Riemannian Motion Policy Fusion through Learnable Lyapunov Function Reshaping

Riemannian Motion Policy Fusion through Learnable Lyapunov Function Reshaping Mustafa Mukadam 1, Ching-An Cheng 1, Dieter Fox 2,3, Byron Boots 2,3, and Nathan Ratliff 3 1 Georgia Institute of Technology, USA 2 University of Washington, USA 3 NVIDIA, USA Abstract: RMPflow is a recently proposed policy-fusion framework based on differential geometry. While RMPflow has demonstrated promising performance, it requires the user to provide sensible subtask policies as Riemannian motion policies (RMPs: a motion policy and an importance matrix function), which can be a difficult design problem in its own right. We propose RMPfusion, a variation of RMPflow, to address this issue. RMPfusion supplements RMPflow with weight functions that can hierarchically reshape the Lyapunov functions of the subtask RMPs according to the current configuration of the robot and environment. This extra flexibility can remedy imperfect subtask RMPs provided by the user, improving the combined policy's performance. These weight functions can be learned by back-propagation. Moreover, we prove that, under mild restrictions on the weight functions, RMPfusion always yields a globally Lyapunov-stable motion policy. This implies that we can treat RMPfusion as a structured policy class in policy optimization that is guaranteed to generate stable policies, even during the immature phase of learning. We demonstrate these properties of RMPfusion in imitation learning experiments both in simulation and on a real-world robot. Keywords: Reactive motion generation, Structured end-to-end learning 1 Introduction Motion planning and control are core techniques to robotics [1, 2, 3]. Ideally a good algorithm must be both computationally efficient and capable of navigating a robot safely and stably across a wide range of environments. Several systems were recently proposed to address this challenge [4, 5, 6] through closely integrating planning and control techniques. In particular, RMPflow [6] is designed to combine reactive policies [7, 8, 9, 10, 11] and planning [12]. Based on differential geometry, RMPflow offers a unified treatment of the nonlinear geometries arising from a robot's internal kinematics and task spaces (e.g.