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Control of the force distribution in locomotion and manipulation systems containing closed kinematic chains is an important problem since many tasks such as walking or grasping depend upon it. The basic problem is to solve for the input joint torques for a particular system trajectory and is usually underspecified. As such, linear programming has been used to obtain a solution which optimizes a weighted combination of energy consumption and load balancings. Inequality constraints on the maximum actuator torques and reaction forces at the tip of each chain of the system are imposed, in addition to equality constraints which specify movement in a desired system trajectory. An example is given in which the joint torques to drive a hexapod locomotion vehicle in a tripod gait are computed.
Orin et al. (Mon,) studied this question.