Prediction and Planning Methods of Bipedal Dynamic Locomotion Over Very Rough Terrains

Although the problem of dynamic locomotion in very rough terrain is critical to the advancement of various areas in robotics and health devices, little progress has been made on generalizing gait behavior with arbitrary paths. Here, we report that perturbation theory, a set of approximation schemes that has roots in celestial mechanics and non-linear dynamical systems, can be adapted to predict the behavior of non closed-form integrable state-space trajectories of a robot’s center of mass, given its arbitrary contact state and center of mass (CoM) geometric path. Given an arbitrary geometric path of the CoM and known step locations, we use perturbation theory to determine phase curves of CoM behavior. We determine step transitions as the points of intersection between adjacent phase curves. To discover intersection points, we fit polynomials to the phase curves of neighboring steps and solve their differential roots. The resulting multi-step phase diagram is the locomotion plan suited to drive the behavior of a robot or device maneuvering in the rough terrain. We provide two main contributions to legged locomotion: (1) predicting CoM state-space behavior for arbitrary paths by means of numerical integration, and (2) finding step transitions by locating common intersection points between neighboring phase curves. Because these points are continuous in phase they correspond to the desired contact switching policy. We validate our results on a human-size avatar navigating in a very rough environment and compare its behavior to a human subject maneuvering through the same terrain.