Mechanisms interacting with their environments that possess complete contact force controllability such as multifingered hands and walking vehicles are considered in this article. In these systems, the redundancy in actuation can be used to optimize the force distribution characteristics. The resulting optimization problems can be highly nonlinear. Here, the redundancy in actuation is characterized using geometric reasoning which leads to simplifications in the formulation of the optimization 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 algorithms developed here are not suited for real-time implementation. However, these algorithms can be used in off-line force planning, and they can be used to develop look-up tables for certain applications. The outputs of these algorithms can also be used as a baseline to evaluate the effectiveness of sub-optimal schemes.

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