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Physics-informed Temporal Difference Metric Learning for Robot Motion Planning
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Proposes self-supervised temporal-difference metric learning (TD loss + Eikonal loss + metric-space distance + attention-based point-cloud conditioning) to solve the Eikonal equation for robot motion planning, with sampling-based MPC for path inference.
Problem
Self-supervised neural motion planners that solve the Eikonal equation fail to preserve its optimal value function and geodesic distance properties, so they struggle in cluttered environments and generalize poorly to unseen scenes.
Approach
Combine an infinitesimal Eikonal loss with a finite-time temporal-difference (Bellman) loss, normal-alignment and causality weights, and parameterize travel time as a metric (L-inf/L-1 hybrid distance) over a learned latent embedding conditioned on the environment point cloud via attention; infer paths with sampling-based MPC instead of gradient descent.
Key results
- On Gibson indoor environments the method reaches 95.1% SR at 0.056 s planning time, versus 68.1% for NTFields and 81.2% for P-NTFields.
- On 2D maze, travel-time error of 0.08 versus 0.58 for NTFields and P-NTFields.
- On C3D, 99.4% SR at 0.025 s, about 10x faster than MPNet (97.0% SR, 0.22 s).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add temporal difference loss L_TD (ablation) | Ours · Maze | Mean absolute travel-time error: 0.21 -> 0.08 | Helped |
| add obstacle alignment loss L_N (ablation) | Ours · Maze | Mean absolute travel-time error: 0.13 -> 0.08 | Helped |
| add causality weighting L_C (ablation) | Ours · Maze | Mean absolute travel-time error: 0.12 -> 0.08 | Helped |
| add Eikonal loss L_E (ablation) | Ours · Maze | Mean absolute travel-time error: 1.13 -> 0.08 | Helped |
| replace the proposed metric with IQE (ablation) | Ours · Maze | Mean absolute travel-time error: 0.08 -> 0.32 | Hurt |
| replace the proposed metric with PQE (ablation) | Ours · Maze | Mean absolute travel-time error: 0.08 -> 0.46 | Hurt |
| replace the proposed metric with MRN (ablation) | Ours · Maze | Mean absolute travel-time error: 0.08 -> 0.19 | Hurt |
| replace the proposed metric with Deep Norm (ablation) | Ours · Maze | Mean absolute travel-time error: 0.08 -> 0.29 | Hurt |
| use sampling-based MPC instead of gradient-based path inference (ablation) | Ours · Indoor Gibson | SR (%): 92.6 -> 95.1 | Helped |
| use sampling-based MPC instead of gradient-based path inference (ablation) | Ours · Indoor Gibson | Time (s): $0.074 \pm 0.057$ -> $0.056 \pm 0.037$ | Helped |
| use the proposed method instead of NTF | robot motion planning · Indoor Gibson | SR (%): 68.1 -> 95.1 | Helped |
| use the proposed method instead of P-NTF | robot motion planning · Cluttered 3D (C3D) | SR (%): {93.4} -> 99.4 | Helped |
Surprising findings
- Using the TD loss alone without the Eikonal loss yields inaccurate value functions, showing the two losses must work together.
- Gradient-based path inference (Our-G) performs worse than the MPC variant but still outperforms NTFields and P-NTFields.
Limitations
- Struggles to generalize to multiple unseen environments in complex Gibson datasets.
- Lower success rate than MPiNet on 7-DOF manipulator (87% vs 91%) and than classical planners in several settings.
- Hyperparameters (TD step, loss weights) need tuning per environment clutter level.
Experimental setup
Datasets: Gibson C3D MPiNet dataset
Benchmarks: 2D maze (FMM reference) Gibson indoor environments Cluttered 3D (C3D) 7-DOF manipulator tabletop 12-DOF dual-arm real-world cabinet
Metrics: success rate path length computation time mean absolute travel-time error
Baselines: NTFields P-NTFields FMM RRTConnect LazyPRM MPNet MPiNet IQE PQE MRN Deep Norm
Builds on: NTFields P-NTFields Quasimetric Reinforcement Learning PointNext PirateNets
Closest papers by meaning
- Potential Based Diffusion Motion Planning (ICML 2024 · similarity 0.85)
- Efficient Robotic Policy Learning via Latent Space Backward Planning (ICML 2025 · similarity 0.85)
- Learning Temporal Distances: Contrastive Successor Features Can Provide a Metric Structure for Decision-Making (ICML 2024 · similarity 0.84)
- Prof. Robot: Differentiable Robot Rendering Without Static and Self-Collisions (CVPR 2025 · similarity 0.84)
- Temporal Task and Motion Planning with Metric Time for Multiple Object Navigation (AAAI 2025 · similarity 0.84)
- Generative Trajectory Stitching through Diffusion Composition (NeurIPS 2025 · similarity 0.84)
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