Characteristics and approximations of optimal force distributions in walking machines on rough terrain

The force distribution problem for legged vehicles on rough terrain is considered. A general formulation of the force distribution problem, In which the feet contact the ground at arbitrary inclinations is presented. Three techniques are used to solve the force distribution problem for two representative tasks. The Moore-Penrose pseudo-inverse, a general numerical optimization scheme and an approximation to the optimal solution are described. The optimal scheme computes the forces which minimize the maximum ratio of tangential foot reaction force to foot normal force. The approximation is used to achieve certain desirable characteristics of the optimal scheme with considerably less computational complexity.<>