# Physics-informed Neural Motion Planning on Constraint Manifolds

arXiv: https://arxiv.org/abs/2403.05765 · HTML: https://mlsanity.com/paper/2403.05765/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 31 references that are in the map.
- First posted on arXiv 9 Mar 2024.

## Builds on (most cited first, 10 of 10)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [EikoNet: Solving the Eikonal equation with Deep Neural Networks](https://mlsanity.com/paper/2004.00361/) (2020)
- [NTFields: Neural Time Fields for Physics-Informed Robot Motion Planning](https://mlsanity.com/paper/2210.00120/) (2022)
- [Neural Manipulation Planning on Constraint Manifolds](https://mlsanity.com/paper/2008.03787/) (2020)
- [Learning Equality Constraints for Motion Planning on Manifolds](https://mlsanity.com/paper/2009.11852/) (2020)
- [Constrained Motion Planning Networks X](https://mlsanity.com/paper/2010.08707/) (2020)
- [Fast Kinodynamic Planning on the Constraint Manifold with Deep Neural Networks](https://mlsanity.com/paper/2301.04330/) (2023)
- [Progressive Learning for Physics-informed Neural Motion Planning](https://mlsanity.com/paper/2306.00616/) (2023)
- [Trajectory Optimization on Manifolds: A Theoretically-Guaranteed Embedded Sequential Convex Programming Approach](https://mlsanity.com/paper/1905.07654/) (2019)
- [Sampling-Based Motion Planning on Sequenced Manifolds](https://mlsanity.com/paper/2006.02027/) (2020)

## Built on by (most cited first, 6 of 6)

- [Physics-informed Value Learner for Offline Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2509.06782/) (2025)
- [Physics-informed Temporal Difference Metric Learning for Robot Motion Planning](https://mlsanity.com/paper/2505.05691/) (2025)
- [Mollified Value Learning](https://mlsanity.com/paper/2602.23280/) (2026)
- [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026)
- [Enforcing Constraints in Generative Sampling via Adaptive Correction Scheduling](https://mlsanity.com/paper/2605.11214/) (2026)
- [Neural Navigation Functions for Zero-Shot Generalizable Motion Planning](https://mlsanity.com/paper/2606.03756/) (2026)

## Abstract (arXiv)

Constrained Motion Planning (CMP) aims to find a collision-free path between the given start and goal configurations on the kinematic constraint manifolds. These problems appear in various scenarios ranging from object manipulation to legged-robot locomotion. However, the zero-volume nature of manifolds makes the CMP problem challenging, and the state-of-the-art methods still take several seconds to find a path and require a computationally expansive path dataset for imitation learning. Recently, physics-informed motion planning methods have emerged that directly solve the Eikonal equation through neural networks for motion planning and do not require expert demonstrations for learning. Inspired by these approaches, we propose the first physics-informed CMP framework that solves the Eikonal equation on the constraint manifolds and trains neural function for CMP without expert data. Our results show that the proposed approach efficiently solves various CMP problems in both simulation and real-world, including object manipulation under orientation constraints and door opening with a high-dimensional 6-DOF robot manipulator. In these complex settings, our method exhibits high success rates and finds paths in sub-seconds, which is many times faster than the state-of-the-art CMP methods.