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Simultaneous Multi-Robot Motion Planning with Projected Diffusion Models
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Proposes SMD, which embeds augmented-Lagrangian constrained projections into the diffusion sampling loop to generate collision-free, kinematically feasible multi-robot trajectories, and introduces a multi-robot motion planning benchmark.
Problem
Diffusion models generate smooth, diverse trajectories but cannot enforce hard constraints (inter-robot and obstacle collision avoidance, kinematic limits), which becomes worse as the number of robots and obstacles grows in multi-robot motion planning.
Approach
Interleave diffusion (SGLD-style) denoising steps with projections onto the feasible set, where the nonconvex collision constraints are relaxed via auxiliary variables and handled by an augmented Lagrangian dual ascent inside the projection operator, avoiding gradient guidance and rejection sampling.
Key results
- On dense maps with 9 robots, SMD achieves 96% success vs. 27% for MMD (reported as a 3.6x improvement).
- On corridor maps with 2 robots, SMD achieves 100% success while DM, MPD, and MMD all report 0%.
- On room maps with 9 robots, SMD reaches 96% success while MPD and MMD fail (0% and 0%).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add Lagrangian-relaxation projections to diffusion sampling | Diffusion-based MRMP · Dense Maps, 9 robots | success rate: 0.2720 -> 0.9600 | Helped |
| Add Lagrangian-relaxation projections to diffusion sampling | Diffusion-based MRMP · Corridor Maps, 2 robots | success rate: 0 -> 1 | Helped |
| Add Lagrangian-relaxation projections to diffusion sampling | Diffusion-based MRMP · Shelf Maps, 3 robots | success rate: 0.5960 -> 1 | Helped |
| Add Lagrangian-relaxation projections to diffusion sampling | Diffusion-based MRMP · Room Maps, 9 robots | success rate: 0.9920 -> 0.9600 | Hurt |
| Add Lagrangian-relaxation projections to diffusion sampling | Diffusion-based MRMP · Dense Maps, 9 robots | collision ratio: 0.3707 -> 0.0044 | Helped |
| Use Lagrangian-relaxation projections instead of MMD | MRMP path planning · Corridor Maps, 2 robots | path length: 1.4208 -> 1.6619 | Hurt |
| Use Lagrangian-relaxation projections instead of MMD | MRMP path planning · Highways Maps, 3 robots | path length: 1.1638 -> 1.1391 | Helped |
| Vary the augmented-Lagrangian scaling factor ζ from 1.01 to 1.09 instead of fixing it at 1.00 (ablation) | SMD projection · MRMP maps | gradient convergence | No clear effect |
Surprising findings
- Classical EECBS achieves near-perfect success but its paths are about 20% longer than SMD's in the reported tables.
- Standard DM achieves 78.4% success for 3 robots in empty maps but drops to 5.2% with basic obstacles.
Limitations
- Inference-time cost is higher than faster classical or learning methods, as the paper's discussion acknowledges.
- Success on dense maps with 9 robots drops to 96%, and the method is centralized; decentralized settings are left for future work.
- Convex feasibility guarantee is stated only up to an arbitrarily small tolerance xi, and the paper notes strong duality does not hold in the application.
Experimental setup
Datasets: MRMP benchmark maps (random and practical) MMD-generated feasible MRMP trajectories
Benchmarks: MRMP benchmark (empty, basic, dense, corridor, shelf, room maps) highways, conveyor, drop-region maps from MMD
Metrics: success rate path length acceleration collision ratio running time
Baselines: Diffusion Models (DM) Motion Planning Diffusion (MPD) Multi-robot Motion Planning Diffusion (MMD) EECBS
Builds on: Motion Planning Diffusion (MPD) Multi-robot Motion Planning Diffusion (MMD) Stochastic Gradient Langevin Dynamics augmented Lagrangian method
Closest papers by meaning
- Multi-Robot Motion Planning with Diffusion Models (ICLR 2025 · similarity 0.91)
- Simulation-Informed Diffusion for Decentralized Multi-robot Motion Planning (NeurIPS 2026 · similarity 0.88)
- Model-based Diffusion for Trajectory Optimization (NeurIPS 2024 · similarity 0.88)
- Multi-Agent Motion Planning for Differential Drive Robots Through Stationary State Search (AAAI 2025 · similarity 0.85)
- Constrained Diffusers for Safe Planning and Control (NeurIPS 2025 · similarity 0.85)
- Potential Based Diffusion Motion Planning (ICML 2024 · similarity 0.84)
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