The Reaction Mass Biped: Geometric Mechanics and Control

Inverted Pendulum based reduced order models offer many valuable insights into the much harder problem of bipedal locomotion. While they help in understanding leg behavior during walking, they fail to capture the natural balancing ability of humans that stems from the variable rotational inertia on the torso. In an attempt to overcome this limitation, the proposed work introduces a Reaction Mass Biped (RMB). It is a generalization of the previously introduced Reaction Mass Pendulum (RMP), which is a multi-body inverted pendulum model with an extensible leg and a variable rotational inertia torso. The dynamical model for the RMB is hybrid in nature, with the roles of stance leg and swing leg switching after each cycle. It is derived using a variational mechanics approach, and is therefore coordinate-free. The RMB model has thirteen degrees of freedom, all of which are considered to be actuated. A set of desired state trajectories that can enable bipedal walking in straight and curved paths are generated. A control scheme is then designed for asymptotically tracking 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 paths of the RMB. Additionally, a discrete dynamical model is also provided along-with an appropriate Geometric Variational Integrator (GVI). In contrast to non-variational integrators, GVIs can better preserve energy terms for conservative mechanical systems and stability properties (achieved through energy-like lyapunov functions) for actuated systems.