Riemannian Motion Policies
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This paper introduces a new mathematical object for modular motion generation called the Riemannian Motion Policy (RMP). An RMP is an acceleration field (dynamical system) coupled with a corresponding Riemannian metric defining directions of importance at each point, typically defined on a nonlinear task space. We derive operators for transforming RMPs through the network of nonlinear maps defining their task spaces and combining multiple RMPs residing at a given task space, and show that these operators optimally preserve the geometric defined by the metrics in a way strongly analogous to the covariant transformations of natural gradients. This framework enables us to bridge the literature by fusing motion policies together across differing motion generation paradigms, from Dynamical Systems and Dynamic Movement Primitives to Optimal Control and Model Predictive Control. RMPs are easy to implement and manipulate, simplify controller design, clarify a number of open questions around how to effectively combine existing techniques, and their properties of geometric consistency, for the first time, make feasible the generic application of a single smooth and reactive motion generation system across a range of robots with zero re-tuning.
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