In this article a hybrid discrete-continuous modeling and control approach to legged mechatronic systems with variable environment contacts such as passive tilting (rotation) about edges is proposed. This approach has important applications in humanoid robot walking, robot jogging, and other areas. An abstracted class of mechatronic systems much simpler, but still related to humanoid robots is considered. Trajectory planning, based on the solution of a hybrid boundary value problem is discussed and the computed periodic trajectories are examined with respect to orbital stability.
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