  This study presents a theoretical method for planning and controlling agile
bipedal locomotion based on robustly tracking a set of non-periodic keyframe
states. Based on centroidal momentum dynamics, we formulate a hybrid
phase-space planning and control method which includes the following key
components: (i) a step transition solver that enables dynamically tracking
non-periodic keyframe states over various types of terrains, (ii) a robust
hybrid automaton to effectively formulate planning and control algorithms,
(iii) a steering direction model to control the robot's heading, (iv) a
phase-space metric to measure distance to the planned locomotion manifolds, and
(v) a hybrid control method based on the previous distance metric to produce
robust dynamic locomotion under external disturbances. Compared to other
locomotion methodologies, we have a large focus on non-periodic gait generation
and robustness metrics to deal with disturbances. Such focus enables the
proposed control method to robustly track non-periodic keyframe states over
various challenging terrains and under external disturbances as illustrated
through several simulations.
