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 under development at OSU called Digits. Moreover, 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.
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