PERFORMANCE-MEASURES FOR CONSTRAINED SYSTEMS

We present a geometric theory of the performance of robot manipulators , applicable to systems with constraints, which may be nonholonomic. T he performance is quantified by a geometrical object, the induced metr ic tensor, from which scalars may be constructed by invariant tensor o perations to give performance measures. The measures thus defined depe nd on the metric structure of configuration and workspace, which shoul d be chosen appropriately for the problem at hand. The generality of t his approach allows us to specify a system of joint connected rigid bo dies 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 th e performance measures for such systems. We illustrate these ideas wit h some computations of measures for the SARCOS dextrous arm, and the P latonic Beast, a multilegged walking machine.