Motion planning of extreme locomotion maneuvers using multi-contact dynamics and numerical integration

Although the problem of maneuvering in extreme terrains has critical weight on the advancement of legged robots and medical assistive devices, little progress has been made on exploring practical solutions to operate in these environments. Here, we report that multi-contact models and perturbation theory, a set of approximation schemes that has roots in celestial mechanics and non-linear dynamical systems, can be adapted to solve non closed-form integrable state-space trajectories of a robot's center of mass, given its arbitrary contact state and center of mass (CoM) path. In this paper we explore a case study of an extreme maneuver involving gap leaping given a support point against a wall board to ascend steps on a ladder. To tackle this problem, we first leverage our previous work on multi-contact dynamics to derive reaction force behavior from inertial movement and internal tension behavior. We then study the nonlinear dynamics of single contact phases along arbitrary paths and leverage perturbation theory to derive state space equations of center of mass behavior. Using this theoretical framework, we consider synthesizing extreme maneuvers in the terrain by means of a motion planner. We derive kinematic trajectories that fulfill dynamic constraints, such as the center of mass' angle of attack. We then use numerical integration to solve the natural dynamics of the robot along the planned path. We leverage our derivations on multi-contact dynamics to search the space of feasible movements and internal tension behaviors during multi-contact. Finally, we propose a new strategy to determine step transitions during jumping and landing maneuvers. Our main contributions are on, (1) developing a methodology to use the multi-contact/grasp matrix and numerical integration to derive state space trajectories of extreme maneuvers, and (2) developing a motion planner that can determine contact transitions to negotiate the terrain.