# Progressive Learning for Physics-informed Neural Motion Planning

arXiv: https://arxiv.org/abs/2306.00616 · HTML: https://mlsanity.com/paper/2306.00616/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 40 references that are in the map.
- First posted on arXiv 1 Jun 2023.

## Builds on (most cited first, 22 of 22)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Value Iteration Networks](https://mlsanity.com/paper/1602.02867/) (2016)
- [Learning Sampling Distributions for Robot Motion Planning](https://mlsanity.com/paper/1709.05448/) (2017)
- [Motion Planning Networks](https://mlsanity.com/paper/1806.05767/) (2018)
- [Motion Planning Networks: Bridging the Gap Between Learning-based and Classical Motion Planners](https://mlsanity.com/paper/1907.06013/) (2019)
- [Informed RRT*: Optimal Sampling-based Path Planning Focused via Direct Sampling of an Admissible Ellipsoidal Heuristic](https://mlsanity.com/paper/1404.2334/) (2014)
- [EikoNet: Solving the Eikonal equation with Deep Neural Networks](https://mlsanity.com/paper/2004.00361/) (2020)
- [Phase Transitions, Distance Functions, and Implicit Neural Representations](https://mlsanity.com/paper/2106.07689/) (2021)
- [Fast Marching Tree: a Fast Marching Sampling-Based Method for Optimal Motion Planning in Many Dimensions](https://mlsanity.com/paper/1306.3532/) (2013)
- [Differentiable Spatial Planning using Transformers](https://mlsanity.com/paper/2112.01010/) (2021)
- [NTFields: Neural Time Fields for Physics-Informed Robot Motion Planning](https://mlsanity.com/paper/2210.00120/) (2022)
- [VisCo Grids: Surface Reconstruction with Viscosity and Coarea Grids](https://mlsanity.com/paper/2303.14569/) (2023)
- [Deeply Informed Neural Sampling for Robot Motion Planning](https://mlsanity.com/paper/1809.10252/) (2018)
- [LEGO: Leveraging Experience in Roadmap Generation for Sampling-Based Planning](https://mlsanity.com/paper/1907.09574/) (2019)
- [Potential Functions based Sampling Heuristic For Optimal Path Planning](https://mlsanity.com/paper/1704.00264/) (2017)
- [Learning Continuous Environment Fields via Implicit Functions](https://mlsanity.com/paper/2111.13997/) (2021)
- [A fast marching algorithm for the factored eikonal equation](https://mlsanity.com/paper/1607.00973/) (2016)
- [Potentially Guided Bidirectionalized RRT* for Fast Optimal Path Planning in Cluttered Environments](https://mlsanity.com/paper/1807.08325/) (2018)
- [Cost-to-Go Function Generating Networks for High Dimensional Motion Planning](https://mlsanity.com/paper/2012.06023/) (2020)

## Built on by (most cited first, 8 of 8)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [Denoising Heat-inspired Diffusion with Insulators for Collision Free Motion Planning](https://mlsanity.com/paper/2310.12609/) (2023)
- [Physics-informed Neural Motion Planning on Constraint Manifolds](https://mlsanity.com/paper/2403.05765/) (2024)
- [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)
- [Data-augmented Learning of Geodesic Distances in Irregular Domains through Soner Boundary Conditions](https://mlsanity.com/paper/2503.04579/) (2025)
- [Neural Navigation Functions for Zero-Shot Generalizable Motion Planning](https://mlsanity.com/paper/2606.03756/) (2026)

## Abstract (arXiv)

Motion planning (MP) is one of the core robotics problems requiring fast methods for finding a collision-free robot motion path connecting the given start and goal states. Neural motion planners (NMPs) demonstrate fast computational speed in finding path solutions but require a huge amount of expert trajectories for learning, thus adding a significant training computational load. In contrast, recent advancements have also led to a physics-informed NMP approach that directly solves the Eikonal equation for motion planning and does not require expert demonstrations for learning. However, experiments show that the physics-informed NMP approach performs poorly in complex environments and lacks scalability in multiple scenarios and high-dimensional real robot settings. To overcome these limitations, this paper presents a novel and tractable Eikonal equation formulation and introduces a new progressive learning strategy to train neural networks without expert data in complex, cluttered, multiple high-dimensional robot motion planning scenarios. The results demonstrate that our method outperforms state-of-the-art traditional MP, data-driven NMP, and physics-informed NMP methods by a significant margin in terms of computational planning speed, path quality, and success rates. We also show that our approach scales to multiple complex, cluttered scenarios and the real robot set up in a narrow passage environment. The proposed method's videos and code implementations are available at https://github.com/ruiqini/P-NTFields.