The VRP Generalized Inverse and Its Application in DCM/VRP-Based Walking Control

A generalized inverse, referred to as the virtual-repellent-point generalized inverse (VRP-GI), is proposed to solve the underdetermined body-wrench distribution problem. The VRP-GI is derived as a modification of the divergent-component-of-motion generalized inverse (DCM-GI) introduced in a previous study. The VRP-GI inherits all the advantages of the DCM-GI, including its computational efficiency. In addition, the VRP-GI ensures a distribution of the body wrench that generates smaller ground reaction moments (GRMs) than the DCM-GI. This feature renders the VRP-GI based body-wrench distribution problem suitable for dynamic walking control. A whole-body walking controller is proposed that makes use of a well-known DCM/VRP gait generation and walking control approach. The controller also comprises control components for tracking the desired angular excursion of the trunk and the spatial trajectories of the hands. These control components do not interfere with the DCM/VRP control component. The performance of the controller is examined via numerical simulations of walking on a flat ground and climbing a staircase and a slope on irregular footholds.