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This paper presents a standing balance controller that explicitly handles pushes. We employ a library of optimal trajectories and the neighboring optimal control method to generate local approximations to the optimal control. We take advantage of a parametric nonlinear optimization method, SNOPT, to generate initial trajectories and then use Differential Dynamic Programming (DDP) to further refine them and get their neighboring optimal control. A library generation method is proposed, which keeps the trajectory library to a reasonable size. We compare the proposed controller with an optimal controller and an LQR based gain scheduling controller using the same optimization criterion. Simulation results demonstrate the performance of the proposed method.