Numerical Constraint Evaluation

Many numerical values are associated with hypotheses. The most important of these are the property values described in Chapter 6, but there could also be other values such as the object position or joint angles. Constraints can be specified on these values and they must hold for the verification to succeed.

The constraints were mainly used for eliminating spurious SURFACE hypotheses and usually tested absolute surface area.

The constraints are specified as part of the model definition process, as a set of statements of the form:

	CONSTRAINT$<name>$ $<constraint>$
The $<constraint>$ must apply in the context of structure $<name>$.
Here:
	$<constraint>$	::= $<pconstraint>$
		$\mid <constraint>$ AND $<constraint>$
		$\mid <constraint>$ OR $<constraint>$
		$\mid$($<constraint>$)
	$<pconstraint>$ ::= $<value> <relation> <number>$
	$<relation>$ ::= $< \mid > \mid = \mid <= \mid >= \mid$ !=
	$<value>$ ::= $<variable> \mid <property>$($<name>$)

The $<value>$ refers to a variable or a property (possibly of a substructure) in the context of the structure being constrained. Other constraint expressions could have been easily added. The verification of these constraints is trivial.

An example of such a constraint for the elbow joint angle jnt3 in the robot armasm ASSEMBLY is:

$$\vbox{ CONSTRAINT armasm (jnt3 $<$ 2.5) OR (jnt3 $>$ 3.78); }$$

which constrains the joint angle to 0.0 - 2.5 or 3.78 - 6.28. Another constraint is:

$$\vbox{ CONSTRAINT uside ABSSIZE(uside) $<$ 1900.0 }$$

which constrains the absolute surface area of uside to be less than 1900 square centimeters. The choice of the verification bounds is up to the modeler.