This paper addresses the problem of the appropriate distribution of forces between the legs of a legged locomotion system for walking on uneven terrain. The legs of the walking machine and the terrain form closed kinematic chains. The system is statically indeterminate and an optimal solution is desired for force control of the legs. In addition, as unisense force limitations are imposed on the wrenches acting at the feet, it is important to be able to determine for any given configuration whether or not a set of valid contact forces can be found which will ensure the stability of the vehicle. Fast and efficient algorithms to solve these problems have been developed. The trade-off between computational simplicity and optimality makes it necessary to resort to suboptimal algorithms. In particular, schemes based on the Moore-Penrose Generalized Inverse, or the pseudo inverse, and linear programming were investigated. An active compliance control scheme with varying leg compliances is shown to be a suitable paradigm for control. A variation of the linear programming technique, that is well-suited to the problem of predicting instability in the vehicle, is also presented.

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