GLOBALLY OPTIMAL FORCE ALLOCATION IN ACTIVE MECHANISMS WITH 4 FRICTIONAL CONTACTS

Mechanisms interacting with their environments that possess complete c ontact force controllability such as multifingered hands and walking v ehicles(2) are considered in this article. In these systems, the redun dancy in actuation can be used to optimize the force distribution char acteristics. The resulting optimization problems can be highly nonline ar. Here, the redundancy in actuation is characterized using geometric reasoning which leads to simplifications in the formulation of the op timization problems. Next, advanced polynomial continuation techniques are adapted to solve for the global optimum of an important nonlinear optimization problem for the case of four frictional contacts. The al gorithms developed here are not suited for real-time implementation. H owever these algorithms can be used in off-line force planning, and th ey can be used to develop look-up tables for certain applications. The outputs of these algorithms can also be used as a baseline to evaluat e the effectiveness of sub-optimal schemes.