The Reaction Mass Biped: Equations of motion, hybrid model for walking and trajectory tracking control

Pendulum models have been studied as benchmark problems for development of nonlinear control schemes, as well as reduced-order models for the dynamics analysis of locomotion of humanoid robots. This work provides a generalization of the previously introduced Reaction Mass Pendulum (RMP), which is a multibody inverted pendulum model, to a bipedal model that can better model bipedal locomotion. The RMP consists of an extensible 'leg' and a 'body' with moving proof masses that give rise to a variable rotational inertia. The Reaction Mass Biped (RMB) introduced here has two legs, one of which takes the role of a stance leg and the other performs as a swing leg during bipedal locomotion. The bipedal walking dynamics model of the RMB is therefore hybrid, with the roles of stance leg and swing leg interchanged after each cycle. The dynamics model is developed using a variational mechanics approach, without using generalized coordinates for the rotational degrees of freedom. This dynamics model has thirteen degrees of freedom, all of which are considered to be actuated in the control design. A set of desired state trajectories that can enable bipedal walking in straight and curved lines are generated. A control scheme is then designed for asymptotically stable tracking of this set of trajectories with an almost global domain of attraction. Numerical simulation results confirm the stability of this tracking control scheme for different walking trajectories of the RMB.