A mixed-integer convex optimization framework for robust multilegged robot locomotion planning over challenging terrain

This paper introduces an optimization-based framework for robust multilegged walking motion planning. Previous approaches use fixed gait sequences, and rely on Zero Moment Point (ZMP) to guarantee dynamic stability. While this combination works well on flat ground, it does not generalize to uneven terrain requiring aggressive gait or gait transition. To overcome such difficulties, in this paper, we present an optimization framework, that can plan both the contact location and gait sequence simultaneously in a mixed-integer convex optimization program. Moreover, we rely on the Contact Wrench Cone (CWC) stability criterion, which generalizes the ZMP criterion to uneven terrain with friction cone constraints, and we plan the walking motion together with the angular momentum through a convex optimization program. Our approach is successfully tested on a LittleDog quadruped over simulated scenarios. We show that on the flat ground, our planner generates a periodic gait, same as Central Pattern Generator + ZMP planner; while on uneven terrain, our planner can successfully generate a motion containing different gaits, with a center-of-mass motion that respects the friction cone constraints, which are violated by ZMP planners. This improvement clearly demonstrates the advantage of our approach over traditional planning strategies.