A three dimensional foot placement planner for locomotion in very rough terrains

Maneuvering through 3D structures nimbly is pivotal to the advancement of legged locomotion. However, few methods have been developed that can generate 3D gaits in those terrains and fewer if none can be generalized to control dynamic maneuvers. In this study, foot placement planning for dynamic locomotion traversing irregular terrains is explored in three dimensional space. Given boundary values of the center of mass´ apexes during the gait, sagittal and lateral phase-plane trajectories are predicted based on multi-contact and inverted pendulum dynamics. To deal with the nonlinear dynamics of the contact motions and their dimensionality, we plan a geometric surface of motion beforehand and rely on numerical integration to solve the models. In particular, we combine multi-contact and prismatic inverted pendulum models to resolve feet transitions between steps, allowing to produce trajectory patterns similar to those observed in human locomotion. Our contributions lay in the following points: (1) the introduction of non planar surfaces to characterize the center of mass´ geometric behavior; (2) an automatic gait planner that simultaneously resolves sagittal and lateral feet placements; (3) the introduction of multi-contact dynamics to smoothly transition between steps in the rough terrains.