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Generating robot motion for multiple tasks in dynamic environments ischallenging, requiring an algorithm to respond reactively while accounting forcomplex nonlinear relationships between tasks. In this paper, we develop anovel policy synthesis algorithm, RMPflow, based on geometrically consistenttransformations of Riemannian Motion Policies (RMPs). RMPs are a class ofreactive motion policies that parameterize non-Euclidean behaviors as dynamicalsystems in intrinsically nonlinear task spaces. Given a set of RMPs designedfor individual tasks, RMPflow can combine these policies to generate anexpressive global policy, while simultaneously exploiting sparse structure forcomputational efficiency. We study the geometric properties of RMPflow andprovide sufficient conditions for stability. Finally, we experimentallydemonstrate that accounting for the natural Riemannian geometry of taskpolicies can simplify classically difficult problems, such as planning throughclutter on high-DOF manipulation systems.

RMPflow: A Geometric Framework for Generation of Multi-Task Motion Policies