Efficient Algorithm for Optimal Force Distribution—The Compact-Dual LP Method

The force distribution problem in a dexterous hand, multiple manipulator system, or a multilegged robot is to solve for the input joint torques and chain contact forces for a particular system task. It is usually underspecified, and an optimal solution may be obtained. This paper presents an efficient algorithm, the Compact-Dual Linear Programming (LP) method, to solve the force distribution problem. In this method, the general solution of the linear equality constraints is obtained by transforming the underspecified matrix into row-reduced echelon form; then, the linear equality constraints of the force distribution problem are eliminated. In addition, the duality theory of linear programming is applied. The resulting method is applicable to a wide range of systems, constraints (e.g., friction constraints, maximum joint torque constraints, etc.), and objective functions and yet is computationally efficient. The significance of this method is demonstrated by solving the force distribution problem of a grasping system under development at Ohio State called DIGITS. With two fingers grasping an object and hard point contact with friction considered, the CPU time on a VAX-11/785 computer is only 1.47 ms. If four fingers are considered and a linear programming package in the IMSL library is utilized, the CPU time is then less than 45 ms. Therefore, it is believed that the general force distribution problem may be solved by the Compact-Dual LP method in real time.