Accelerating Motion Planning via Optimal Transport

This repository implements Motion Planning via Optimal Transport (mpot) in PyTorch. The philosophy of mpot follows the Monte Carlo methods' argument: more samples discover more and better modes with high enough initialization variances. Within the multi-modal motion planning scope, mpot performs brute-force parallel planning on GPU, mitigating local minima traps common in optimization-based motion planning.

For those interested in standalone Sinkhorn Step as a general-purpose batch gradient-free solver for non-convex optimization problems, please check out ssax.

Paper

This work has been accepted to NeurIPS 2023. Please find the paper on arXiv.

Requirements

• Python >= 3.9
• PyTorch >= 2.0 (with CUDA for GPU acceleration)
• See pyproject.toml for the full dependency list

Installation

Activate your conda/virtual environment, navigate to the mpot root directory, and run:

pip install -e .

mpot requires GPU for practical performance. Please verify PyTorch CUDA support:

python -c "import torch; print(torch.cuda.is_available())"

Examples

Planar Occupancy Map

python examples/mpot_occupancy.py

Planar Signed Distance Field (SDF)

python examples/mpot_sdf.py

Panda Robot Arm (7-DOF, dense obstacles)

python examples/mpot_panda.py

Every run uses a different random seed. The resulting optimization visualizations are stored in the current directory. Refer to the example scripts for playing around with options and different goal points.

Note: For all cases, we normalize the joint space to the joint and velocity limits, then perform Sinkhorn Step on the normalized state-space. Changing any hyperparameters may require tuning again.

Tuning Tips

The most sensitive parameters are:

Parameter	Description	Guidance
polytope	Polytope geometry for directional probing	cube for dim < 10; orthoplex or simplex for higher dimensions
step_radius	Step size per iteration	Start small (0.03-0.15), increase if convergence is slow
probe_radius	Probing radius (must be >= step_radius)	Controls exploration range around current waypoints
num_probe	Probe points per polytope vertex	3-5 is usually sufficient
epsilon	Decay rate of step/probe size	0.01-0.05 typical
ent_epsilon	Sinkhorn entropy regularization	1e-2 to 5e-2 balances coupling sharpness vs. speed
Cost weights	w_coll, w_smooth	Application-dependent; tune for your environment

Troubleshooting

CUDA Memory Issues:

export PYTORCH_CUDA_ALLOC_CONF=max_split_size_mb:512

Common Issues:

• If optimization diverges, reduce step_radius and probe_radius
• For high-dimensional problems (e.g., 7-DOF robot), use orthoplex polytope to reduce vertex count
• Reduce num_particles_per_goal if running out of GPU memory

Acknowledgement

The Gaussian Process prior implementation is adapted from Sasha Lambert's mpc_trajopt.

Citation

If you found this repository useful, please consider citing:

@article{le2023accelerating,
  title={Accelerating motion planning via optimal transport},
  author={Le, An T and Chalvatzaki, Georgia and Biess, Armin and Peters, Jan R},
  journal={Advances in Neural Information Processing Systems},
  volume={36},
  pages={78453--78482},
  year={2023}
}