The reaction wheel stabilizer (RWS) concept for bipedal stabilization consists of a wheel that can be accelerated in order to impart a reaction torque on the rest of the biped. The beneficial effects of such a device (or emulation of such a device through limb motion) on transient body motions are not well understood. This work quantifies this phenomenon by comparing optimal trajectories for robots with and without an RWS in terms of energy efficiency and dynamic feasibility when attempting to execute speed transitions and disturbance response motions. Robots with RWS systems are able to more efficiently execute abrupt speed transitions, showing up to a 60% improvement in efficiency for single step transitions. In responding to forward push disturbances, the RWS improves efficiency by between 20 and 60% over the range of tested disturbances. These savings are significantly larger than those shown previously for periodic walking.

Reaction wheel systems (RWSs) are beneficial in improving bipedal walking stability, and theoretical work has shown that they can also improve the efficiency of preplanned walking motions. This work provides the first demonstration of RWS-related efficiency improvements on a physical robot and identifies the energy-saving paradigm. Gaits for a five-link planar biped are generated via trajectory optimization with and without reaction wheels. Comparisons of the resulting system behavior show a 5-10% efficiency advantage for robots with an RWS under typical walking conditions and a larger advantage near regions of marginal dynamic feasibility. The savings are mainly accomplished by enabling trajectories with better joint motor utilization, not by minimizing impact losses or acting as a kinetic energy recovery system. The RWS also improves centroidal angular momentum regulation, with the reduction in centroidal angular momentum amplitude reaching 30% at high speeds. Simulations and experiments with a five-link planar biped validate the efficiency improvements seen in optimization. This demonstrates the viability of using efficient inertial actuators to improve the efficiency of complex walking robots.

Inertial actuators, such as reaction wheels, have the potential to improve the stability and robustness of bipedal robots. While the stabilizing capabilities of reaction wheels follow naturally from physical laws, the effects on walking efficiency are less clear. This work examines those effects by comparing energy-optimal periodic gaits for a variety of under-actuated, five-link planar biped configurations. When energy consumption is normalized by total mass, bipeds equipped with reaction wheels have decreased walking cost compared to unequipped bipeds of the same mass across a wide range of conditions. At speeds equal to or higher than the optimal walking speed, reaction wheels can reduce walking cost by approximately 8%. When walking with large step lengths, reaction wheels decrease walking costs by more than 20% and allow bipeds to take longer steps. Efficiency improvements scale with the momentum capacity of the reaction wheel, but saturate for particularly large reaction wheels.