Riemannian Motion Policies

Abstract

We introduce the Riemannian Motion Policy (RMP), a new mathematical object for modular motion generation. An RMP is a second-order dynamical system (acceleration field or motion policy) coupled with a corresponding Riemannian metric. The motion policy maps positions and velocities to accelerations, while the metric captures the directions in the space important to the policy. We show that RMPs provide a straightforward and convenient method for combining multiple motion policies and transforming such policies from one space (such as the task space) to another (such as the configuration space) in geometrically consistent ways. The operators we derive for these combinations and transformations are provably optimal, have linearity properties making them agnostic to the order of application, and are strongly analogous to the covariant transformations of natural gradients popular in the machine learning literature. The RMP framework enables the fusion of motion policies from different motion generation paradigms, such as dynamical systems, dynamic movement primitives (DMPs), optimal control, operational space control, nonlinear reactive controllers, motion optimization, and model predictive control (MPC), thus unifying these disparate techniques from the literature. RMPs are easy to implement and manipulate, facilitate controller design, simplify handling of joint limits, and clarify a number of open questions regarding the proper fusion of motion generation methods (such as incorporating local reactive policies into long-horizon optimizers). We demonstrate the effectiveness of RMPs on both simulation and real robots, including their ability to naturally and efficiently solve complicated collision avoidance problems previously handled by more complex planners.

Learning Stable Vector Fields on Lie Groups

“…An important research direction is in the composition of these vector fields to achieve complex robot motions. Thus, evaluating the perfomance of our proposed stable vector fields integrated with other vector fields, as in RMP [16] is left for future works.…”

“…In contrast with TP-GMM [15], SVF are inherently stable, generating stable motions beyond the expert demonstrations. These properties makes SVF ideal for human-robot interaction or to combine them with other vector fields as in Riemannian Motion Policies (RMP) [16].…”

Geometric Fabrics: Generalizing Classical Mechanics to Capture the Physics of Behavior

“…A geometric fabric system as described in Subsection VII is subject to local minima since the target attractor is greedy. In many environments, though, simple heuristics can coarsely shape the behavior en route so that these local avoidance behaviors are sufficient for global navigation as well (similar to the heuristics described in [22] Section V-D).…”

RMPs for Safe Impedance Control in Contact-Rich Manipulation

“…Riemannian motion policies (RMPs) are a mathematical framework that decomposes complex robot motion behavior into individual behaviors specified in more interpretable task spaces [3]. RMPs enable the controllers to be expressed in their appropriate task spaces and then manage the transforms and flow of control between those spaces to the robot's configuration space, which is where control must ultimately occur.…”

“…We present RMP-VICES, a controller that accounts for the geometry of the arm and its surrounding environment by generating motor torques that drive the arm to avoid joint limits and obstacles. We leverage Riemannian motion policies (RMPs), which allow a user to specify different behaviors Department of Computer Science, Brown University, Providence RI in more convenient 'task' manifolds and then synthesize them [3], [4]. Most importantly, RMPs have a mechanism (the Riemannian metric of these task spaces/manifolds) for designating the priority of these behaviors, which can vary based on the current position and velocity of the arm.…”