Riemannian Motion Policies
This work addresses the challenge of integrating disparate motion generation methods in robotics, offering a foundational approach that unifies techniques like dynamical systems and optimal control.
The paper tackles the problem of modular motion generation by introducing Riemannian Motion Policies (RMPs), which combine motion policies and Riemannian metrics to enable geometrically consistent fusion and transformation across different spaces, resulting in a unified framework that simplifies controller design and efficiently handles complex tasks like collision avoidance.
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.