Phase space planning and optimization of foot placements in rough planar terrains

Operating and maneuvering in difficult terrains has remained a challenging problem in the field of legged robots. One of the major challenges arises from the high dimensionality inherent in planning foot placements coupled with center of mass motion along terrains that are multifaceted and highly diverse. Previous work has resolved these issues to an extent by constraining the center of mass to fixed trajectories or using predetermined foot placements. To deal with these challenges, this paper proposes a new set of strategies: (1) an optimized geometric Hermite curve with minimum curvature and length is used to plan the motion of the center of mass (2) single contact model dynamics for state-space approximations of center of mass behavior are used to resolve feet transitions between steps in planar environments and (3) vertical center of mass phase space trajectories are optimized to produce an overall plan with minimum energy. This framework allows us to synthesize complex maneuvers in rough terrains and to develop optimal contact transition and foot placement plans that consider the robot´s configuration and constraints. Experimental results show that for any potential locations of foot contacts, our planner generates smooth and optimal trajectories for center of mass motion as well as a minimum energy plan for transitioning between foot placements.