Hybrid Dynamical System Methods for Legged Robot Locomotion with Variable Ground Contact

Abstract

This thesis investigates the variable contact situations of rigid robot feet in legged robot locomotion. One major goal is to include the rotation around foot edges in locomotion cycles. For walking robots they are referred to as the toe roll phase and the heel roll phase. The alternation between underactuated motion phases and completely actuated motion phases is believed to contribute in a decisive manner in enabling dynamic locomotion. Dynamic locomotion comprises e.g. walking, running, hopping, standing up, and many more motion patterns characterized by variable contact with the environment. A control-theoretic approach to legged robot locomotion is presented that uses an event-based hybrid (discrete-continuous) model with underlying rigid-body assumption. Events occur whenever the ground contact situation changes; this is either when a contact resolves or when a contact is established. The continuous time dynamics that is generally different for all contact situations is allowed to switch at these contact changes. Then discontinuous collision behavior is taken into account. To obtain periodic locomotion cycles, a trajectory planning algorithm is proposed where the boundary value problem is solved that relates the initial and final configuration of the robot. The resulting periodic robot locomotion is investigated for orbital stability using Poincare map analysis of the hybrid trajectories. Finally, a hybrid control strategy is presented for balance control which makes use of the invariance control method. Throughout this thesis, the methods are demonstrated for three example robots: a compass gait robot, a monoped robot, and a gymnast robot.