Extending Riemmanian Motion Policies to a Class of Underactuated Wheeled-Inverted-Pendulum Robots

Abstract

Riemannian Motion Policies (RMPs) have recently been introduced as a way to specify second-order motion policies defined on robot task spaces. RMP-based approaches have the advantage of being more general than traditional approaches based on operational space control; for example, the generalized task inertia in an RMP can be fully state-dependent, which is particularly effective in designing collision avoidance bahaviors. But until now RMPs have been applied only to fully actuated systems, i.e. systems for which each degree of freedom (DoF) can be directly actuated by a control input. In this paper, we present a method that extends the RMP formalism to a class of underacutated systems whose dynamics are amenable to a decomposition into a fully-actuated subsystem and a residual dynamics. We show the efficacy of the approach by constructing a suitable decomposition for a Wheeled-Inverted-Pendulum (WIP) humanoid robot and applying our method to derive motion policies for combined locomotion and manipulation tasks. Simulation results are presented for a 7-DoF system with one degree of underactuation.