GEOMETRIC OPTIMIZATION ALGORITHMS FOR ROBOT KINEMATIC DESIGN

This article addresses the problem of designing a robotic mechanism su ch that its end-effector frame comes closest to reaching a set of desi red goal frames. We formulate this as an optimization problem, in whic h the kinematic parameters are selected to minimize the total distance between the end-effector frame and each goal frame. The objective fun ction is defined in terms of a class of distance metrics on the rigid body motions that are invariant with respect to choice of fixed refere nce frame. A main contribution of this article is an explicit expressi on for the gradient of this objective function with respect to the kin ematic parameters. With this analytic gradient, efficient optimization algorithms can now be developed for the design of general spatial mec hanisms. Our design methodology is illustrated with an example involvi ng the base positioning of two cooperating robots. (C) 1995 John Wiley & Sons, Inc.