Optimal force distribution of multiple cooperating robots using nonlinear programming dual method

Abstract

An optimal force distribution scheme of multiple cooperating robots is proposed. General formulations of the optimal force distribution problem are built into quadratic programming with linear equality and quadratic inequality constraints. The quadratic constraints are due to the norm constraints of grasping forces and the approximation of maximum joint torque constraints which is used for simplification of the problem. This paper presents a technique for solving these general optimal force distribution problems. The original problem is transformed into a compact problem by eliminating the linear equality constraints. Then, the compact problem is transformed into a dual problem to be solved by using Lagrange multipliers and nonlinear programming dual method. This technique reduces the problem size considerably and makes the problem almost unconstrained so that no initial feasible points are needed. These features exhibit the efficiency of this technique. Simulation results for two cooperating PUMA robots indicating the ability of real time applications of the proposed technique are presented.