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.

References in corpus (2)

• Newton methods for k-order Markov Constrained Motion Problems
• Approximately Optimal Continuous-Time Motion Planning and Control via Probabilistic Inference

Cited by in corpus (21)

• A Review of Robot Learning for Manipulation: Challenges, Representations, and Algorithms
• Learning Stability Certificates from Data
• RMPflow: A Computational Graph for Automatic Motion Policy Generation
• Geometric Fabrics for the Acceleration-based Design of Robotic Motion
• Bayesian Optimization Meets Riemannian Manifolds in Robot Learning
• Riemannian Motion Policy Fusion through Learnable Lyapunov Function Reshaping
• DexPilot: Vision Based Teleoperation of Dexterous Robotic Hand-Arm System
• STORM: An Integrated Framework for Fast Joint-Space Model-Predictive Control for Reactive Manipulation
• Learning Vision-based Reactive Policies for Obstacle Avoidance
• RMPflow: A Geometric Framework for Generation of Multi-Task Motion Policies
• Scaling Local Control to Large-Scale Topological Navigation
• Supervised Learning and Reinforcement Learning of Feedback Models for Reactive Behaviors: Tactile Feedback Testbed
• RMP2: A Structured Composable Policy Class for Robot Learning
• Optimization Fabrics for Behavioral Design
• Neural Autonomous Navigation with Riemannian Motion Policy
• RoCUS: Robot Controller Understanding via Sampling
• Reactive Human-to-Robot Handovers of Arbitrary Objects
• Stable, Concurrent Controller Composition for Multi-Objective Robotic Tasks
• Imitation Learning via Simultaneous Optimization of Policies and Auxiliary Trajectories
• Hierarchical Neural Dynamic Policies
• Optimization Fabrics