Weighted Barrier Functions for Computation of Force Distributions with Friction Cone Constraints

We present a novel Weighted Barrier Function (WBF) method of efficiently computing optimal grasping force distributions for multifingered hands. Second-order conic friction constraints are not linearized, as in many previous works. The force distributions are smooth and rapidly computable, and they enable flexibility in selecting between firm, stable grasps or looser, more efficient grasps. Furthermore, fingers can be disengaged and re-engaged in a smooth manner, which is a critical capability for a large number of manipulation tasks. We present efficient solution methods that do not incur the increased computational complexity associated with solving the Semi-Definite Programming formulations presented in previous works. We present results from static and dynamic simulations which demonstrate the flexibility and computational efficiency associated with WBF force distributions.