to be a ‘source’. That is, mathematical knowledge provides a pre-existing set of components and operations we can put in correspondence to the hypothesised components and operations of our target. Mathematics just happens to be a particularly widely applicable analogy (Leatherdale, 1974).

It is worth explicitly noting that the source is not in the same relation to the hypothesis as the technology, i.e. what is used to implement the hypothesis in a simulation. Confusion arises because the same system can sometimes be used both as a source and as a technology. Mathematics is one example, and another of particular current relevance is the computer. The computer can be used explicitly as a source to suggest structures and functions that are part of the hypothesis (such as the information processing metaphor in cognition), or merely as a convenient way of representing and manipulating the structures and functions that have been independently hypothesised. It would be better if terms like ‘computational neuroscience’ that are sometimes used strongly in the ‘source’ sense – computation as an explanatory notion for neuroscience - were not so often used more loosely in the ‘technology’ sense: "not every research application that models neural data with the help of a computer should be called computational neuroscience" (Schwartz, 1990, p.x). Clarity is not served by having (self-labelled) ‘computational neuroethologists’ e.g. Beer (1990) and Cliff (1991) who apparently reject ‘computation’ as an explanation of neuroethology.

2.4 Biorobotic models

Figure 1 suggests several different ways in which robots and animals might be related through modelling. First, there is a long tradition in which robots have been used as the source in explaining animal behaviour. Since at least Descartes (1662), regarding animals as merely complex machines, and explaining their capabilities by analogy with man-made systems has been a common strategy. It was most explicitly articulated in the cybernetic approach, which, in Weiner's subtitle to "Cybernetics" (1948), concerned "control and communication in the animal and the machine". It also pertains to the information processing approaches common today, in which computation is the source for explaining brains. Much work in biomechanics involves directly applying robot-derived analyses to animal capacities, for example Walker (1995) attempts "to analyse the strengths and weaknesses of the ancient design of racoon hands from the point of view of robotics" (p.187).

Second, animals can be regarded as the source for hypotheses in robot construction. This is one widely accepted usage of the term ‘biorobotics’ – sometimes called 'bio-mimetic' or 'biologically-inspired' robotics. For example Ayers et al. (1998) suggest "the set of behavioural acts that a lobster or lamprey utilises in searching for and identifying prey is exactly what an autonomous underwater robot needs to perform to find mines". Pratt & Pratt (1998b) in their construction of walking machines "exploit three different natural mechanisms", the knee, ankle and swing of animal legs to simplify control. The connection to biology can range from fairly exact copies of mechanisms e.g. Franceschini et al.'s (1992) electronic copy of the elementary motion detection circuitry of the fly, to adopting some high level principles e.g. using the ethological concept of 'releasing stimuli' to control a robot via simple environmental cues (Connell, 1990) or the approach described in Mataric (1998).

For the following discussion, however, I wish to focus on a third relationship: robots used as simulations of animals, or how "robots can be used as physical models of animals to address specific biological questions" (Beer et al., 1998, p.777). The potential for building such models has increased enormously in recent years due to advances in both robot technology and neuroethological understanding, allowing "biologists/ethologists/neuroscientists to use robots instead of purely computational models in the modelling of living systems" Sharkey & Ziemke, 1998, p.164)

The following criteria have been adopted for the inclusion of work in what follows as ‘biorobotic modelling’, to avoid the necessity of discussing an unmanageably large body of work in robotics and biological modelling:

It must be robotic: the system should be physically instantiated and have unmediated contact with the external environment; the transduction is thus constrained by physics. The intention is to rule out purely computer-based models (i.e. where the environment as well as the animal is represented in the computer); and also computer sensing systems that terminate in descriptions rather than actions. This somewhat arbitrarily discounts verbal behaviour (e.g. visual classification) as sufficient; but to do so is consistent with most people’s understanding of 'robotic'.

It must be biological: one aim in building the system should be to address a biological hypothesis or demonstrate understanding of a biological system. The intention is to rule out systems that might use some biological mechanisms but have no concern about altering them in ways that make it a worse representation e.g. industrial robot arms, most computer vision, most neural net controllers. It also rules out much of the ‘behaviour-based’ approach in robotics which uses "algorithms specifying robot behaviours that have analogy to behaviours of life-form[s]" (Yamaguchi, 1998, p.3204) but makes no serious attempt to compare the results to natural systems. Probably the largest set of borderline cases thus excluded is the use of various learning mechanisms for robot behaviour, except those specifically linked to animal behavioural or physiological studies.

There is already a surprisingly substantial amount of work even applying these criteria. The earliest examples come from mid-century, where theories of equilibrium (Ashby, 1952 learning (Shannon, 1951) and sensorimotor control (Grey Walter, 1961) were tested by building ‘animal’ machines of various kinds - a number of other early examples are discussed in Young (1969). Current work tends to be more focused on specific biological systems, and ranges across the animal kingdom, from nematodes to humans. Table 1 lists a selection of recent studies, and to illustrate the approach I will describe three examples here in more detail.

  1. A robot model of rat hippocampus: Burgess et al. (1997,1998, 2000) have presented a model of the rat hippocampus implemented on a robot. "The use of a robot ensures the realism of the assumed sensory inputs and enables true evaluation of the navigational capability" (Burgess et al., 1997, p.1535). The robot uses edge-filtering on a camera image to sense the distance of walls in its environment and a combination of visual and odometric information to link the distance to the allocentric direction of the walls, rotating in place to cover a sufficient field of view. They argue that these mechanisms "provide realistic simulation…since the rat's visual and odometric system appear to be relatively unsophisticated" (Burgess et al., 2000, p.306). This sensory information is encoded computationally by sensory 'cells' that effectively have 'receptive fields' for different directions and distances of walls. These feed to an array of 'entorhinal cells' which combine connections from sensory cells. These connect to the layer of 'place cells' with the connection pattern modifiable by competitive learning: thus representing the learnt place dependent activity of cells observed in rat hippocampus. These cells further connect to a small number of goal cells, which also receive input from 'head direction' cells. By Hebbian learning of these connections when a goal is encountered, the network forms a representation which can be used to guide the robot's movement back to a goal position from novel locations.

  2. "[To] maintain close contact with the experimental situations in which the place cell data constraining the model was collected, the robot was tested in simple rectangular environments" (Burgess et al., 2000, p.306). The results show the robot is capable of good self localisation while wandering in the environment and can reliably return to the goal position from novel locations. The effects of changing the environment (e.g. the proportions of the rectangle, or adding a new barrier) on the place cell representation and the search behaviour can be compared to the results in rats; some predictions from the model have been supported (Burgess et al., 2000). They further predict that cells with 'receptive fields' for direction and distance of barriers will be found within or upstream of the entorhinal cortex, but this is yet to be confirmed.
  3. A robot model of desert ant navigation: The impressive homing capabilities of the desert ant Catyglyphis have been the subject of long study (Wehner, 1994). Several aspects of this behaviour have been investigated in robot models that operate in the same Sahara environment (Lambrinos et al., 1997; Moller et al., 1998; Lambrinos et al., 2000). Insects can use the polarisation pattern of the sky as a compass, with three 'POL' neurons in the brain integrating the response from crossed-pairs of filters at three different orientations. This sensor-neural morphology has been duplicated in the robot. Two different models for extracting compass direction were considered: a 'scanning' mechanism that rotates to find a peak response which indicates the solar meridian (as had been previously proposed for the ant); and a novel 'simultaneous' mechanism that calculates the current direction from the pattern of neural output. The 'simultaneous' mechanism was substantially more efficient as the robot (or ant) does not need to rotate 360 degrees each time it wants to refer to the compass. This compass was successfully used in a path integration algorithm, reducing the error in the robot's return to its starting location.

  4. A further development of the robot allowed the testing of hypotheses about landmark navigation. A conical mirror placed above a camera enabled the robot to get a 360 degree view of the horizon comparable to that of the ant. The 'snapshot' model proposed by Cartwright & Collett 1983 was implemented first: this matches the landmarks in a current view with a stored view, to create a set of vectors whose average is a vector pointing approximately in the home direction. The ability of this model to return the robot to a location was demonstrated in experiments with the same black cylinders as landmarks as were used for the ant experiments. Further, a simplification of the model was proposed, in which the robot (or animal) only stores an 'average landmark vector' rather than a full snapshot, and it was shown that the same homing behaviour could be reproduced. To provide "insights as to how the visual homing might be implemented in insect brains" (p.243) , it has recently been implemented in analog electronic hardware (Moller, 2000) and successfully tested on a robot in reproductions of experiments performed on bees in which landmarks are moved or removed.
  5. A robot model of human motor control: Schaal & Sternad (2001) present a comparison of human and robot behaviour to analyse the control of motor trajectories. This is used to addressed a critical question - does the apparent '2/3 power law' relating endpoint velocity to path curvature in human movement represent an explicit parameter implemented directly in the nervous system, or is it merely the by-product of other control mechanisms? The study measured humans making cyclic drawing motions, and modelled the behaviour using a 7 degree-of-freedom anthropomorphic robot arm, with PID control of joint movements based on simple sinusoidal target trajectories. The frequency, amplitude and phase of the sinusoids were estimated from measurements on the human subjects. They found that "As in the human data, for small perimeter values [the 2/3 law] was produced quite accurately, but, as in the human subjects, the same deterioration of power law fits were apparent for increasing pattern size" (p.67). Moreover they could explain these deviations as a consequence of non-linearities in the kinematic transform from joint control to end-effector trajectories, and explain the power law as emergent from mechanisms for ensuring smooth movement in joint space.

It can thus be seen that useful results for biology have been already been gained from robotic modelling. But it is still pertinent to ask: Why use robots to simulate animals? How does this methodology differ from alternative approaches to modelling in biology? To answer these questions it is necessary to understand the different ways in which models can vary, which will now be examined.

3. Dimensions for describing models

Figure 2: Dimensions for describing models

Figure 2 presents a seven-dimensional view of the 'space' of possible biological models. If the 'origin' is taken to be using the system itself as its own model (to cover the view expressed by Rosenblueth & Wiener (1945) as "the best material model of a cat is another, or preferably the same, cat" p.316) then a model may be distanced from its target in terms of abstraction, approximation, generality or relevance. It may copy only higher levels of organisation, or represent the target using a very different material basis, or only roughly reproduce the target's behaviour. Exactly what is meant here by each of listed dimensions, and in what ways they are (and are not) related will be discussed in detail in what follows. They are presented as an attempt to capture, with a manageable number of terms, as much as possible of the variation described and discussed in the literature on modelling, and to separate various issues that are often conflated.

Though it is generally more popular in the literature to classify models into types (see for example the rather different taxonomies provided by Achinstein (1968), Haefner, (1996), Harre (1970b) and Black (1962)), there are precedents for this kind of dimensional description of models. Some authors attempt to use a single dimension. For example Shannon (1975) presents a diagram of models situated on a single axis that goes from ‘exact physical replicas’ at one end to ‘highly abstracted symbolic systems’ at the other. By contrast, Schultz & Sullivan (1972) present a list of some 50-odd different dimensions by which a model may be described. One set of dimensions widely discussed in ecological modelling was proposed by Levins in 1966. He suggested that models could vary in realism, precision and generality (in his 1993 reply to Orzack & Sober's (1993) critique he notes that this was not intended to be a ‘formal or exhaustive’ description). Within the ‘systems’ approach to modelling the most commonly discussed dimensions are ‘complexity’, ‘detail’ and ‘validity’ as well as more practical or pragmatic considerations such as cost (e.g. Rothenberg (1989) includes ‘cost-effectiveness’ as part of his definition of simulation). Brooks & Tobias (1996) discuss some proposed methods for measuring these factors, and also point out how some of the connections between these factors are not as simple as seems to be generally thought.

Many of the debates about 'appropriate' biological simulation assume that there are strict relations between certain aspects of modelling. Neural nets are said to be more accurate than symbol processing models because they are lower level; Artificial Life models are said to be general because they are abstract; neuromorphic models are said to be more realistic because they use a physical implementation. However, none of these connections follow simply from the nature of modelling but depend on background assumptions about biology. Is inclusion of a certain level essential to explaining behaviour? Can general laws of life be found? Are physical factors more important than information processing in understanding perception? The arguments for using robot models in biology, as for any other approach, reflect particular views about biological explanation. This will be further discussed in section 4 which applies the defined dimensions to describe the biorobotic approach.

3.1 Biological Relevance

Is the biological target system clearly identified? Does the model generate hypotheses for biology?

Models can differ in the extent to which they are intended to represent, and to address questions about, some real biological system. Work in biorobotics varies in biological relevance. For example Huber & Bulthoff (1998) use a robot to test the hypothesis that a single motion-sensitive circuit can control stabilisation, fixation and approach in the fly. This work is more directly applicable to biology than the robot work described by Srinivasan et al. (1999) utilising bee-inspired methods of motor control from visual flow-fields, which does not principally aim to answer questions about the bee. Similarly, the ‘robotuna’ (Triantafyllou & Triantafyllou, 1995) and 'robopike' were specifically built to test hypotheses for fish swimming - "The aim of these robots is to help us learn more about the complex fluid mechanics that fish use to propel themselves" (Kumph, 1998) - whereas the pectoral fin movements implemented on a robot by Kato & Inaba (1998), though based on close study of Black bass, are not tested primarily for how well they explain fish swimming capability.

Another expression of this dimension is to distinguish between investigation of "the model as a mathematical statement and the model as empirical claim about some part of the physical world" (Orzack & Sober, 1993, p.535).Investigating a model for its own sake is often regarded critically. Hoos (1981) describes as "modilitis…being more interested in the model than the real world and studying only the portions of questions that are amenable to quantitative treatment" (p.42). Bullock (1997) criticises Artificial Life where "simulations are sometimes presented as ‘artificial worlds’ worthy of investigation for their own sake…However this practice is theoretically bankrupt, and such [result] statements have no scientific currency" (p.457). But Caswell (1988), for example, defends the need to investigate ‘theoretical problems’ raised by models independently of their fit to reality. Langton's (1989) advocacy of investigating ‘life as it could be’ is an example. As in 'pure' maths, the results may subsequently prove to have key applications, but of course there is no guarantee that the "model-creating cycle" will not end up "spiralling slowly but surely away from reality" (Grimm, 1994, p.645) without any reconnection occurring.

It is worth explicitly mentioning in this context that a model that is 'irrelevant' for biology might have utility in other respects. Models may serve for purposes of communication or education; or be employed for prediction and control. Moreover, there may be some value in investigating the technological aspects of a model: the mechanisms may have utility independent of their adequacy in explaining their origin. Arkin (1998) describes robots that abstract and use "underlying details" from biological sciences "unconcerned with any impact on the original discipline" (p.32). Such 'models' should then be evaluated with respect to engineering criteria (6), rather than how well they represent some natural system.

Biologically 'irrelevant' models, then, are those too far removed from biology to connect their outcomes back to understanding the systems that inspired them. For a non-robotic example, doubts are expressed about the relevance of artificial neural networks by e.g. Miall (1989): "it is not clear to what extent artificial networks will help in the analysis of biological networks" (p.11). The main criteria for relevance could be taken to be the ability of the model to generate testable hypotheses about the biological system it is drawn from. For example the robot studies of Triantafyllou & Triantafyllou (1995) mentioned above suggest that fish use the creation of vortexes as a means of efficient tail-fin propulsion.

Arbib & Liaw (1995) provide their as definition of a ‘biological model’: "a schema-based model … becomes a biological model when explicit hypotheses are offered as to how the constituent schemas are played over particular regions of the brain" (p.56) (in their case, this involves the use of simulated and robot models of the visual guidance of behaviour in the frog). Generalised, this seems an appropriate test for relevance: are the mechanisms in the model explicitly mapped back to processes in the animal, as hypotheses about its function? In biorobotics this may sometimes concern neural circuitry, e.g. in a model of auditory localisation of the owl (Rucci et al. 1999). But it can also occur at a relatively high level, such as using ‘shaping’ methods in learning (Saksida et al., 1997) or involve testing a simple algorithm such as the sufficiency of a small set of local rules to explain collecting and sorting behaviour in ants (Melhuish et al., 1998; Holland et al, 1999). The point is to use the robot model to make a serious attempt at addressing biological questions, at whatever level these may exist.

This notion of 'relevance' appears to be what at least some authors mean by the term 'realism' in describing models. Churchland & Sejnowski (1988) appear to define 'realistic' in this way "realistic models, which are genuinely and strongly predictive of some aspect of nervous system dynamics or anatomy" vs. "simplifying models, which though not so predictive, demonstrate that the nervous system could be governed by specific principles" (p.744). But this is rather different to their definition in Sejnowski et al. (1988) of a realistic model as a "large scale simulation that tries to incorporate as much of the cellular detail as is available" made "realistic by adding more variables and more parameters" (p.1300). It seems unlikely that they believe only models ‘realistic’ in the latter sense can be ‘realistic’ in the former sense - indeed they argue in Churchland et al. that "a genuine perfect model, faithful in every detail, is as likely to be incomprehensible as the system itself" (p.54). However, 'realistic' is often used to mean 'detailed', or 'not abstract'. For example: Beer et al. (1998) specify ‘realistic’ in relation to robot models as "literally try to emulate in every detail a particular species of insect" (p. 32); Manna & Pnueli (1991) define realism as ‘degree of detail’; Palsson & Lee (1993) directly equate ‘realistic’ to ‘complex’- a decision on realism is how many factors to include; and Orzack & Sober (1993) redefine Levins' (1966) realism as "takes into account more independent variables known to have an effect" (p.534).

However it is clear that Levins (1966) was concerned to argue against the assumption that a model can only be made 'realistic' by being more detailed. His discussion of ‘real & general’ models includes a number of quite simple and abstract examples: the issue of realism is the extent to which they improve understanding of the biological system, i.e. what I have here called relevance. Schultz & Sullivan (1972) make a useful distinction between modelling that tries to build a complete "picture of reality" versus building a device for learning about reality: i.e. it may be possible for a model to be too detailed (or 'realistic' in one sense) to actually be productive of hypotheses (or 'realistic' in the other sense). Collin & Woodburn (1998) similarly refer to the possibility of "a model in which the incorporated detail is too complex...for it to contribute anything to the understanding of the system" (p.15-16). The relevance of a model to biology, and the detail it includes, are separable issues which should not be conflated under the single term 'realism'.

3.2 Level

What are the base units of the model?

This dimension concerns the hierarchy of physical/processing levels that a given biological model could attempt to represent. Any hypothesis will usually have ‘elemental units’ whose "internal structure does not exist or can be ignored" (Haefner, 1996, p.4). In biology these can range from the lowest known mechanisms such as the physics of chemical interactions through molecular and channel properties, membrane dynamics, compartmental properties, synaptic & neural properties, networks and maps, systems, brains and bodies, perceptual and cognitive processes, up to social and population processes (Shepherd, 1990). The level modelled in biorobotics usually includes mechanisms of sensory transduction, for example the sonar sensors of bats (Kuc, 1997) including the pinnae movements (Peremans et al., 1998), or of motor control, such as the six legs of the stick insect (Pfeiffer et al., 1995) or the multi-jointed body of the snake (Hirose, 1993). The central processing can vary from a rule-based level through high level models of brain function such as the control of eye movements (Schall & Hanes, 1998), to models of specific neuron connectivity hypothesised to underlie the behaviour, such as identified neural circuitry in the cricket (Webb & Scutt, 2000), and even the level of dendritic tree structure that explains the output of particular neurons such as the ‘looming’ detector found in the locust and modelled on a robot by Blanchard et al. (1999). The data for the model may come from psychophysics (e.g. Clark's (1998) model of saccades), developmental psychology (Scassellati, 1998) or evolutionary studies (Kortmann & Hallam, 1999), but most commonly comes from neuroethological investigations.

This notion of level corresponds to what Churchland & Sejnowski 1988 call ‘levels of organisation’ and as they note this does not map onto Marr's well-known discussion of ‘levels of analysis’ (1982). Marr's levels (computational, algorithmic and implementational) apply rather to any explanation across several levels of organisation and describes how one level (be that network, neuron or channel) considered as an algorithm relates to the levels above (computation) and below (implementation). In fact this point was made clearly by Feibleman (1954): "For any organisation, at any given level, its mechanism lies at the level below and its purpose at the level above"(p.61).

One source of the conflict over the 'correct level' for biological modelling may be that levels in biology are relatively close in spatio-temporal scale, as contrasted with macro and micro levels in physics by Spriet & Vansteenkiste (1982). They point out that "determination of an appropriate level is consequently less evident" (p.46) in biological sciences. Thus it is always easy to suggest to a modeller that they should move down a level; while it is obviously impractical to pursue the strategy of always working at the lowest level. Koch (1990) makes the interesting point that low-level details may be unimportant in analysing some forms of collective neural computation, but may be critical for others - the 'correct level' may be problem specific, and "which really are the levels relevant to explanation of in the nervous system is an empirical, not an a priori, question" (Churchland et al., 1990, p.52).

Another problem related to levels is the misconception that the level of a model determines its biological relevance. A model is not made to say more about biology just by including lower-level mechanisms. For example, using a mechanism at the ‘neural’ level doesn’t itself make a model realistic: most ‘neural network’ controlled robots have little to do with understanding biology (Zalzala & Morris, 1996). Moreover, including lower levels will generally make the model more complex, which may result in its being intractable and/or incomprehensible. Levins (1993) provides a useful example from ecological models: it is realistic to include a variable for the influence of ‘nutrients’; less realistic to include specific variables for ‘nitrogen’ and ‘oxygen’ if thereby other nutrient effects are left out. It is also important to distinguish level from accuracy (see below) as it is quite possible to inaccurately represent any level. Shimoyama et al. (1996) suggest that to "replicate functionality and behaviour…not necessarily duplicate their anatomy" in building robot models of animals is to be "not completely faithful" (p.8): but a model can ‘faithfully’ replicate function at different levels.

3.3 Generality

How many systems does the model target?

A more general model is defined as one that "applies to more real-world [target] systems" (Orzack & Sober, 1993, p.534). Some researchers in biorobotics appear sanguine about the possibility of generality e.g. Ayers et al. (1998) claim "locomotory and taxis behaviours of animals are controlled by mechanisms that are conserved throughout the animal kingdom" and thus their model of central pattern generators is taken to be of high generality. Others are less optimistic about general models. Hannaford et al (1995), regarding models of motor control with ‘broad’ focus, opines "because of their broad scope, it is even more difficult for these models to be tested against the uncontroversial facts or for them to predict the results of new reductionist experiments". This suggests that increasing generality decreases relevance, so it should be noted that, strictly speaking, a model must be relevant to be general - if it doesn't apply to any specific system, then how can it apply to many systems (Onstad, 1988)? But a model does not have to be general to be relevant.

The obvious way to test if a model is general is to show how well it succeeds in representing a variety of different specific systems. For many models labelled 'general' this doesn’t happen. When it is attempted, it usually requires a large number of extra situation or task specific assumptions to actually get data from the model to compare to the observed target. This is a common criticism of optimal foraging studies (Pierce & Ollanson, 1987): that provided enough task specific assumptions are made, any specific data can be made to fit the general model of optimality. A similar critique can be made of 'general' neural nets (Verschure, 1996) - a variety of tasks can be learned by a common architecture, but only if the input vectors are carefully encoded in a task specific manner. Raaijmakers (1994) makes a similar point for memory models in psychology and pertinently asks – is this any better than building specific models in the first place?

The most common confusion regarding generality is that what is abstract will thereby be general. This can often be found in writings about artificial life simulations, and Estes (1975) for example makes this claim for psychological models. Shannon (1975) talks about "the most abstract and hence the most general models" (p.10) and Haefner (1996) suggests more detail necessarily results in less generality. Sejnowski et al (1988) describe ‘simplifying models’ as abstracting from individual neurons and connectivity to potentially provide ‘general findings’ of significance for the brain. Sometimes this argument is further conflated with 'levels', for example Wilson (1999) discusses how "component neurons may be described at various levels of generality" (p.446) contrasting the 'abstraction' of spike rates to the 'detail' of ionic currents - but an ionic current description is actually more general as it applies to both spiking and non-spiking neurons. The membrane potential properties of neurons are very general across biology but not particularly abstract; whereas logical reasoning is quite abstract but not very general across biological systems. Obviously some concepts are both abstract and general – such as feedback – and many concepts are neither. Moreover precisely the opposite claim, i.e. that more detail makes models more general, is made by some authors e.g. Black (1962), Orzack & Sober (1993). The reasoning is that adding variables to a model will increase its scope, because it now includes systems where those variables have an influence, whereas before it was limited to systems where they do not.

Grimm (1994) points out that insofar as generality appears to be lost when increasing detail, it may simply be because the systems being modelled are in fact unique, rather than because of an inherent trade-off between these factors. This raises the important issue that "generality has to be found, it cannot simply be declared" (Weiner, 1995, p.155). That is to say the generality of a model depends on the true nature of the target(s). If different animals function in different ways then trying to generalise over them won’t work – you are left studying an empty set. Robertson (1989) makes the same point with regard to neural networks "[neural] circuits that are unique in their organisation and operation demand unique models if such models are to be useful" (p.262); Taylor (1989) similarly argues for ecology that simple models are "not shortcuts to ecological generality". Consequently, one strategy is to instead work on understanding specific systems, from which general mechanisms, if they exist, will emerge (Arbib & Liaw, 1995). Biology has often found that the discovery and elucidation of general mechanisms tends to come most effectively from close exploration of well-chosen specific instantiations (Miklos, 1993) such as the fruitfly genome or squid giant axon.

3.4 Abstraction

How many elements and processes from the target are included in the model?

Abstraction concerns the number and complexity of mechanisms included in the model; a more detailed model is less abstract. The 'brachiator' robot models studied by Saito & Fukuda (1996) illustrate different points on this spectrum: an early model was a simple two-link device, but in more recent work they produce a nine-link, 12 degree-of-freedom robot body with its dimensions based on exact measurements from a 7-8 year-old female simiang skeleton. 'Abstraction' is not just a measure of the simplicity/complexity of the model however (Brooks & Tobias, 1996) but is relative to the complexity of the target. Thus a simple target might be represented by a simple, but not abstract, model, and a complex model still be an abstraction of a very complex target.

Some degree of abstraction is bound to occur in most model building. Indeed it is sometimes taken as a defining characteristic of modelling - "A model is something simple made by the scientist to help them understand something complicated" (Segev, 1992, p.414). It is important to note that abstraction is not directly related to the level of modelling: a model of a cognitive process is not, of its nature, more or less abstract than a model of channel properties. The amount of abstraction depends on how the modeller chooses to describe and represent the processes, not what kind of processes they represent. Furthermore, the fact that some models - such as biorobots - have a hardware 'medium' (see below) does not make them necessarily less abstract than computer simulations. A simple pendulum might be used as an abstract physical model for a leg, whereas a symbolic model of the leg may include any amount of anatomical detail. As Etienne (1998) notes "Robots tend to simulate behaviour and the underlying neural events on the basis of a simplified architecture and therefore less precisely than computers" (p.286).

How much abstraction is considered appropriate seems to largely reflect the ‘tastes’ of the modeller: should biology aim for simple, elegant models or closely detailed system descriptions? Advocates of abstraction include Maynard Smith (1974) "Should we not therefore put into the model everything that we think might be important? …construction of such complex models is a waste of time" (p.116), and Molenaar (1994) "precisely by simplification and abstraction that models are most useful" (p.101). The latter gives as reasons for preferring more abstract models that complex models are harder to implement, understand, replicate or communicate. An important point is they thereby become hard for reviewers to critique or check (e.g. Rexstad & Innis (1985) report a surprising number of basic errors in published models they were attempting to reimplement to test simplification techniques). Simpler models are easier to falsify and reduce the risk of merely data-fitting, by having fewer free parameters. Their assumptions are more likely to be transparent. Another common argument for building a more abstract model is to make the possibility of an analytical solution more likely (e.g. the abstraction of neural ‘sprouting’ proposed by Elliot et al., 1996).

However abstraction carries risks. The existence of an attractive formalism might end up imposing its structure on the problem so that alternative, possibly better, interpretations are missed. Segev (1992) argues that in modelling neurons, we need to build complex detailed models to discover what are appropriate simplifications. Details abstracted away might turn out to actually be critical to understanding the system. As Kaplan (1964) notes the issue is often not just ‘over-simplification’ per se, but whether we have "simplified in the wrong way" or that "what was neglected is something important for the purposes of that very model"(p.281). For explaining biological behaviour, abstracting away from the real problems of sensorimotor interaction with the world is argued, within biorobotics, to be an example of the latter kind: in this case, abstraction reduces relevance because the real biological problem is not being addressed.

3.5 Structural Accuracy

Is the model a true representation of the target?

Accuracy is here intended to mean how well the mechanisms in the model reflect the real mechanisms in the target. This is what Zeigler calls structural validity: "if it not only produces the observed real system behaviour but truly reflects the way in which the real system operates to produce this behaviour" (1976, p.5) as distinct from replicative and predictive validity, i.e. how well the input/output behaviour of the system matches the target (7). This notion has also been dubbed "strong equivalence" (Fodor, 1968). Brooks & Tobias (1996) call this the ‘credibility’ of the model, and Frijda (1967) suggests "[input/output] performance as such is not as important as convincing the reader that the reasons for this performance are plausible" (p.62). Thus Hannaford et al. (1995) lay out their aims in building a robot replica of the human arm as follows: "Although it is impossible to achieve complete accuracy, we attempt to base every specification of the system’s function and performance on uncontroversial physiological data".

One major issue concerning the accuracy of a model is "how can we know?" (this is also yet another meaning of 'realism'). The anti-realist interpretation of science says that we cannot. The fact that certain theories appear to work as explanations is not evidence to accept that they represent reality, because the history of science has shown us to be wrong before (the ‘pessimistic meta-induction’, Laudan, 1981). On the other hand, if they do not approximately represent reality then how can we build complex devices that actually work based on those theoretical assumptions (the ‘no miracle argument', Putnam 1975)? Not wishing to enter this thorny territory, it will suffice for current purposes to argue for no more than an instrumentalist position. If we can’t justifiably believe our models, we can justifiably use them (Van Fraassen, 1980). Accuracy in a model means there is "acceptable justification for scientific content of the model" (Rykiel, 1996, p.234) relative to the contemporary scientific context in which it is built; and that it is rational (Cartwright, 1983) to attempt "experimental verification of internal mechanisms" (Reeke & Sporns, 1993, p.599) suggested by the model.

Inaccuracies in models should affect our confidence in using the model to make inferences about the workings of the real system (Rykiel, 1996), but do not rule out all inference provided "assumptions …[are] made explicit so that the researcher can determine in what direction they falsify the problem situation and by how much" (Ackoff, 1962, p.109). Horiuchi & Koch (1999) make this point for neuromorphic electronics "By understanding the similarities and differences…and by utilising them carefully, it is possible to maintain the relevance of these circuits for biological modelling" (p.243). Thus accuracy can be distinguished from relevance. It is possible for a model to address 'real' biological questions without utilising accurate mechanisms. Many mathematical models in evolutionary theory fit this description. Dror & Gallogly (1999) describe how "computational investigations that are completely divorced, in practice and theory, from any aspect of the nervous system…can still be relevant and contribute to understanding the biological system" (p.174), for example as described by Dennett (1984) to "clarify, sharpen [and] systematise the purely semantic level characterisation" (p.203) of the problem to be solved.

Accuracy is not synonymous with 'amount of detail' included in the model. This is well described by Schenk (1996) in the context of 'tree' modelling. He notes that researchers often assume a model with lots of complex detail is accurate, without actually checking that the details are correct. Or, a particular simplification may be widely used, and justified as a necessary abstraction, without looking at alternatives that may be just as abstract but more accurate. Similarly, it has already been noted that accuracy does not relate directly to the level of the representation – a high-level model might be an accurate representation of a cognitive process where a low-level model may turn out not to be accurate to brain biology.

A widely used term that overlaps with both 'relevance' and 'accuracy' is ‘biological plausibility’. This can be taken simply to mean the model is applicable to some real biological system; or used to describe whether the assumptions on which the model are based are biologically accurate. More weakly, it is sometimes used to mean that the model "does not require biologically unrealistic computations" (Rucci et al., 1999, p.?). In fact this latter usage is probably a better interpretation of 'plausible', that is, it describes models where the mechanism merely could be like the biology, rather than those where there are stronger reasons to say the mechanism is like the biology - the latter is 'biological accuracy', and neither is a pre-requisite for 'biological relevance' in a model.

3.6 Match

To what extent does the model behave like the target?

This dimension describes how the model's performance is assessed. In one sense it concerns testability: can we potentially falsify the model by comparing its behaviour to the target? For example, the possibility that the lobster uses instantaneous differences in concentration gradients between its two antennules to do chemotaxis was ruled out by testing a robot implementation of this algorithm in the real lobster's flow-tank (Grasso et al. 2000). However assessment of a biorobot may be simply in terms of its capabilities rather than directly relate back to biology. While a significant role for robot models is the opportunity to compare different control schemes for their success (e.g. Ferrell (1995) looks at three different controllers, two derived from biology, for six-legged walking) simply reporting what will work best on a (possibly inaccurate) robot model does not necessarily allow us to draw conclusions about the target animal behaviour.

When a direct comparison with biology is attempted, there is still much variability on this dimension regarding the nature of the possible match between the behaviours. Should the behaviours be indistinguishable or merely similar? Are informal, expert or systematic statistical investigations to be used as criteria for assessing similarity? Is a qualitative or quantitative match expected? Can the model both reproduce past data and predict future data? Some modelling studies provide little more than statements that, for example, "the overall behaviour looked quite similar to that of a real moth" (Kuwana et al., 1995, p.375). Others make more direct assessment, e.g. Harrison & Koch (1999) have tested their analog VLSI optomotor system in the real fly's flight simulator and "repeated an experiment often performed on flies", showing for example that the transient oscillations observed in the fly emerge naturally from inherent time-delays in the processing on the chip. Even where biological understanding is not the main aim of the study, it is possible that "animals provide a benchmark" for evaluating the robot system, such as Berkemeier & Desai's (1996) comparison of their "biologically-styled" leg design to the hindlimb of a cat at the level of force and stiffness parameters.

There are inevitable difficulties in drawing strong conclusions about biological systems from the results of robot models. As with any model, the performance of similar behaviour is never sufficient to prove the similarity of mechanisms - this is the problem of underdetermination. Some authors are concerned to stress that behavioural match is never sufficient evidence for drawing conclusions about the accuracy or relevance of a model (e.g. Deakin, 1990; Oreskes et al., 1994). Uttal (1990) goes so far as to say that "no formal model is verifiable, validatable or even testable with regard to internal mechanisms" and claims this is "generally accepted throughout other areas of science". But the widespread use of models in exactly the way so deplored suggests that most modelers think a reasonable defence for the practice can be made in terms of falsification or coincidence. If the model doesn’t match the target then we can reject the hypothesis that led to the model or at least know we need to improve our model. If it does match the target, better than any alternatives, then the hypothesis is supported to the extent that we think it unlikely that such similar behaviour could result from completely different causes. This is sometimes more formally justified by reference to Bayes’ theorem (Salmon, 1996).

However there are some limitations to this defence. Carrying out the comparison of model and target behaviours can be a sufficiently complex process that neither of the above points apply. First, how can we be sure that the measurements on the real system are correct? If the model doesn’t match we may reject the measurements rather than the model. Second, an interpretation process is required to convert the behaviour of the model and target into comparable form. This interpretation process may be wrong, or more worryingly, may be adjusted until the ‘match’ comes out right - "interpretive steps may inadvertently contain key elements of the mechanism" (Reeke & Sporns, 1993, p.598). Third, it is not uncommon for models to have their parameters ‘tuned’ to improve the match. As Hopkins & Leipold 1996 demonstrate, this practice can in fact conceal substantial errors in the model equations or in the data. Finally Bower & Koch (1992) provide a sobering view of the likelihood of a model being rejected on the basis of failure to match experiments:

"experiments needed to prove or disprove a model require a multi-year dedicated effort on the part of the experimentalist…falsification of any one such model through an experimentum crucis can be easily countered by the introduction of an additional ad hoc hypothesis or by a slight modification of the original model. Thus the benefit, that is, the increase in knowledge, derived from carrying out such time- and labour- intensive experiments is slight" (p.459)

3.7 Medium

What is the simulation built from?

Hypotheses can be instantiated as models in various different forms, and hardware implementation is one of the most striking features of biorobotics compared to other biological models. Doucet & Sloep (1992) list ‘mechanical’, ‘electric’, ‘hydraulic’, ‘scale’, ‘map’, ‘animal’, ‘game’ and ‘program’ as different forms a model might take. A popular taxonomy is 'iconic', 'analog' and 'symbolic' models (e.g. Black, 1962; Schultz & Sullivan, 1972; Kroes, 1989; Chan & Tidwell, 1993) but the definitions of these terms do not stand up to close scrutiny. ‘Iconic’ originally derives from ‘representation’, meaning something used to stand in for something else, and is used that way by some authors (Harre, 1970b; Suppe, 1977) to mean any kind of analogy-based model. However, it is now often defined specifically as using "another instance of the target type" (Chan & Tidwell, 1993), or "represent the properties by the same properties with a change of scale" (Schultz & Sullivan, 1972, p.6). One might assume this meant identity of materials for the model and the target, as discussed below, but the most cited example is Watson & Crick’s scale model of DNA, which was built of metal, not deoxyribonucleic acid. Yet 'analog' models are then distinguished from 'iconic' as models that introduce a "change of medium" (Black, 1962) to stand in for the properties. A popular example of an analog model is the use of electrical circuit models of mechanical systems. Some authors include computer models as analogs e.g. Achinstein (1968) whereas others insist they are symbolic e.g. Lambert & Brittan (1992). But whether the properties are shared or analogous or ‘merely’ symbolically represented depends entirely on how the properties are defined: whether the 'essence' of a brain is its chemical constitution, its connectivity pattern or its ability to process symbols depends on what you are trying to explain. All models are 'iconic', or share properties, precisely from the point of view that makes the model usefully stand in for the target for a particular purpose (Durbin (1989) calls this "the analogy level"). Hence I will abandon this distinction and consider the medium more literally as what the model is actually built from.

A model can be constructed from the same materials as its target. Bulloch & Syed (1992) describe ‘culture models’ i.e. the reconstruction of simplified networks of real neurons in vitro as models of networks in vivo; and Miklos (1993) argues for the use of transgenic techniques to "build novel biological machines to test our hypotheses" (p.843). Kuwana et al. (1995) use actual biological sensors - the antennae of moths – on their robot model and note these are 10,000 times more sensitive than available gas sensors. In these cases the representation of the target properties is by identity in the model properties.

However most models are not constructed from the same materials. They may share some physical properties with their targets, e.g. a vision chip and an eye both processes real photons. Gas sensing is substituted for pheromone sensing in Ishida et al.'s (1999) robot model of the moth, but they replicate other physical features of the sensor, for example the way that the moths wings act as a fan to draw air over the sensors. Models may use similar physical properties. This may mean that the properties can be described by the same mathematics e.g. the subthreshold transistor physics used in neuromorphic design are said to be equivalent to neuron membrane channel physics (Etienne-Cummings et al, 1998). Or it may be a 'looser' mapping. The robot model of chemotaxis in C. Elegans (Morse et al., 1998) uses a light source as an analog for a chemical gradient in a petri dish, while preserving a similar sensor layout and sensitivity. Models may also use quite different properties to stand in for the properties specified in the target e.g. a number in the computer processor labelled ‘activity’ to represent the firing rate of a neuron, or the use of different coloured blocks in a robot arena to represent 'food' and 'mates'.

In fact nearly all models use all these modes of representation to various extents in creating correspondences to the hypothesised target variables. Thus 'symbolic' computer simulations frequently use time to represent time (Schultz & Sullivan, 1972); 'iconic' scale models tend to use materials of analogous rigidity rather than the same materials; mathematical models can be treated as a short-hand for building a physically 'analogous' system. Rather than sharply contrasting 'kinds' of models, what is of relevance are the constraints the medium imposes on the operation of the model. What makes a representation more ‘symbolic’ is that the medium is more arbitrary or neutral with respect to representing the target properties. Symbols rest on "arbitrary conventions…no likeness or unlikeness it may bear to a its subject matter counts as a reason why it is a symbol for, or of, a " (Harre, 1970, p.38). More ‘physical’ models are chosen because the medium has some pre-existing resemblance to the properties we wish to represent, such as the use of analog VLSI to implement neural processing (Mead, 1989). The medium may contribute directly to the accuracy and relevance of the model, or simply make it easier to implement, run or evaluate as described by Quinn & Espenscheid (1993):

"Even in the most exhaustive [computer] simulations some potentially important effects may be neglected, overlooked or improperly modelled. It is often not reasonable to attempt to account for the complexity and unpredictability of the real world. Hence implementation in hardware is often a more straightforward and accurate approach for rigorously testing models of nervous systems" (p.380)

Doucet & Sloep (1992) point out "the way physical models operate is, as it were, ruled by nature itself…rules for functioning of conceptual [symbolic] models…we make ourselves" (p.281). Symbolic models may implicitly rely on levels of precision in processing that are unlikely to be possible to real systems. Computer programs can represent a wider range of possible situations than we can physically model, but physical models cannot break the laws of physics.

4. The position of biorobotics

In section 2.4 I discussed in what sense biorobots can be considered biological models - in particular, how robots can be used as physical simulations of organisms, to test hypotheses about the control of behaviour. How, then, does biorobotics differ from other modelling approaches in biology? If it is suggested that "the use of a robot ensures the realism" (Burgess et al., 1997, p.1535) of a model, does this mean making the model more relevant for biology, making it more detailed, making it more accurate, making it more specific (or general?), making it a 'low-level' model, making the performance more lifelike, or just that the model is operating with 'real' input and output?

In this section, I will use the framework developed above to clarify how biorobotics differs, on various dimensions, from other kinds of biological models. I will also advance arguments for why the resulting position of biorobots in modelling 'space' is a good one for addressing some fundamental questions in explaining biological behaviour. I do not intend to suggest that it is the only correct approach - "there is no unique or correct model" (Fowler, 1997, p.8) of a system. However "there are good and bad models" (op. cit.) relative to the purposes of the model builder. Thus this discussion will also illustrate for what purposes in understanding biology biorobotics appears to have particular strengths.

4.1 Relevance to biology

A notable feature that distinguishes recent biorobotic research from earlier biologically-inspired approaches in robotics (such as the 'behaviour-based' approach articulated by Brooks Brooks (1986) and Arkin (1998)) is the increased concern as to whether and how the robot actually resembles some specified biological target. Thus most of the robot studies listed in table 1 cite the relevant biological literature that has guided decisions on what to build, how to build it, and how to assess it; frequently a biological investigator has initiated or collaborated directly in the research. The likelihood of being able to apply the results back to biology is thus increased, even where this was not the primary aim in the initial robot construction. Biorobotics has been able to confirm, develop and refute theories in several areas of biology, as already described in a number of examples above.

A distinction was drawn in previous sections between using biorobots as biological models and using them for engineering, and it is sometimes argued that these are incompatible, or at least orthogonal, concerns (e.g. Hallam, 1998; Pfeifer, 1996). Nevertheless many of those working in biorobotics claim to be doing both. For example Hirose et al. (1996) include as ‘biorobotics’ both "build robots that emulate biological creatures" and "use development of robots to understand biological and ethological concepts" (p.95). Espenschied et al. (1996) in describing their work on robot models of insect walking claim "results that demonstrate the value of basing robot control on principles derived from biology…also…provide insight into the mechanisms of locomotion in animals and humans" (p.64). Lambrinos et al. (1997) regarding their robot model of desert ant navigation suggest "On the one hand, the results obtained …provide support for the underlying biological models. On the other hand…computationally cheap navigation methods for mobile robots are derived" (p.?). Raibert (1986) in discussing methods for legged locomotion points out "In solving problems for the machine, we generate a set of plausible algorithms for the biological system. In observing the biological behaviour, we explore plausible behaviours for the machine" (p.195).

Indeed, even where the explicit aim in building the robot model is said to be just ‘engineering’ or just ‘biology’, the process of doing one is very likely to involve some of the other. It is the engineering requirement of making something that actually works that creates much of the hypothesis testing power of robotic models of biological systems. This is well described by Raibert (1986):

"To the extent that an animal and a machine perform similar locomotion tasks, their control systems and mechanical structure must solve similar problems. By building machines we can get new insights into these problem, and we can learn about possible solutions. Of particular value is the rigor required to build physical machines that actually work" (p.3)

In the other direction, building a robot 'inspired' by an animal source presupposes a certain degree of knowledge about that source. If as Ayers et al. (1998) claim "biologically-based reverse engineering is the most effective procedure" to design robots, then we need to understand the biology to build the robots - in Ayers' case this has involved exhaustive analysis of the underlying 'units' of action in the locomotion behaviour of the lobster. That is, our goal is as defined by Shimoyama et al. (1996) "to understand activation and sensing of biological systems so that we can build equivalents" (p.8) or Leoni et al. (1998) "a proper comprehension of human biological structures and cognitive behaviour …is fundamental to design and develop a [humanoid] robot system" (p.2274). The robot designer’s motives thus overlap substantially with those of the biologist.

4.2 Level

It is sometimes argued in biorobotics that this methodology should focus on lower levels, or working from 'bottom-up'. In fact Taddeucci & Dario (1998a) describe explicitly, in the context of models of eye-hand control, what most biorobotics researchers do implicitly i.e. work both top-down and bottom-up on the problems. The possible influence of lower level factors is kept in mind, and the exploration of the interaction of levels is engaged in. While this is perhaps true of many other modelling approaches, robotic implementation specifically supports the consideration and integration of different levels of explanation because of its emphasis on requiring a complete, behaving system as the outcome of the model. For example, Hannaford at al. (1995) primarily consider their robot arm as a "mechanism or platform with which to integrate information", particularly the interaction of morphology and neural control. Thus the context of the behaviour of the organism is always included in a robot model, counteracting the tendency in biological studies to lose sight of this context in close study of small parts of the underlying mechanisms.

The level of mechanism modelled by the robot will reflect the level of information currently available from biology. Interest in a particular level of explanation (such as single neuron properties) may bias the choice of target system e.g. towards invertebrate systems in which identified neurons have been mapped (Franceschini, 1996). On the other hand, interest in a particular target may determine the level at which an accurate model can be attempted. For example, Etienne (1998) reviews the behavioural and physiological data on mammalian navigation and concludes that lack of information about the actual interactions of the neural systems "leaves the field wide open to speculative modelling" (p.283) at the level of networks.

In addition, biorobotic systems emphasise the 'physical' level in the performance of sensing and action. That is, the dynamics of the physical interaction of the robot/animal and its environment are seen to be as critical in explaining its behaviour as the processing or neural connectivity (Chiel & Beer, 1997). It is often found that engaging closely in modelling the periphery simplifies central or higher level processing. For example, Mura & Shimoyama (1998) note that copying the circuitry of insect visual sensors "closely integrates sensing and early stage processing" to "ease off decision making at a higher processing level" (p.1859), and Kubow & Full (1999) discuss the extent to which running control is actually done by the mechanical characteristics of the cockroach’s legs. Some of the most interesting results from biorobotic modelling are demonstrations that surprisingly simple control hypotheses can suffice to explain apparently complex behaviours when placed in appropriate interaction with the environment. Examples include the use of particular optical motion cues to achieve obstacle avoidance that slows down the robot in cluttered environments without explicit distance cues being calculated (Franceschini et al. 1992), the 'choice' between sound sources with different temporal patterns resulting from a simple four-neuron circuit in the robot cricket (Webb & Scutt, 2000), and the use of limb linkage through real world task constraints to synchronise arm control (Williamson, 1998).

4.3 Generality

In engineering, robots built for specific tasks have to date been more successful than 'general purpose' ones. Similarly in biorobotics the most successful results to date have been in the context of modelling specific systems - particular competencies of particular animals. There is some doubt whether modelling 'general' animal competencies (e.g. by simulating 'hypothetical' animals such as Pfeifer's (1996) 'fungus eater' or Bertin & van de Grind's (1996) 'paddler') will tell us much about any real biological system. Without regrounding the generalisations by demonstrating the applicability of the results to some specific real examples, the problem modelled may end up being 'biological' only in the terminology used to describe it.

An example of the tendency to more specificity is the shift in research described by Nelson & Quinn (1998) from generic six-legged walkers (Espenscheid, 1996) to a robot that closely copies the anatomy and mechanics of the cockroach. As they explain, the desired movement capabilities for the robot - fast running and climbing abilities - depend on quite specific properties such as the different functions of the rear, middle and front pair of legs. Hence the specific morphology has to be built into the robot if it is to be able to exploit features such as the propulsive power of the rear legs and the additional degrees of freedom in the front legs that enable the cockroach to climb.

If important factors in understanding behaviour lie in the specific sensorimotor interface, then it is necessary to model specific systems in sufficient detail to encompass this. 'Generalising' a sensorimotor problem can result in changing the nature of the problem to be solved. What is lost are the properties described by Wehner (1987) as 'matched filters', the specific fit of sensor (or motor) mechanisms to the task. The sound localisation of crickets is a good illustration. Crickets have a unique auditory system in which the two ears are connected by a tracheal tube to form a pressure difference receiver. This gives them good directionality but only for a specific frequency - that of the calling song they need to localise. Copying this mechanism in a robot model it was possible to demonstrate that this factor alone can suffice to reproduce the cricket's ability to respond only to songs with the carrier frequency of conspecifics (Lund et al., 1997).

Note that while 'matched filters' are by their nature specific to particular animals, the concept is a general one. Similarly, while the neural circuitry modelled in the cricket robot is highly specific to the task (and hence very efficient) the idea it uses of exploiting timing properties of neural firing is a general one. Thus we can see general principles emerging from the modelling of specific systems. Moreover, the 'engineering' aspect of biorobotics enhances the likelihood of discovering such generalities as it attempts to transfer or apply mechanisms from biology to another field, the control of man-made devices.

4.4 Abstraction

It might be assumed that the aims discussed so far of increasing relevance by having a clearly identified target system, and increasing specificity rather than trying to invent general models, require that biorobotic models become more detailed. Beer et al. (1997) suggests as a principal for this approach "[generally to] err by including more biology than appears necessary" (p.33). However others believe that abstraction does not limit relevance e.g. McGeer (1990) "it seems reasonable to suppose that our relatively simple knee jointed model has much to say about walking in nature" (p.1643). Indeed has been suggested that a key advantage of biorobotics is the discovery of ‘simpler’ solutions to problems in biology because it takes an abstract rather than analytic approach (Meyer, 1997). It is clear that some quite abstract robot representations have usefully tested some quite specific biological hypotheses. For example, there is minimal representation of biological details in the physical architecture of Beckers et al's (1996) robot 'ants', Burgess et al.'s (1997) 'rat' or indeed the motor control of the robot 'cricket' mentioned above, but nevertheless it was possible to demonstrate interesting resemblance in the patterns of behaviour of the robots and the animals, in a manner appropriate to testing the hypotheses in question.

Rather than being less abstract, it might better be said that biorobotics has adopted different abstractions from simulations (or from standard robot control methods (Bekey,1996 ; Pratt & Pratt, 1998a)). Robots are not less abstract models just because they are physically implemented - a two-wheeled robot is a simpler model of motor control than a six-legged simulation. What does distinguish abstraction in biorobotics from simulations is that it usually occurs by leaving out details, substitution, or simplifying the representation, rather than by idealising the objects or functions to be performed. Thus even two-wheeled motor control has to cope with friction, bumps, gravity and so on whereas a six-legged computer simulation may restrict itself to representing only the kinematic problems of limb control and ignore the dynamics entirely.

Different aspects of the systems are often abstracted to different degrees in biorobotics. Thus models involving quite complex sensors often use very simple two-wheeled motor control rather than equally complex actuators. Edelman et al. (1992) describe relatively complex neural models but test them in rather abstract tasks. Though some robots are tested in quite complex environments, the majority have a simplified environment constructed for them (though in some cases this is not much different from the controlled environment used to test the animals). Pfeifer (1996) and Cruse (2000) have made the point that this imbalance in abstraction may itself lead to a loss of biological relevance. What is needed is to ensure that the assumptions involved in the abstraction are clear, and justified. A good example is the description by Morse et al. (1998) of the simplifications they adopted in their robot model of chemotaxis in C. elegans, such as the biological evidence for abstracting the motor control as a constant propulsive force plus a steering mechanism provided by contraction of opposing muscles.

4.5 Accuracy

If 'highest possible accuracy' was considered to be the aim in biorobotics, then there are many ways in which existing systems can be criticised. Most robot sensors and actuators are not directly comparable to biological ones: they differ in basic capability, precision, range, response times and so on. Binnard (1995) in the context of building a robot based on some aspects of cockroach mechanics, suggests that the "tools and materials…are fundamentally different" (p. 44), particularly in the realm of actuators. Ayers (1995) more optimistically opines that "Sensors, controlling circuits and actuators can readily be designed which operate on the same principles as their living analogs". The truth is probably somewhere in between these extremes. Often the necessary data from biology is absent or not in a form that can easily be translated into implementation (Delcomyn et al., 1996). The process of making hypotheses sufficiently precise for implementation often requires a number of assumptions that go well beyond what is accurately known of the biology. As for abstraction, there is also a potential problem in having a mismatch in the relative accuracy of different parts of the system. For example it is not clear how much is learnt by using an arbitrary control system for a highly accurate anatomical replica of an animal; or conversely applying a detailed neural model to control a robot carrying out a fundamentally different sensorimotor task.

Biorobotics researchers are generally more concerned with building a complete, but possibly rough or inaccurate model, than with strict accuracy per se. That is, the aim is to build a complete system that connects action and sensing to achieve a task in an environment, even if this limits the individual accuracy of particular parts of the model because of necessary substitutions, interpolations and so on. While greater accuracy is considered worth striving for, a degree of approximation is considered a price worth paying for the benefits of gaining a more integrated understanding of the system and its context, in particular the "tight interdependency between sensory and motor processing" (Pichon et al., 1989, p.52). This is exemplified in their robot 'fly' by the use of self movement to generate the visual input required for navigation.

Projects that set out to build 'fully accurate' models tend not to get completed, and we can learn more from several somewhat inaccurate models than from one incomplete one. In several cases the accuracy has then been increased iteratively, for example, the successive moves from a slower, larger robot implementation of the cricket robot (Webb, 1994), to a robot capable of processing sound at cricket speed (Lund et al., 1998), and then to a controller that more closely represents the cricket’s neural processing (Webb & Scutt, 2000). Indeed, Levins (1966) argues that building multiple models is a useful strategy to compensate for inevitable inaccuracies because results common to all the models are 'robust' with respect to the individual inaccuracies of each.

4.6 Match

It should be admitted that the assessment of the behaviour relative to the target is still weak in most studies in biorobotics. It is more common to find only relatively unsupported statements that a robot "exhibited properties which are consistent with experimental results relating to biological control systems" (Leoni et al., 1998, p.2279). One encouraging trend in the direction of more carefully assessing the match is the attempt to repeat experiments with the same stimuli for the robot and the animal. For example Touretsky & Saksida (1997) describe how they "apply our model to a task commonly used to study working memory in rats and monkeys- the delayed match to sample task" (p.219), and Sharpe & Webb (1998) draw on data in ant chemical trail-following behaviour for methods and critical experiments to assess a robot model's ability to follow similar trails under similar condition variations, such as changes in chemical concentration. Some behaviours lend themselves more easily than others to making comparisons – for example the fossilised worm trails reproduced in a robot model by Prescott & Ibbotson (1997) provide a clear behavioural 'record' to attempt to copy with the robot.

The accuracy of the robot model may impose its own limits on the match. Lambrinos et al. (1997) note, when testing their polarisation compass and landmark navigation robot in the Sahara environment, that despite the same experimental conditions "it is difficult to compare the homing precision of these agents, since both their size and their method of propulsion are completely different" (p.?). There is also the inherent problem in any modelling, that reproducing the same behaviour is not proof that the same underlying mechanism is being used by the robot and the animal. There are some of ways in which the biorobotics approach can attempt to redress these limitations. By having a specific target, usually chosen because there is substantial existing data, more extensive comparisons can be made. Using a physical medium and more accurately representing environmental constraints reduces the possibility that the ‘world model’ is being tuned to make the animal model work, rather than the reverse. The interpretation of the behaviour is more direct. Voegtlin & Verschure (1999) argue, in their robot implementation of models of classical conditioning, that by combining levels, and thus satisfying constraints from "anatomy, physiology and behaviour" the argument from match is strengthened.

Finally, biorobotic modelling has been instrumental in driving the collection of further data from the animal. Quinn & Ritzmann (1998) describe how building a cockroach-inspired robot has "required us to make detailed neurobiological and kinematic observations of cockroaches" (p.239). Correctly matching the behaviour is perhaps less important then revealing what it is we need to know about the animal to select between possible mechanisms demonstrated in the robot.

4.7 Medium

The most distinctive feature of the biorobotics approach is the use of hardware to model biological mechanisms. It is also perhaps the most often questioned - what is learnt that could not be as effectively examined by computer simulation? One justification relates to the issue of building 'complete' models discussed above - the necessity imposed by physical implementation that all parts of the system function together and produce a real output. Hannaford et al. (1995) argue that "Physical modelling as opposed to computer simulation is used to enforce self consistency among co-ordinate systems, units and kinematic constraints" in their robot arm.

Another important consideration is that using identity in parts of a model can sometimes increase accuracy at relatively little cost. Using real water or air-borne plumes, or real antennae sensors, saves effort in modelling and makes validation more straightforward. Dean (1998) proposes that by capturing the body and environmental constraints, robots provide a stronger "proof in principle" that a certain algorithm will produce the right behaviour. In engineering, demonstration of a real device is usually a more convincing argument than simulated results. Thus one direction of current efforts in biorobotics is the attempt to find materials and processes that will support better models. Dario et al. (1997) review sensors and actuators available for humanoid robots. Kolacinski & Quinn (1998) discuss elastic storage and compliance mechanisms for more muscle-like actuators. Mojarrad & Shahinpoor (1997) describe polymeric artificial muscles that replicate undulatory motions in water, which they use to test theoretical models of animal swimming. On a similar basis some researchers use dedicated hardware for the entire control system (i.e. not a programmed microcontroller). Franceschini et al.'s (1992) models of the fly motion detection system used to control obstacle avoidance are developed as fully parallel, analog electronic devices. Maris & Mahowald 1998 describe a complete robot controller (including contrast sensitive retina and motor spiking neurons) implemented in analog VLSI. Cited advantages of hardware implementations include the ability to exploit true parallelism, and increased emphasis on the ‘pre-processing’ done by physical factors such as sensor layout. It is important to note, however, that simply using a more ‘physical’ medium does not reduce the need for "ensuring that the relevant physical properties of the robot sufficiently match those of the animal relative to the biological question of interest" (Beer et al., 1998, p.777). Electronic hardware is not the same medium as that used biology, and may lend itself to different implementations – a particular problem is that neural connectivity is three dimensional where electronic circuits are essentially two-dimensional.

However a more fundamental argument for using physical models is that an essential part of the problem of understanding behaviour is understanding the environmental conditions under which it must be performed - the opportunities and constraints that it offers. If we simulate these conditions, then we include only what we already assume to be relevant, and moreover represent it in a way that is inevitably shaped by our assumptions about how the biological mechanism works. Thus our testing of that mechanism is limited in a way that it is not if we use a real environment, and the potential for further discovery of the actual nature of the environment is lost. Thus Beckers et al. (1996) et al suggest "systems for the real world must be developed in the real world, because the complexity of interactions available for exploitation in the real world cannot be matched by any practical simulation environment" (p.183). Flynn & Brooks (1989) argue that "unless you design, build, experiment and test in the real world in a tight loop, you can spend a lot of time on the wrong problems" (p.15).

5. Conclusions

"It was by learning the inner workings of nature that man became a builder of machines" (Hoffer, cited by Arkin, 1998, p.31).

"We've only rarely recognised any mechanical device in an organism with which we weren't already familiar from engineering" (Vogel, 1999, p.311)

Biorobotics, as the intersection of biology and robotics, spans both views represented by the quotes above - understanding biology to build robots, and building robots to understand biology. It has been argued that robots can be 'biological models' in several different senses. They can be modelled on animals - the biology as a source of ideas when attempting to build a robot of some target capability. They can be models for animals - robotic technology or theory as a source of explanatory mechanisms in biology. Or they can be models of animals - robots as a simulation technology to test hypotheses in biology. Work on this last kind of 'biorobot', and the potential contribution it can make to biology, has been the main focus of discussion in this paper.

To assess biorobotics in relation to other kinds of simulations in biology, a multidimensional description of approaches to modelling has been proposed. Models can be compared with respect to their relevance, the level of organisation represented, generality, abstraction, structural accuracy, behavioural match, and the physical medium used to build them. Though interrelated, these dimensions are separable: models can be relevant without being accurate, general without being abstract, match behaviour at different levels, and so on. Thus a decision with respect to one dimension does not necessarily constrain a modeller with respect to another.

I agree with Levins (1993) that a dimensional description should not be primarily considered as a means of ranking models as 'better' or 'worse' but rather as an elucidation of potential strategies. The strategy of biorobots has here been characterised as: increasing relevance and commitment to really testing biological hypotheses; combining levels; studying specific systems that might illustrate general factors; abstracting by simplification rather than idealisation; aspiring to accuracy but concerned with building complete systems; looking for a closer behavioural match; and using real physical interaction as part of the medium. The motivations for this strategy have been discussed in detail above, but can be compactly summarised as the view that biological behaviour needs to be studied in context, that is in terms of the real problems faced by real animals in real environments.

Thus the justification of the biorobotic approach is grounded in a particular perspective on the issues that need to be addressed. Different approaches to modelling will reflect differing views about the processes being modelled, and the nature of the explanations required. One aim of this paper is to encourage other modellers to clarify their strategies and the justification for them - even if it is only by disagreement over the included dimensions. Indeed, different views of 'models' reflect different views of the 'nature of explanation', as has been long discussed in the philosophy of science. It has not been possible to pursue all these meta-issues, some of which seem in any case to have little relevance to everyday scientific use of simulation models. What is critical is that the conclusions that can be drawn from a model are only as good as the representation provided by that model. In this respect, by working on real problems in real environments, robots can make good models of real animals.


1.Although Suppe(1977) distinguishes this ‘representational’ use of 'model' from ‘model’ used in the mathematical sense of a semantic interpretation of a set of axioms such that they are true. There is not space in this article to discuss this model theoretic approach in the philosophy of science (Carnap, 1966; Nagel,  1961; Suppe,  1977) or the formal systems theoretic approach to models developed by Zeigler (1976), and adopted in many subsequent works (e.g variants in Halfon, 1983; Maki & Thompson, 1973; Spriet & Vansteenkiste, 1982; Widman & Loparo, 1989. These formal/logical definitions are in any case not easy to apply to real examples of models in science where “Modelling is certainly an art, involving a number of logical gaps” (Redhead, 1980, p.162).

2. Black (1962) suggests this generic usage of 'model' is “a pretentious substitute for theory”  whereas Stogdill (1970) calls it “an unpretentious name for a theory”.

3.  Implementation is sometimes taken to mean actually reproducing a real copy of the system (Harnad, 1989), i.e. replication; this is not intended here.

4. It should be acknowledged that there are several, fairly widespread, definitions of simulation more restricted than the usage I have adopted here. First there is the usage that contrasts iterative solutions for mathematical systems to analytical solutions (Forrester, 1972). Second, there is the emphasis on simulations being processes i.e. ‘dynamic’ vs. ‘static’ models or an “operating model…one that is itself a process” (Schultz & Sullivan, 1972, p.?). These distinctions have some validity, but I am going to ignore them for convenience, as analytical and static models stand in the same relationship to targets and hypotheses as iterative or temporal ones. Third is the usage of ‘simulation’ to refer to relatively detailed models of specific systems (e.g. of a particular species in certain niche) as opposed to more ‘general’ models (e.g. of species propagation) which may also be implemented on computers for iterative solutions (e.g. Levins, 1993; Maynard Smith, 1974). Fourth is the distinction of simulations as models that only attempt to match input-output behaviour (e.g. Ringle, 1979; Dreyfus, 1979) as opposed to models that are supposed to have the same internal mechanisms as their target. These latter distinctions often carry the implication that ‘simulations’ are used for applications and ‘models’ for science, i.e. these distinctions tend to be polemic rather than principled (Palladino, 1991), and they are certainly not clear-cut.

5. The term ‘source’ is taken from Harre (1970b) who discusses this notion extensively. Unfortunately the term 'source' is also occasionally used for what I have called the ‘target’, by some authors.

6. 'Biologically-inspired' robots can be criticised at times for using 'biological' as an excuse for not evaluating the mechanism against other engineered solutions, while using 'inspired' as a disclaimer for being required to show it applies to biology.

7. Some authors do use 'accuracy' in the sense of 'replicative validity' e.g. Bhalla et al. (1992) “accuracy is defined as the average normalized mean square difference between the simulator output and the reference curve” p.453). The term 'match' is used instead in this article (see section 3.7).

Table 1: Examples of biorobot research. This is intended to be a representative sampling not a fully comprehensive listing.
Subject area Examples References
Simple sensorimotor control  
Moth pheromone tracking Kuwana, Shimoyama, & Miura, 1995; Ishida, Kobayashi, Nakamoto, & Moriisumi, 1999; Kanzaki, 1996, 
Ant trail following Sharpe & Webb, 1998; Russell, 1998
Lobster plume following Grasso, Consi, Mountain, & Atema, 1996; Ayers et al., 1998 
C. elegans gradient climb Morse, Ferree, & Lockery, 1998
Cricket phonotaxis Webb, 1995; Lund, Webb, & Hallam, 1998; Webb & Scutt, 2000
Owl sound localisation Rucci, Edelman, & Wray, 1999
Human localisation Horiuchi, 1997; Huang, Ohnishi, & Sugie, 1995
Bat sonar Kuc, 1997; Peremans, Walker, & Hallam, 1998
Locust looming detection Blanchard, Verschure, & Rind, 1999; Indiveri, 1998
Frog snapping Arbib & Liaw, 1995
Fly motion detection to control movement Franceschini, Pichon, & Blanes, 1992; Hoshino, Mura, Morii, Suematsu, & Shimoyama, 1998; Huber & Bulthoff, 1998; 1997; Harrison & Koch, 1999
Praying mantis peering Lewis & Nelson, 1998
Human oculomotor reflex Horiuchi & Koch, 1999; Shibata & Schaal, 1999
Saccade control Clark, 1998; Schall & Hanes, 1998
Ant polarized light compass Lambrinos et al., 1997
Lobster anemotaxis Ayers et al., 1998
Cricket wind escape Chapman & Webb, 1999
Trace fossils Prescott & Ibbotson, 1997
Complex motor control  
Stick insect Cruse et al., 1998; Pfeiffer et al., 1995
Cockroach Espenschied et al., 1996; Nelson & Quinn, 1998; Binnard, 1995
Four-legged mammal Ilg et al., 1998; Berkemeier & Desai, 1996
Tail propulsion Triantafyllou & Triantafyllou, 1995; Kumph, 1998
Pectoral fin Kato & Inaba, 1998
Undulation Patel et al., 1998
Flagellar motion Mojarrad & Shahinpoor, 1997
Insect wings


Miki & Shimoyami 1998;Fearing, 1999

Pornsin-Sirirak & Tai, 1999

Spinal circuits Hannaford et al., 1995
Cerebellar control Fagg et al., 1997
Grasping Leoni et al., 1998
Rhythmic movement Schaal & Sternad, 2001
Haptic exploration Erkman et al., 1999
  Special issue Advanced Robotics 11(6): 1997

Brooks & Stein, 1993

Hirai et al., 1998

Running & Hopping 1986
Brachiation Saito & Fukuda, 1996
Mastication Takanobu et al., 1998
Snakes Hirose, 1993, Review in Worst, ,
Paper wasp nest construct Honma, 1996
Ant/bee landmark homing Moller, 2000; Möller et al., 1998 
Rat hippocampus Burgess et al., 1997 

Gaussier et al., 1997

review Gelenbe et al., 1997
Collective behaviours Beckers et al., 1996

Melhuish et al., 1998

Learning Edelman et al., 1992; Sporns, forthcoming

Scutt & Damper, 1997

Saksida et al., 1997

Voegtlin & Verschure, 1999

Chang & Gaudiano, 1998



Achinstein, P. (1968). Concepts of Science: A philosophical analysis . Baltimore: John Hopkins Press.

Ackoff, R. L. (1962). Scientific Method. New York: John Wiley & Sons.

Amit, D. J. (1989). Modeling brain function: the world of attractor neural networks. Cambridge: Cambridge Uuniversity Press.

Arbib, M., & Liaw, J. (1995). Sensorimotor transformations in the worlds of frogs and robots. Artificial Intelligence, 72: 53-79.

Arkin, R. C. (1998). Behaviour-based robotics. Cambridge, MA: MIT Press.

Ashby, W. R. (1952). Design for a brain. London: Chapman and Hall.

Ayers, J. (1995). A reactive ambulatory robot architecture for operation in current and surge. Proceedings of the Autonomous Vehicles in Mine Countermeasures Symposium. Naval Postgraduate School(pp. 15-31). http://www.dac.neu.edu/msc/nps95mcm%20manuscript.html

Ayers, J., Zavracky, P., Mcgruer, N., Massa, D., Vorus, V., Mukherjee, R., & Currie, S. (1998). A modular behavioural-based architecture for biomimetic autonomous underwater robots. Autonomous Vehicles in Mine Countermeasures Symposium .http://www.dac.neu.edu/msc/biomimeticrobots98.html

Barto, A. G. (1991). Learning and incremental dynamic programming. Behavioral and Brain Sciences, 14:94-95.

Beckers, R., Holland, O. E., & Deneubourg, J. L. (1996). From local actions to global tasks: stigmergy and collective robotics. Artificial Life IV, 181-189.

Beer, R. D. (1990). Intelligence as Adaptive Behaviour: an experiment in computational neuroethology. London: Academic Press.

Beer, R. D., Chiel, H. J., Quinn, R. D., & Ritzmann, R. E. (1998). Biorobotic approaches to the study of motor systems. Current Opinion in Neurobiology, 8:777-782.

Beer, R., Quinn, R., Chiel, H., & Ritzmann, R. (1997). Biologically inspired approaches to robotics. Communications of the ACM, 40: 31-38.

Bekey, G. (1996). Biologically inspired control of autonomous robots. Robotics and Autonomous Systems, 18: 21-31.

Berkemeier, M., & Desai, K. (1996). Design of a robot leg with elastic energy storage, comparison to biology, and preliminary experimental results. Proceedings - IEEE International Conference on Robotics and Automation, 1996: 213-218.

Bertin, R. J. V., & van de Grind, W. A. (1996). The influence of light-dark adaptation and lateral inhibition on phototaxic foraging: a hypothetical animal study. Adaptive Behaviour, 5:141-167.

Bhalla, U. S., Bilitch, D. H., & Bower, J. M. (1992). Rallpacks: a set of benchmarks for neural simulators. Trends in Neurosciences, 15:453-58.

Binnard, M. B. (1995). Design of a Small Pneumatic Walking Robot. ftp://ftp.ai.mit.edu/pub/users/binn/SMthesis.zip.

Black, M. (1962). Models and Metaphors. Ithaca: Cornell University Press.

Blanchard, M., Verschure, P. F. M. J., & Rind, F. C. (1999). Using a mobile robot to study locust collision avoidance responses. International Journal of Neural Systems, 9:405-410.

Bower, J. M. (1992). Modeling the nervous system. Trends in Neurosciences, 15:411-412.

Bower, J. M., & Koch, C. (1992). Experimentalists and modelers:can we all just get along? Trends in Neurosciences, 15:458-461.

Braithwaite, R. B. (1960). Models in the Empirical Sciences. in E. Nagel, P. Suppes, & A. Tarski (editors), Logic methodology and philosophy of science(pp. 224-231). Stanford: Stanford University Press.

Brooks, R. A. (1986). Achieving artificial intelligence through building robots. A.I. Memo 899 M.I.T. A.I. Lab.

Brooks, R. A., & Stein, L. A. (1993). Building Brains for Bodies. A.I. Memo No. 1439. MIT A.I. Lab:

Brooks, R. J., & Tobias, A. M. (1996). Choosing the best model: level of detail, complexity and model performance. Mathematical Computer Modelling, 24:1-14.

Bulloch, A. G. M., & Syed, N. I. (1992). Reconstruction of neuronal networks in culture. Trends in Neurosciences, 15:422-427.

Bullock, S. (1997). An exploration of signalling behaviour by both analytic and simulation means for both discrete and continuous models. 4th European Conference on Artificial Life. Cambridge MA: MIT Press.

Bunge, M. (1973). Method, Model and Matter. Holland: D. Reidal Publishing co.

Burgess, N., Donnett, J. G., Jeffery, K. J., & O'Keefe, J. (1997). Robotic and neuronal simulation of the hippocampus and rat navigation. Philosophical Transactions of the Royal Society, B, 352:1535-1543.

Burgess, N., Donnett, J. G., & O'Keefe, J. (1998). Using a mobile robot to test a model of the rat hippocampus. Connection Science, 10:291-300.

Burgess, N., Jackson, A., Hartley, T., & O'Keefe, J. (2000). Predictions derived from modelling the hippocampal role in navigation. Biological Cybernetics, 83:301-312.

Carnap, R. (1966). Philosophical Foundations of Physics. New York: Basic Books.

Cartwright, B., & Collett, T. (1983). Landmark learning in bees. Journal of Comparative Physiology A, 151: 521-543.

Cartwright, N. (1983). How the laws of physics lie. Oxford: Clarendon Press.

Caswell, H. (1988). Theories and models in ecology - a different perspective. Ecological Modelling, 43:33-44.

Chan, K. H., & Tidwell, P. M. (1993). The reality of Artificial Life: can computer simulations become realizations? submission to Third International Conference on Artificial Life.

Chang, C., & Gaudiano, P. (1998). Application of biological learning theories to mobile robot avoidance and approach behaviours. Journal of Complex Systems, 1:79-114.

Chao, Y. R. (1960). Models in Linguistics and Models in General. in E. Nagel, P. Suppes, & A. Tarski (editors), Logic, methodology and philosophy of science(pp. 558-566). Stanford: Stanford University Press.

Chapman, T., & Webb, B. (1999). A neuromorphic hair sensor model of wind-mediated escape in the cricket. International Journal of Neural Systems, 9:397-403.

Chiel, H., & Beer, R. (1997). The brain has a body: adaptive behaviour emerges from interactions of nervous system, body and environment. Trends in Neurosciences, 20:553-557.

Churchland, P. S., Koch, C., & Sejnowski, T. J. (1990). What is computational neuroscience? E. L. Schwartz (editor), Computational Neuroscience. Cambridge, Mass.: MIT Press.

Churchland, P. S., & Sejnowski, T. J. (1988). Perspectives on Cognitive Neuroscience. Science, 242:741-745.

Clark, J. J. (1998). Spatial attention and saccadic camera motion. Proceedings - IEEE International Conference on Robotics and Automation, 1998: 3247-3252.

Cliff, D. (1991). Computational neuroethology: a provisional manifesto. in J.-A. Meyer, & S. W. Wilson (editors), From animals to animats(pp. 29-39). Cambridge, MA: MIT Press.

Colby, K. M. (1981). Modeling a paranoid mind. Behavioural and Brain Sciences, 4:515-560.

Collin, C., & Woodburn, R. (1998). Neuromorphism or Pragmatism? A formal approach. in L. Smith, & A. Hamilton (editors), Neuromorphic Systems: Engineering Silicon from Neurobiology. London: World Scientific.

Conant, R. C., & Ashby, W. R. (1991). Every good regulator of a system must be a model of that system. reprinted in G. J. Klir (editor), Facets of System Science. New York: Plenum Press.

Connell, J. H. (1990). Minimalist Mobile Robotics: A colony style architecture for an Artificial Creature. Boston: Academic Press.

Crick, F. (1989). The recent excitement about neural networks. Nature, 337:129-132.

Croon, M. A., & van de Vijver, F. J. R. (1994). Introduction. in M. A. Croon, & F. J. R. van de Vijver (editors), Viability of mathematical models in the social and behavioural science. Lisse: Swets and Zeitlinger.

Cruse, H. (2000). (draft paper). AAAI 1998 Fall Symposium on Robots and Biology.

Cruse, H., Kindermann, T., Schumm, M., Dean, J., & Schmitz, J. (1998). Walknet - a biologically inspired network to control six-legged walking. Neural Networks, 11: 1435-1447.

Dario, P., & et al. (1997). Sensors and actuators for humanoid robots. Advanced Robotics, 11:567-584.

Deakin, M. A. B. (1990). Modelling Biological Systems. in T. L. Vincent, A. I. Mees, & L. S. Jennings (editors), Dynamics of complex interconnected biological systems(pp. 2-16). Boston: Birkhauser.

Dean, J. (1998). Animats and what they can tell us. Trends in Cognitive Sciences, 2:60-67.

Delcomyn, F., Nelson, M., & CocatreZilgien, J. (1996). Sense organs of insect legs and the selection of sensors for agile walking robots. International Journal of Robotics Research, 15: 113-127.

Dennett, D. C. (1979). Brainstorms: Philosophical Essays on Mind and Psychology. Sussex: Harvester Press.

Descartes, R. (1662). Trait de l'homme. translation 1911 E. S. Haldane, & G. R. T. Ross. Cambridge: Cambridge University Press.

Doucet, P., & Sloep, P. B. (1992). Mathematical modelling in the life sciences. Chichester: Ellis Horwood.

Dreyfus, H. L. (1979). A framework for misrepresenting knowledge. in M. Ringle (editor), Philosophical Perspectives in Artificial Intelligence. Sussex: Harvester Press.

Dror, I. E., & Gallogly, D. P. (1999). Computational analyses in cognitive science: in defense of biological implausibility. Psychonomic Bulletin and Review, 6:173-182.

Durbin, R. (1989). On the correspondence between network models and the nervous system. in R. Durbin, C. Miall, & G. Mitchison (editors), The computing neuron. Wokingham: Addison-Wesley.

Edelman, G. M., Reeke, G. N., Gall, W. E., Tononi, G., Williams, D., & Sporns, O. (1992). Synthetic neural modeling applied to a real world artifact. Proceedings of the National Academy of Sciences, 89:7267-7271.

Elliott, T., Howarth, C. I., & Shadbolt, N. R. (1996). Neural competition and statistical mechanics. Proceedings of Royal Society B, 263:601-606.

Erkman, I., Erkman, A. M., Takkaya, A. E., & Pasinlioglu, T. (1999). Haptic perception of shape and hollowness of deformable objects using the Anthrobot-III robot hand. Journal of Robotic Systems, 16:9-24.

Espenschied, K., Quinn, R., Beer, R., & Chiel, H. (1996). Biologically based distributed control and local reflexes improve rough terrain locomotion in a hexapod robot. Robotics and Autonomous Systems, 18: 59-64.

Estes, W. K. (1975). Some targets for mathematical psychology. Journal of Mathematical Psychology, 12:263-282.

Etienne, A. S. (1998). Mammalian navigation, neural models and robotics. Connection Science, 10:271-289.

Etienne-Cummings, R., Van der Spiegel, P., & Mueller, P. (1998). Neuromorphic and digital hybrid systems. L. Smith, & A. Hamilton (editors), Neuromorphic Systems: Engineering Silicon from Neurobiology. London: World Scientific.

Fagg, A., Sitkoff, N., Barto, A., & Houk, J. (1997). Cerebellar learning for control of a two-link arm in muscle space. Proceedings -IEEE International Conference on Robotics and Automation, 1997: 2638-2644.

Fearing, R. S. (1999) Micromechanical Flying Insect [Web Page]. URL http://robotics.eecs.berkeley.edu/~ronf/mfi.html.

Feibleman, J. K. (1954). Theory of integrative levels. British Journal of the Philosophy of Science, 5:59-66.

Ferrell, C. (1995). Comparison of three insect-inspired locomotion controllers. Robotics and Autonomous Systems, 16: 135-159.

Flynn, A. M., & Brooks, R. A. (1989). Battling Reality. A.I. Memo 1148 M.I.T. A.I. Lab.

Fodor, J. A. (1968). Psychological Explanation. Random House.

Fodor, J. A., & Pylyshyn, Z. (1988). Connectionism and cognitive architecture: a critical analysis. Cognition, 28:3-71.

Forrester, J. W. (1972). Principles of Systems. Cambridge, Mass: Wright-Allen Press.

Fowler, A. C. (1997). Mathematical Models in the Applied Sciences. Cambridge: Cambridge University Press.

Franceschini, N. (1996). Engineering applications of small brains. FED Journal, 7:38-52.

Franceschini, N., Pichon, J. M., & Blanes, C. (1992). From insect vision to robot vision. Philosophical Transactions of the Royal Society B, 337:283-294.

Frijda, N. J. (1967). Problems of computer simulation. Behavioural Science, 12:59-.

Gaussier, P., Banquet, J. P., Joulain, C., A. Revel, A., & Zrehen, S. (1997). Validation of a hippocampal model on a mobile robot. in Vision, Recognition, Action: Neural Models of Mind and Machine Boston, Massachusetts.

Gelenbe, E., Schmajuk, N., Staddon, J., & Reif, J. (1997). Autonomous search by robots and animals: a survey. Robotics and Autonomous Systems, 22: 23-34.

Giere, R. N. (1997). Understanding Scientific Reasoning. Orlando: Harcourt Brace.

Gordon, G. (1969). System simulation. New Jersey: Prentice Hall.

Grasso, F., Consi, T., Mountain, D., & Atema, J. (1996). Locating odor sources in turbulence with a lobster inspired robot. In Maes, P., Mataric, M. J., Meyer, J. A., Pollack, J., and Wilson, S. W. (editors) Sixth International Conference on Simulation of Adaptive Behaviour: From animals to animats 4 Cambridge, Mass.: MIT Press.

Grasso, F., Consi, T., Mountain, D., & Atema, J. (2000). Biomimetic robot lobster performs chemo-orientation in turbulence using a pair of spatially separated sensors: Progress and challenges . Robotics and Autonomous Systems, 30:115-131.

Grimm, V. (1994). Mathematical models and understanding in ecology. Ecological Modelling, 75/76:641-651.

Haefner, J. W. (1996). Modeling Biological Systems. New York: Chapman and Hall.

Halfon, E. (1983). Is there a best model structure? I Modeling the fate of a toxic substance in a lake. Ecological Modelling, 20:135-152.

Hallam, J. (1998). Can we mix robotics and biology? Workshop on Biomorphic Robots Victoria BC Canada.

Hannaford, B., Winters, J., Chou, C.-P., & Marbot, P.-H. (1995). The anthroform biorobotic arm: a system for the study of spinal circuits. Annals of Biomedical Engineering, 23:399-408.

Harnad, S. (1989). Minds, machines and Searle. Journal of Experimental and Theoretical Artificial Intelligence, 1:5-25.

Harre, R. (1970a). The method of science. London: Wykeham.

Harre, R. (1970b). The principles of scientific thinking. Chicago: Chicago University Press.

Harrison, R. R., & Koch, C. (1999). A robust analog VLSI motion sensor based on the visual system of the fly. Autonomous Robotics, 7:211-224.

Hesse, M. B. (1966). Models and analogies in science. Notre Dame University Press.

Hirai, K., Hirose, M., Haikawa, Y., & Takenaka, T. (1998). The development of the Honda humanoid robot. Proceedings - IEEE International Conference on Robotics and Automation, 1998: 1321-1326.

Hirose, S., Raibert, M., & Pack, R. T. (1996). General systems group report (International Workshop on Biorobotics). Robotics and Autonomous Systems, 18:95-99.

Hirose, S. (1993). Biologically Inspired Robotics. Oxford: Oxford University Press.

Holland, O., & Melhuish, C. (1999). Stigmergy, self-organization and sorting in collective robotics. Artificial Life, 5:173-202.

Honma, A. (1996). Construction robot for three-dimensional shapes based on the nesting behavior of paper wasps. Seimitsu Kogaku Kaishi/Journal of the Japan Society for Precision Engineering, 62: 805-809.

Hoos, I. R. (1981). Methodology, Methods and Models. in F. E. Emery (editor), Systems Thinking: 2. Suffolk: Penguin.

Hopkins, J. C., & Leipold, R. J. (1996). On the dangers of adjusting parameter values of mechanism-based mathematical models. Journal of Theoretical Biology, 183:417-427.

Horiuchi, T. (1997). An auditory localization and co-ordinate transform chip. in Advances in Neural Information Processing Systems 8. Cambridge MA: MIT Press.

Horiuchi, T. K., & Koch, C. (1999). Analog VLSI-based modeling of the primate oculomotor system. Neural Computation, 11:243-264.

Hoshino, H., Mura, F., Morii, H., Suematsu, K., & Shimoyama, I. (1998). A small sized panoramic scanning visual sensor inspired by the fly's compound eye. Proceedings - IEEE International Conference on Robotics and Automation (pp. 1641-1646).

Huang, J., Ohnishi, N., & Sugie, N. (1995). A Biomimetic System for Localization and Separation of Multiple Sound Sources. IEEE Trans. on Instrumentation and Measurement, 44:733-738.

Huber, S. A., & Bulthoff, H. H. (1998). Simulation and robot implementation of visual orientation behaviour of flies. in Pfeifer, R., Blumberg, B., Meyer, J. A., and Wilson, S. W. (editors)From animals to animats 5 (pp. 77-85). Cambridge, Mass.: MIT Press.

Hughes, R. I. G. (1997). Models and representation. Philosophy of Science , 64:S325-S336.

Ilg, W., Berns, K., Jedele, H., Albiez. J., Dillmann, R., Fischer, M., Witte, H., Biltzinger, J., Lehmann, R., & Schilling, N. (1998a). BISAM: from small mammals to a four-legged walking machine. in Pfeifer, R., Blumberg, B., Meyer, J. A., and Wilson, S. W. (editors)From animals to animats 5 Cambridge, Mass.: MIT Press.

Indiveri, G. (1998b). Analog VLSI Model of Locust DCMD Neuron Response for Computation of Object Approach. L. Smith, & A. Hamilton (editors), Neuromorphic Systems: Engineering Silicon from Neurobiology. London: World Scientific.

Ishida, H., Kobayashi, A., Nakamoto, T., & Moriisumi, T. (1999). Three dimensional odor compass. IEEE Transactions on Robotics and Automation, 15: 251-257.

Kacser, H. (1960). Kinetic models of development and heredity. in Symposia of the Society for Experimental Biology Models and analogues in biology. Cambridge: Cambridge University Press.

Kanzaki, R. (1996). Behavioral and neural basis of instinctive behavior in insects: odor- source searching strategies without memory and learning. Robotics and Autonomous Systems, 18: 33-43.

Kaplan, A. (1964). The conduct of enquiry. San Francisco: Chandler.

Kato, M., & Inaba, T. (1998). Guidance and control of fish robot with apparatus of pectoral fin motion. Proceedings - IEEE International Conference on Robotics and Automation, 1: 446-451.

Klir, J., & Valach, M. (1965). Cybernetic Modelling. London: ILIFFE Books Ltd.

Koch, C. (1999). Biophysics of Computation. Oxford: Oxford University Press.

Kolacinski, M., & Quinn, R. D. (1998). A novel biomimetic actuator system. Robotics and Autonomous Systems, 25:1-18.

Kortmann, R., & Hallam, J. (1999). Studying animals through artificial evolution: the cricket case. in Proceedings of the Fifth European Conference on Artificial Life Berlin: Springer-Verlag.

Kroes, P. (1989). Structural analogies between physical systems. British Journal for the Philosophy of Science, 40:145-154.

Kubow, T. M., & Full, R. J. (1999). The role of the mechanical system in control: a hypothesis of self-stabilisation in the cockroach. Philosophical Transactions of the Royal Society of London B, 354:849-861.

Kuc, R. (1997). Biomimetic sonar recognizes objects using binaural information. Journal of the Acoustical Society of America, 102: 689-696.

Kumph, J. M. (1998) MIT Robot Pike Project [Web Page]. URL http://www.mit.edu/afs/athena/org/t/towtank/OldFiles/www/pike/index.html.

Kuwana, Y., Shimoyama, I., & Miura, H. (1995). Steering control of a mobile robot using insect antennae. IEEE International Conference on Intelligent Robots and Systems, 2: 530-535.

Lamb, J. R. (1987). Computer simulation of biological systems. Molecular and Cellular Biochemistry, 73:91-98.

Lambert, K., & Brittan, G. G. (1992). An introduction to the philosophy of science. 4th ed.. Atascadero, CA: Ridgview Publishing.

Lambrinos, D., Maris, M., Kobayashi, H., Labhart, T., Pfeifer, R., & Wehner, R. (1997). An autonomous agent navigating with a polarized light compass. Adaptive Behaviour, 6: 175-206.

Lambrinos, D., Moller, R., Labhart, T., Pfeifer, R., & Wehner, R. (2000). A mobile robot employing insect strategies for navigation. Robotics and Autonomous Systems, 30:39-64.

Langton, C. G. (1989). Artificial Life. Addison-Wesley.

Laudan, L. (1981). A confutation of convergent realism. Philosophy of Science, 48:218-249.

Leatherdale, W. H. (1974). The role of analogy, model and metaphor in science. Amsterdam: North Holland Publishing Co.

Leoni, F., Guerrini, M., Laschi, C., Taddeucci, D., Dario, P., & Staritao, A. (1998). Implementing robotic grasping tasks using a biological approach. Proceedings -IEEE International Conference on Robotics and Automation, 3: p 2274-2280.

Levins, R. (1993). A response to Orzack and Sober: formal analysis and the fluidity of science. Quarterly Review of Biology, 68:547-555.

Levins, R. (1966). The strategy of model building in population biology. American Scientist, 54:421-431.

Lewis, M. A., & Nelson, M. E. (1998). Look before you leap:peering behaviour for depth perception. in Pfeifer, R., Blumberg, B., Meyer, J. A., and Wilson, S. W. (editors)From animals to animats 5 (pp. 98-103). Cambridge, Mass.: MIT Press.

Lund, H. H., Webb, B., & Hallam, J. (1997). A robot attracted to the cricket species Gryllus Bimaculatus. P. Husbands, & I. Harvey (editors), Fourth European Conference on Artificial Life(pp. 246-255). Cambridge MA: MIT Press.

Lund, H. H., Webb, B., & Hallam, J. (1998). Physical and temporal scaling considerations in a robot model of cricket calling song preference. Artificial Life, 4:95-107.

Maki, D. P., & Thompson, M. (1973). Mathematical Models and Applications. Englewood Cliffs, NJ: Prentice-Hall.

Manna, Z., & Pnueli, A. (1991). On the faithfulness of formal models. Lecture Notes in Computer Science, 520:28-42.

Maris, M., & Mahowald, M. (1998). Neuromorphic sensory motor mobile robot controller with pre-attention mechanism. L. Smith, & A. Hamilton (editors), Neuromorphic Systems: Engineering Silicon from Neurobiology. London: World Scientific.

Marr, D. (1982). Vision. San Francisco: W.H. Freeman.

Mataric, M. J. (1998). Behavior-based robotics as a tool for synthesis of artificial behavior and analysis of natural behavior. Trends in Cognitive Sciences, 2:82-87.

Maynard Smith, J. (1974). Models in Ecology. Cambridge: Cambridge University Press.

Maynard Smith, J. (1988). Did Darwin get it Right? London: Penguin.

McGeer, T. (1990). Passive Walking with Knees. IEEE Conference on Robotics and Automation (pp. 1640-1645).

Mead, C. (1989). Analog VLSI and Neural Systems . Reading, Mass: Addison-Wesley.

Melhuish, C., Holland, O., & Hoddell, S. (1998). Collective sorting and segregation in robots with minimal sensing. in Pfeifer, R., Blumberg, B., Meyer, J. A., and Wilson, S. W. (editors)From animals to animats 5 Cambridge, Mass.: MIT Press.

Meyer, J. (1997). From natural to artificial life: biomimetric mechanisms in animat designs. Robotics and Autonomous Systems, 22: 3-21.

Miall, C. (1989). The diversity of neuronal properties. in R. Durbin, C. Miall, & G. Mitchison (editors), The computing neuron. Wokingham: Addison-Wesley.

Miklos, G. L. G. (1993). Molecules and cognition: the latterday lessons of levels, language and lac. Journal of Neurobiology, 24:842-890.

Milinski, M. (1991). Models are just protheses for our brains. Behavioral and Brain Sciences, 14.

Mojarrad, M., & Shahinpoor, M. (1997). Biomimetic robotic propulsion using polymeric artificial muscles. Proceedings - IEEE International Conference on Robotics and Automation, 3: 2152-2157.

Molenaar, I. M. (1994). Why do we need statistical models in the social and behavioural sciences. in M. A. Croon, & F. J. R. van de Vijver (editors), Viability of mathematical models in the social and behavioural science. Lisse: Swets and Zeitlinger.

Möller, R. (2000). Insect visual homing strategies in a robot with analog processing. Biological Cybernetics, 83:231-243.

Möller, R., Lambrinos, D., Pfeifer, R., Labhart, T., & Wehner, R. (1998). Modeling Ant Navigation with an autonomous agent. in Pfeifer, R., Blumberg, B., Meyer, J. A., and Wilson, S. W. (editors)From animals to animats 5 Cambridge, Mass.: MIT Press.

Morgan, M. S. (1997). The technology of analogical models: Irving Fisher's monetary worlds. Philosophy of Science , 64:S304-S314.

Morse, T. M., Ferree, T. C., & Lockery, S. R. (1998). Robust spatial navigation in a robot inspired by chemotaxis in Caenorrhabditis elegans. Adaptive Behaviour, 6: 393-410.

Mura, F., & Shimoyama, I. (1998). Visual guidance of a small mobile robot using active, biologically- inspired, eye movements. Proceedings - IEEE International Conference on Robotics and Automation, 3: p 1859-1864.

Nagel, E. (1961). The structure of science . London: Routledge & Kegan Paul.

Nelson, G. M., & Quinn, R. D. (1998). Posture control of a cockroach-like robot. Proceedings - IEEE International Conference on Robotics and Automation, 1: 157-162.

Onstad, D. W. (1988). Population-dynamics theory - the roles of analytical, simulation, and supercomputer models. Ecological Modelling, 43:111-124.

Oreskes, N., Shrader-Frechette, K., & Belitz, K. (1994). Verification, validation and confirmation of numerical models in the earth sciences. Science, 263:641-646.

Orzack, S. H., & Sober, E. (1993). A critical assessment of Levin's The strategy of model building in the social sciences (1966). Quarterly Review of Biology, 68:533-546.

Palladino, P. (1991). Defining ecology - ecological theories, mathematical-models, and applied biology in the 1960s and 1970s. Journal of the History of Biology, 24:223-243.

Palsson, B. O., & Lee, I. (1993). Model complexity has a significant effect on the numerical value and interpretation of metabolic sensitivity coefficients. Journal of Theoretical Biology, 161:299-315.

Patel, G. N., Holleman, J. H., & DeWeerth, S. P. (1998). Analog VLSI model of intersegmental coordination with nearest neighbour coupling. in M. I. Jordan, M. J. Kearns, & S. A. Solla (editors), Advances in Neural Information Processing Systems 10(pp. 719-726). Cambridge MA: MIT Press.

Pattee, H. H. (1989). Simulations, realizations and theories of life. in C. Langton (editor), Artificial Life. Redwood City, Cal: Addison-Wesley.

Peirce, G. J., & Ollanson, J. G. (1987). Eight reasons why optimal foraging theory is a complete waste of time. Oikos, 49:111-125.

Peremans, H., Walker, A., & Hallam, J. C. T. (1998). 3D object localization with a binaural sonar head - inspirations from biology. Proceedings - IEEE International Conference on Robotics and Automation, 2795-2800.

Pfeifer, R. (1996). Building "fungus eaters": design principles of autonomous agents. From animals to animats 4: Proceedings of the 4th International Conference on Simulation of Adaptive Behaviour, 3-11. Cambridge MA: MIT Press.

Pfeiffer, F., Etze, J., & Weidemann, H. (1995). Six-legged technical walking considering biological principles. Robotics and Autonomous Systems, 14: 223-232.

Pichon, J.-M., Blanes, C., & Franceschini, N. (1989). Visual guidance of a mobile robot equipped with a network of self-motion sensors. Wolfe, W. J. and Chun, W. H. (editors)Mobile Robots IV Philadelphia(pp. 44-53). Bellingham: Society of Photo-optical Instrumentation Engineers.

Pornsin-Sirirak, N., & Tai, Y.-C. (1999) Microbat [Web Page]. URL http://secretary.erc.caltech.edu/~tai/research/nick/.

Pratt, J., & Pratt, G. (1998a). Intuitive control of a planar biped walking robot. Proceedings - IEEE International Conference on Robotics and Automation, 2014-2021.

Pratt, J. E., & Pratt, G. A. (1998b). Exploiting natural dynamics in the control of a planar biped walking robot. Proceedings of the Thirty-sixth Annual Allerton Conference on Communication, Control and Computing.

Prescott, T. J., & Ibbotson, C. (1997). A robot trace-maker: modelling the fossil evidence of early invertebrate behaviour. Artificial Life, 3:289-306.

Putnam, H. (1975). Philosophical Papers vol. 1. Cambridge: Cambridge University Press.

Quinn, R. D., & Espenscheid, K. S. (1993). Control of a hexapod robot using a biologically inspired neural network. in R. D. Beer, R. E. Ritzmann, & T. McKenna (editors), Biological Neural Networks in Invertebrate Neuroethology and Robotics. London: Academic Press.

Quinn, R. D., & Ritzmann, R. E. (1998). Construction of a hexapod robot with cockroach kinematics benefits both robotics and biology. Connection Science, 10:239-254.

Raaijmakers, J. G. W. (1994). Mathematical models in memory research. in M. A. Croon, & F. J. R. van de Vijver (editors), Viability of mathematical models in the social and behavioural science. Lisse: Swets and Zeitlinger.

Raibert, M. H. (1986). Legged robots that balance. Cambridge, Mass: MIT Press.

Redhead, M. (1980). Models in Physics. British Journal for the Philosophy of Science, 31:145-163.

Reeke, G. N., & Sporns, O. (1993). Behaviourally based modeling and computational approaches to neuroscience. Annual Review of Neuroscience, 16:597-623.

Rexstad, E., & Innis, G. S. (1985). Model simplification - Three applications. Ecological Modelling, 27:1-13.

Ringle, M. (1979). Philosophy and A.I. in M. Ringle (editor), Philosophical Perspectives in Artificial Intelligence. Sussex: Harvester Press.

Robertson, M. (1989). Idiosyncratic motor units generating innate motor patterns: neurones and circuits in the locust flight system. in R. Durbin, C. Miall, & G. Mitchison (editors), The computing neuron. Wokingham: Addison-Wesley.

Rosenblueth, A., & Wiener, N. (1945). The role of models in science. Philosophy of Science, 12:316-321.

Rothenberg, J. (1989). The nature of modeling. in L. E. Widman, K. A. Loparo, & N. R. Nielson (editors), Artificial Intelligence, Simulation and Modelling. New York: John Wiley and sons.

Rucci, M., Edelman, G., & Wray, J. (1999). Adaptation of orienting behavior: from the barn owl to a robotic system. Ieee Transactions on Robotics and Automation, 15: p 96-110.

Russell, R. (1998). Odour sensing robot draws inspiration from the insect world. Lithgow, B. and Cosic, I. (editors)Proceedings of the 2nd International Conference on Bioelectromagnetism Melbourne, Australia(pp. 49-50). IEEE.

Rykiel, E. (1996). Testing ecological models: the meaning of validation. Ecological Modelling, 90:229-244.

Saito, F., & Fukuda, T. (1996). A first result of the brachiator III - a new brachiation robot modeled on a siamang. in Langton, C. and Shimohara, K. (editors)Proceedings of ALife V Cambridge MA: MIT Press.

Saksida, L. M., Raymond, S. M., & Touretzky, D. S. (1997). Shaping robot behavior using principles from instrumental conditioning. Robotics and Autonomous Systems, 22:231-249.

Salmon, W. C. (1996). Rationality and objectivity in science or Tom Kuhn meets Tom Bayes. reprinted in D. Papineau (editor), The Philosophy of Science. Oxford: Oxford University Press.

Scassellati, B. (1998). Imitation and mechanisms of joint attention: a developmental structure for building social skills on a humanoid robot. in C. Nehaniv (editor), Computation for Metaphors, Analogy and Agents: Springer Lecture Notes in Artificial Intelligence(Vol. 1562). Berlin: Springer-Verlag.

Schaal, S., & Sternad, D. (2001). Origins and violations of the 2/3 power law in rhythmic three-dimensional arm movements. Experimental Brain Research, 136:60-72.

Schall, J., & Hanes, D. (1998). Neural mechanisms of selection and control of visually guided eye movements. Neural Networks, 11: p 1241-1251.

Schenk, H. (1996). Modeling the effects of temperature on growth and persistence of tree species: a critical review of tree population models. Ecological Modelling, 92:1-32.

Schultz, R. L., & Sullivan, E. M. (1972). Developments in simulation in social and administrative science. in H. Guetzkow, P. Kotter, & R. L. Schultz (editors), Simulation in Social and Administrative Science. New Jersey: Prentice Hall.

Schwartz, E. L. (1990). Introduction. E. L. Schwartz (editor), Computational Neuroscience. Cambridge, Mass.: MIT Press.

Scutt, T., & Damper, R. (1997). Biologically-motivated learning in adaptive mobile robots. SMC '97 IEEE International Conference on Systems, Man and Cybernetics (pp. 475-480).

Segev, I. (1992). Single neuron models: oversimple, complex and reduced. Trends in Neurosciences, 15:414-421.

Sejnowski, T. J., Koch, C., & Churchland, P. S. (1988). Computational Neuroscience. Science, 241:1299-1305.

Selverston, A. I. (1993). Modeling of neuronal circuits: what have we learned? Annual Review of Neuroscience, 16:531-546.

Shannon, C. E. (1951). Presentation of a Maze-Solving Machine. in Foerster, V. (editor)Transactions of 8th Conference of the Josiah Macy Foundation .

Shannon, R. E. (1975). Systems Simulation: the art and science. Englewood Cliffs, NJ: Prentice Hall.

Sharkey, N. E., & Ziemke, T. (1998). Editorial: Biorobotics . Connection Science, 10:163-166.

Sharpe, T., & Webb, B. (1998). Simulated and situated models of chemical trail following in ants. Pfeifer, Rolf, Blumberg, Bruce, Meyer, Jean-Arcady, and Wilson, Stewart W.From Animals to Animats 5: Proceedings of the Fifth International Conference on the Simulation of Adaptive Behaviour Zurich(pp. 195-204). Cambridge, MA: MIT Press.

Shepherd, G. M. (1990). The significance of real neuron architectures for neural network simulations. in E. L. Schwartz (editor), Computational Neuroscience. Cambridge, Mass.: MIT Press.

Shibata, T., & Schaal, S. (1999). Robot gaze stabilisation based on mimesis of oculomotor dynamics and vestibulocerebellar learning. Advanced Robotics, 13:351-352.

Shimoyama, I., Bekey, G., & Asaad, S. (1996). Introduction - Special Issue from International Workshop on Biorobotics. Robotics and Autonomous Systems, 18:7-11.

Sporns, O. (forthcoming). The emergence of complex neuronal properties in an embodied model of the visual system. in T. Consi, & B. Webb (editors), Biorobotics. AAAI Press.

Spriet, J. A., & Vansteenkiste, G. C. (1982). Computer-aided modelling and simulation . London: Academic Press.

Srinivasan, M. V., Chahl, J. S., Weber, K., & Venkatesh, S. (1999). Robot navigation inspired by principles of insect vision. Robotics and Autonomous Systems , 26:203-216.

Srinivasan, M. V., & Venkatesh, S. (1997). From Living Eyes to Seeing Machines. Oxford: Oxford University Press.

Stogdill, R. M. (1970). Introduction: the student and model building. in R. M. Stogdill (editor), The process of Model Building in the Behavioral Sciences. Ohio: Ohio State University Press.

Suppe, F. (1977). The structure of scientific theories. Urbana: University of Illinois Press.

Taddeucci, D., & Dario, P. (1998a). Experiments in Synthetic psychology for tactile perception in robots: steps toward implementing humanoid robots. Proceedings - IEEE International Conference on Robotics and Automation, 2262-2267.

Takanobu, H., Yajima, T., Nakazawa, M., Takamishi, A., Ohtsuki, K., & Onishi, M. (1998b). Quantification of masticatory efficiency with a masticatory robot. Proceedings - IEEE International Conference on Robotics and Automation, 1635-1640.

Taylor, P. J. (1989). Revising models and generating theory. Oikos, 54:121-126.

Touretsky, D. S., & Saksida, L. M. (1997). Operant conditioning in Skinnerbots. Adaptive Behaviour, 5:219-247.

Triantafyllou, M. S., & Triantafyllou, G. S. (1995). An efficient swimming machine. Scientific American, 272:40-48.

Ulinski, P. S. (1999). Modeling Cortical Circuitry. in P. S. Ulinski, E. G. Jones, & A. Peters (editors), Cerebral Cortex(Vol. 13pp. 1-17). New York: Kluwer Academic.

Uttal, W. R. (1990). On some two-way barriers between models and mechanisms. Perception and Psychophysics, 48:188-203.

Van Fraassen, B. C. (1980). The scientific image. Oxford: Clarendon Press.

Verschure, P. F. M. J. (1996). Connectionist Explanation: taking positions in the Mind-Brain dilemma. In G. Dorfner (editor), Neural Networks and a New AI(pp. 133-188). London: Thompson.

Voegtlin, T., & Verschure, P. F. M. J. (1999). What can robots tell us about brains? A synthetic approach towards the study of learning and problem solving. Reviews in the Neurosciences, 10:291-310.

Vogel, S. (1999). Cat's paws and catapults. London: Penguin Books.

Walker, I. D. (1995). A successful multifingered hand design - the case of the racoon. IEEE/RSJ International Conference on Intelligent Robots and Systems, 186-193. Los Alamitos, Calif.: IEEE Computer Society Press.

Walter, W. G. (1961). The Living Brain. Harmondsworth, Middlesex: Penguin Books.

Wartofsky, M. W. (1979). Models: representation and the scientific understanding. Dordrecht: D.Reidel.

Webb, B. (1995). Using robots to model animals: a cricket test. Robotics and Autonomous Systems, 16: 117-134.

Webb, B. (1991). Do computer simulations really cognize? Journal of Experimental and Theoretical Artificial Intelligence, 3:247-254.

Webb, B. (1994). Robotic Experiments in Cricket Phonotaxis. Cliff, David, Husbands, Philip, Meyer, Jean-Arcady, and Wilson, Stewart W.From Animals to Animats 3: Proceedings of the Third International Conference on the Simulation of Adaptive Behaviour Brighton(pp. 45-54). Cambridge, MA: MIT Press.

Webb, B., & Scutt, T. (2000). A simple latency dependent spiking neuron model of cricket phonotaxis. Biological Cybernetics, 82:247-269.

Wehner, R. (1987). Matched filters - neural models of the external world. Journal of Comparative Physiology A, 161:511-531.

Wehner, R. (1994). The polarization-vision project: championing organismic biology. in K. Schildberger, & N. Elsner (editors), Neural Basis of Behavioural Adaptations(pp. 103-143). Stuttgart: Gustav Fischer Verlag.

Weiner, J. (1995). On the practice of ecology. Journal of Ecology, 83:153-158.

Weitzenfeld, J. S. (1984). Valid reasoning by analogy. Philosophy of Science, 51:137-149.

Widman, L. E., & Loparo, K. A. (1989). A critical survey. L. E. Widman, K. A. Loparo, & N. R. Nielson (editors), Artificial Intelligence, Simulation and Modelling. New York: John Wiley and sons.

Wiener, N. (1948). Cybernetics. Cambridge MA: MIT Press.

Williamson, M. W. (1998). Rhythmic robot arm control using oscillators. 1998 IEEE/RSJ International Conference on Intelligent Robots and Systems, 77-83. Los Alamitos, Calif.: IEEE Computer Society Press.

Wilson, H. R. (1999). Non-fourier cortical processes in texture, form and motion perception. in P. S. Ulinski, E. G. Jones, & A. Peters (editors), Cerebral Cortex(Vol. 13pp. 445-477). New York: Kluwer Academic.

Yamaguchi, H. (1998). A cooperative hunting behaviour by mobile robot troops. in Proceedings of the IEEE Conference on Robotics and Automation (pp. 3204-3209).

Young, J. F. (1969). Cybernetics. London: Iliffe Books Ltd.

Zalzala, A. M. S., & Morris, A. S. (editors). (1996). Neural networks for robotic control: Theory and Applications. London: Ellis Horwood.

Zeigler, B. P. (1976). Theory of Modelling and Simulation. New York: John Wiley.