Efficient algorithm for optimal force distribution in multiple-chain robotic systems - the compact-dual LP method

The authors present a general and efficient algorithm, the compact-dual LP (linear programming) method, to solve the force distribution problem for multiple-chain robotic systems. 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. The duality theory of linear programming is also applied. The resulting method is applicable to a wide range of systems, constraints (friction constraints, 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 for a grasping system. With two-finger grasping and object and hard point contact with friction considered, the CPU (central processing unit) time on a VAX-11/785 computer is only 1.47 ms. If four fingers are considered, then the CPU time is less than 45 ms, which should be suitable for real-time application.