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Physics-informed Neural Motion Planning on Constraint Manifolds

Ruiqi Ni, Ahmed H. Qureshi

TL;DR

This work introduces C-NTFields, the first physics-informed neural network framework for constrained motion planning on kinematic constraint manifolds, enabling CMP by directly solving a viscosity-augmented Eikonal equation without requiring expert demonstration data. By combining TSR-based manifold sampling, a manifold-aware speed model, a Fourier-feature neural time field architecture, and a bidirectional planning scheme, the approach yields sub-second planning in high-dimensional settings, including 6-DOF manipulation tasks and real-world executions. It achieves orders-of-magnitude reductions in data generation and training time compared to imitation-learning baselines, while delivering high success rates and high-quality paths with robust manifold adherence. The method shows strong advantages in object manipulation under orientation constraints and door-opening tasks, indicating practical impact for complex robot manipulation and potentially for legged locomotion under contact constraints.

Abstract

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.

Physics-informed Neural Motion Planning on Constraint Manifolds

TL;DR

This work introduces C-NTFields, the first physics-informed neural network framework for constrained motion planning on kinematic constraint manifolds, enabling CMP by directly solving a viscosity-augmented Eikonal equation without requiring expert demonstration data. By combining TSR-based manifold sampling, a manifold-aware speed model, a Fourier-feature neural time field architecture, and a bidirectional planning scheme, the approach yields sub-second planning in high-dimensional settings, including 6-DOF manipulation tasks and real-world executions. It achieves orders-of-magnitude reductions in data generation and training time compared to imitation-learning baselines, while delivering high success rates and high-quality paths with robust manifold adherence. The method shows strong advantages in object manipulation under orientation constraints and door-opening tasks, indicating practical impact for complex robot manipulation and potentially for legged locomotion under contact constraints.

Abstract

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.
Paper Structure (17 sections, 11 equations, 3 figures, 2 tables)

This paper contains 17 sections, 11 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Background
  4. Problem Definition
  5. Eikonal Equation Formulation
  6. Proposed Method
  7. Manifold Configuration Sampling
  8. Expert Speed Model for Constraint Manifold
  9. Eikonal Equation Formulation
  10. Neural Network Architecture
  11. Training Procedure
  12. Planning Procedure
  13. Evaluation
  14. Abalation Analysis
  15. Comparison Analysis
  16. ...and 2 more sections

Figures (3)

  • Figure 1: From left to right images show the paths by our method (orange), P-NTFields (red), and HM (yellow). The statistical results are based on this environment's 100 different starts and goal pairs.
  • Figure 2: Without obstacles (left) and with obstacles (right) in 3D geometric constraint environments. The paths shown are from our method (orange), CBiRRT (pink), and CoMPNetX (green). The table shows the statistical results for different start and goal pairs in these settings.
  • Figure 3: Two different real-world manipulator cases: the first row shows the door opening task, whereas the second shows the manipulator moving an object from the cabinet's top shelf to the lower shelf by crossing two relatively thin obstacles.