# Composable Geometric Motion Policies using Multi-Task Pullback Bundle Dynamical Systems

arXiv: https://arxiv.org/abs/2101.01297 · HTML: https://mlsanity.com/paper/2101.01297/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jan 2021.

## Built on by (most cited first, 4 of 4)

- [How to Reuse and Compose Knowledge for a Lifetime of Tasks: A Survey on Continual Learning and Functional Composition](https://mlsanity.com/paper/2207.07730/) (2022)
- [Composable Energy Policies for Reactive Motion Generation and Reinforcement Learning](https://mlsanity.com/paper/2105.04962/) (2021)
- [Learning Dynamical Systems Encoding Non-Linearity within Space Curvature](https://mlsanity.com/paper/2403.11948/) (2024)
- [A Constrained-Optimization Approach to the Execution of Prioritized Stacks of Learned Multi-Robot Tasks](https://mlsanity.com/paper/2301.05346/) (2023)

## Abstract (arXiv)

Despite decades of work in fast reactive planning and control, challenges remain in developing reactive motion policies on non-Euclidean manifolds and enforcing constraints while avoiding undesirable potential function local minima. This work presents a principled method for designing and fusing desired robot task behaviors into a stable robot motion policy, leveraging the geometric structure of non-Euclidean manifolds, which are prevalent in robot configuration and task spaces. Our Pullback Bundle Dynamical Systems (PBDS) framework drives desired task behaviors and prioritizes tasks using separate position-dependent and position/velocity-dependent Riemannian metrics, respectively, thus simplifying individual task design and modular composition of tasks. For enforcing constraints, we provide a class of metric-based tasks, eliminating local minima by imposing non-conflicting potential functions only for goal region attraction. We also provide a geometric optimization problem for combining tasks inspired by Riemannian Motion Policies (RMPs) that reduces to a simple least-squares problem, and we show that our approach is geometrically well-defined. We demonstrate the PBDS framework on the sphere mathbb S2 and at 300-500 Hz on a manipulator arm, and we provide task design guidance and an open-source Julia library implementation. Overall, this work presents a fast, easy-to-use framework for generating motion policies without unwanted potential function local minima on general manifolds.