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RMPflow is a recently proposed policy-fusion framework based on differentialgeometry. While RMPflow has demonstrated promising performance, it requires theuser to provide sensible subtask policies as Riemannian motion policies (RMPs:a motion policy and an importance matrix function), which can be a difficultdesign problem in its own right. We propose RMPfusion, a variation of RMPflow,to address this issue. RMPfusion supplements RMPflow with weight functions thatcan hierarchically reshape the Lyapunov functions of the subtask RMPs accordingto the current configuration of the robot and environment. This extraflexibility can remedy imperfect subtask RMPs provided by the user, improvingthe combined policy's performance. These weight functions can be learned byback-propagation. Moreover, we prove that, under mild restrictions on theweight functions, RMPfusion always yields a globally Lyapunov-stable motionpolicy. This implies that we can treat RMPfusion as a structured policy classin policy optimization that is guaranteed to generate stable policies, evenduring the immature phase of learning. We demonstrate these properties ofRMPfusion in imitation learning experiments both in simulation and on areal-world robot.

Riemannian Motion Policy Fusion through Learnable Lyapunov Function Reshaping