Optimal force distribution in multiple-chain robotic systems

The force-distribution problem in multiple-chain robotic systems is to solve for the setpoints of the chain contact forces and input joint torques for a particular system task. It is usually underspecified, and an optimal solution may be obtained. The generality of the compact-dual linear programming (LP) method that can accept a variety of linear objective functions for different applications over a wide range of multiple-chain systems (multilegged vehicles, dexterous hands, and multiple manipulators) is demonstrated; and the solutions for several common problems of force distribution including slippage avoidance, minimum effort, load balance, and temporal continuity are proposed. This is illustrated by solving the force-distribution problem of a grasping system being developed called Digits. Efficiency considerations and elimination of redundant constraints are also discussed. With four fingers grasping an object, considering a conservative friction coefficient (for safety margins on friction constraints) and using a combined objective function for achieving the goals of minimum effort, load balance, and temporal continuity, the CPU time on a VAX-11/785 computer is less than 45 ms (using a linear programming package in the IMSL library). Therefore, it is believed that rather general use of the compact-dual LP method may be made to define a suitable objective function for a particular application and to solve the corresponding force-distribution problem in real time