Quadratic optimization of force distribution in walking machines

Energy efficiency remains a problem in walking machines. One approach to improving energy efficiency involves solving for an optimal set of foot forces which minimizes the power supplied to DC motor actuators at each instant. Energy regenerated by the motors, which may be significant, is generally lost and should be explicitly taken into account to produce the optimal force distribution. A method to produce this optimal solution using quadratic programming is developed in this paper. The results are compared to three suboptimal quadratic programming approaches which minimize internal forces, a weighted norm of joint torques, and finally power without accounting for regeneration, all on a simulated hexapod. It is found that the common approach of minimizing internal forces may often result in poor energy efficiency.