Efficient algorithms for optimal force distribution in multiple-chain robotic systems

Abstract

A two-level hierarchical control scheme is proposed to solve the large-scale control problem for multiple-chain robotic systems forming simple closed-kinematic loops. These robotic systems include dexterous hands, multiple manipulators, and multilegged vehicles. The upper-level coordinator collects all the necessary information and solves the inter-chain coordination problem which is, in fact, the force distribution problem. The corresponding constrained, optimal solutions (which are the set-points of chain contact forces and input joint torques) decouple this large-scale system into m lower-level subsystems. Then, m local controllers may be assigned to solve the associated chain force and motion control problems in parallel. This dissertation concentrates on developing a general and efficient optimal algorithm which may solve the force distribution problem in real time. To begin with, the governing equations for force distribution are derived. This general dynamic formulation is applicable to all three types of systems considered through some changes in parameters. A computationally efficient optimal algorithm called the Compact-Dual LP (Linear Programming) method for solving the force distribution problem is, then, devised. 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. Also, 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 the Compact-Dual LP method is demonstrated by solving the force distribution problem of a grasping system under development at OSU called DIGITS. With 2 fingers grasping an object and hard point contact considered, the CPU time on a VAX-11/785 computer is only 1.47 ms. If 4 fingers are considered, a combined objective function for minimum effort, load balance, and temporal continuity is applied, and a linear programming package in the IMSL library is utilized, then the CPU time is 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.