# Diffeomorphic Obstacle Avoidance for Contractive Dynamical Systems via Implicit Representations

arXiv: https://arxiv.org/abs/2504.18860 · HTML: https://mlsanity.com/paper/2504.18860/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 70 references that are in the map.
- First posted on arXiv 26 Apr 2025.

## Builds on (most cited first, 29 of 29)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods](https://mlsanity.com/paper/2202.11762/) (2022)
- [iSDF: Real-Time Neural Signed Distance Fields for Robot Perception](https://mlsanity.com/paper/2204.02296/) (2022)
- [Learning Certified Control using Contraction Metric](https://mlsanity.com/paper/2011.12569/) (2020)
- [Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overview](https://mlsanity.com/paper/2110.00675/) (2021)
- [Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design](https://mlsanity.com/paper/1503.03144/) (2015)
- [Kernelized Movement Primitives](https://mlsanity.com/paper/1708.08638/) (2017)
- [ImitationFlow: Learning Deep Stable Stochastic Dynamic Systems by Normalizing Flows](https://mlsanity.com/paper/2010.13129/) (2020)
- [Learning Stabilizable Nonlinear Dynamics with Contraction-Based Regularization](https://mlsanity.com/paper/1907.13122/) (2019)
- [Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systems](https://mlsanity.com/paper/2005.13143/) (2020)
- [Neural Contraction Metrics for Robust Estimation and Control: A Convex Optimization Approach](https://mlsanity.com/paper/2006.04361/) (2020)
- [Learning Riemannian Stable Dynamical Systems via Diffeomorphisms](https://mlsanity.com/paper/2211.03169/) (2022)
- [Regularized Deep Signed Distance Fields for Reactive Motion Generation](https://mlsanity.com/paper/2203.04739/) (2022)
- [Neural Contractive Dynamical Systems](https://mlsanity.com/paper/2401.09352/) (2024)
- [Representing Robot Geometry as Distance Fields: Applications to Whole-body Manipulation](https://mlsanity.com/paper/2307.00533/) (2023)
- [Configuration Space Distance Fields for Manipulation Planning](https://mlsanity.com/paper/2406.01137/) (2024)
- [Learning Neural Contracting Dynamics: Extended Linearization and Global Guarantees](https://mlsanity.com/paper/2402.08090/) (2024)
- [Avoiding Dense and Dynamic Obstacles in Enclosed Spaces: Application to Moving in Crowds](https://mlsanity.com/paper/2105.11743/) (2021)
- [JacNet: Learning Functions with Structured Jacobians](https://mlsanity.com/paper/2408.13237/) (2024)
- [Contractive Dynamical Imitation Policies for Efficient Out-of-Sample Recovery](https://mlsanity.com/paper/2412.07544/) (2024)
- [Learning Contraction Policies from Offline Data](https://mlsanity.com/paper/2112.05911/) (2021)
- [Neural Gaits: Learning Bipedal Locomotion via Control Barrier Functions and Zero Dynamics Policies](https://mlsanity.com/paper/2204.08120/) (2022)
- [Distance and Collision Probability Estimation from Gaussian Surface Models](https://mlsanity.com/paper/2402.00186/) (2024)
- [RMMI: Reactive Mobile Manipulation using an Implicit Neural Map](https://mlsanity.com/paper/2408.16206/) (2024)
- [The e-Bike Motor Assembly: Towards Advanced Robotic Manipulation for Flexible Manufacturing](https://mlsanity.com/paper/2304.10595/) (2023)
- [On the Design of Region-Avoiding Metrics for Collision-Safe Motion Generation on Riemannian Manifolds](https://mlsanity.com/paper/2307.15440/) (2023)
- [Extended Neural Contractive Dynamical Systems: On Multiple Tasks and Riemannian Safety Regions](https://mlsanity.com/paper/2411.11405/) (2024)

## Built on by (most cited first, 1 of 1)

- [Geometric Contact Flows: Contactomorphisms for Dynamics and Control](https://mlsanity.com/paper/2506.17868/) (2025)

## Abstract (arXiv)

Ensuring safety and robustness of robot skills is becoming crucial as robots are required to perform increasingly complex and dynamic tasks. The former is essential when performing tasks in cluttered environments, while the latter is relevant to overcome unseen task situations. This paper addresses the challenge of ensuring both safety and robustness in dynamic robot skills learned from demonstrations. Specifically, we build on neural contractive dynamical systems to provide robust extrapolation of the learned skills, while designing a full-body obstacle avoidance strategy that preserves contraction stability via diffeomorphic transforms. This is particularly crucial in complex environments where implicit scene representations, such as Signed Distance Fields (SDFs), are necessary. To this end, our framework called Signed Distance Field Diffeomorphic Transform, leverages SDFs and flow-based diffeomorphisms to achieve contraction-preserving obstacle avoidance. We thoroughly evaluate our framework on synthetic datasets and several real-world robotic tasks in a kitchen environment. Our results show that our approach locally adapts the learned contractive vector field while staying close to the learned dynamics and without introducing highly-curved motion paths, thus outperforming several state-of-the-art methods.