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This study presents a theoretical framework for planning and controllingagile bipedal locomotion based on robustly tracking a set of non-periodic apexstates. Based on the prismatic inverted pendulum model, we formulate a hybridphase-space planning and control framework which includes the following keycomponents: (1) a step transition solver that enables dynamically trackingnon-periodic apex or keyframe states over various types of terrains, (2) arobust hybrid automaton to effectively formulate planning and controlalgorithms, (3) a phase-space metric to measure distance to the plannedlocomotion manifolds, and (4) a hybrid control method based on the previousdistance metric to produce robust dynamic locomotion under externaldisturbances. Compared to other locomotion frameworks, we have a larger focuson non-periodic gait generation and robustness metrics to deal withdisturbances. Such focus enables the proposed control framework to robustlytrack non-periodic apex states over various challenging terrains and underexternal disturbances as illustrated through several simulations. Additionally,it allows a bipedal robot to perform non-periodic bouncing maneuvers overdisjointed terrains.

A Framework for Planning and Controlling Non-Periodic Bipedal Locomotion