A Gait Optimization Smoothing Penalty Function Method for Bipedal Robot via DMOC**The authors would like to thank National High Technology Research and Development Program of China(863 Program), grant No.2006AA04Z251, and The National Natural Fund Project, grant No.60974067 and The Founds of Jilin Province Science and Technology, grant No.2013577, 2013267, 2013287, 2014636.

Abstract

For periodic gait optimization problem of bipedal walking robot, based on discrete mechanics and optimal control (DMOC), a class of smoothing penalty function method is proposed. The optimal control strategy and trajectory are solved by a new smoothing exact penalty function algorithm. The algorithm can quickly converge to a stable gait cycle independent the selection of the initial gait, otherwise, the algorithm only needs one step correction and then generate a stable gait cycle. Numerical simulation results show that the algorithm is feasible and effective. The algorithm makes the bipedal robot walk efficiently and stably on the even terrain.