Balance Stabilization with Angular Momentum Damping Derived from the Reaction Null-Space

Abstract

A balance stabilizer is proposed that has the capability of absorbing high-energy collisions without reactive stepping. The stabilizer is based on the spatial dynamics formulation and has the unique feature that the trunk rotation can be specified in an independent way from the desired rate of change of the system (centroidal) angular momentum. The formulation is based on the momentum equilibrium principle for floating-base robots and the relativity of angular momentum revealed in the companion paper [1]. The stabilizer injects angular momentum damping via the so-called relative angular acceleration (RAA) derived from the reaction null-space (RNS) of the system. The damping is used to increase the robustness of the balance stabilizer at critical states such as foot roll. It is shown how to embed the RAA stabilizer into a joint-torque controller whereby the motion and force optimization tasks are solved in a single step, yielding a formulation that does not rely upon a general solver. The performance of the controller is examined via simulations whereby external impact-type disturbances are applied to the robot. One part of the impact energy is accommodated via the trunk rotations by lowering the respective PD feedback gains immediately after impact onset. It is then dissipated with higher gains, while recovering the stability of the posture. Another part of the impact energy yields foot roll; this part is dissipated with the angular momentum damping realized through an appropriate arm motion. When in a single stance, the angular momentum damping control yields a movement in the swing leg in addition to that in the arms. The motion in the leg injects additional angular momentum damping, such that a high-energy impact can be accommodated that would otherwise require a reactive stepping.