Optimal trajectory design for parametric excitation walking

Parametric excitation walking is one of methods that realize a passive dynamic like walking on the level ground. In parametric excitation walking, up-and-down motion of the center of mass restores mechanical energy and sustainable gait is generated. Walking ability and walking performance strongly depend on the reference trajectory of the center of mass. In this paper, we propose an optimization method for the reference trajectory of parametric excitation walking. There are two problems for optimization. One is that search space of a reference trajectory is inherently infinite dimensional. Another is that it takes long simulation time to generate steady gait for a given reference trajectory. Therefore, the proposing optimization method adopts the following strategy. For the former, we confine the reference trajectory to the quartic spline curve and take the parameter of spline curve as decision variables. For the latter, we discretize the search space and adopt a local search method usually used in combinational optimization problems. We apply the proposed method to a kneed biped robot, and optimize the reference trajectory of its swing leg.