Performance Measures for Constrained Systems

We present a geometric theory of the performance of robot manipulators, applicable to systems with constraints, which may be non-holonomic. The performance is quantified by a geometrical object, the induced metric tensor, from which scalars may be constructed by invariant tensor operations to give performance measures. The measures thus defined depend on the metric structure of configuration and work space, which should be chosen appropriately for the problem at hand. The generality of this approach allows us to specify a system of joint connected rigid bodies with a large class of metrics. We describe how the induced metric can be computed for such a system of joint connected rigid bodies and describe a MATLAB program that allows the automatic computation of the performance measures for such systems. We illustrate these ideas with some computations of measures for the SARCOS dextrous arm, and the Platonic Beast, a multi-legged walking machine.