Sampling-Based Control via Entropy-Regularized Optimal Transport

Vincent Pacelli^†, Akash Ratheesh^†, Evangelos A. Theodorou

Autonomous Control and Decision Systems Laboratory
Georgia Institute of Technology

^†Equal Contribution

Abstract

Sampling-based model predictive control methods like MPPI and CEM are essential for real-time control of nonlinear robotic systems, particularly where discontinuous dynamics preclude gradient-based optimization. However, these methods derive from information-theoretic objectives that are agnostic to the geometry of the control problem, leading to pathological behaviors such as mode-averaging when the cost landscape is complex. We present OT-MPC, a sampling-based algorithm that overcomes these limitations through an entropy-regularized optimal transport formulation. By computing an optimal coupling between candidate control sequences and low-cost proposals, OT-MPC refines candidates toward nearby promising samples while coordinating updates across the ensemble to maintain coverage of the solution space. We derive closed-form, gradient-free updates via the Sinkhorn algorithm, enabling real-time performance. Experiments on navigation, manipulation, and locomotion tasks demonstrate improved success rates over existing methods.

Highlights

Two Quadrotor Load Carry

Franka Push-T

Go2 Ramp

Go2 Box Pushing

Experiments

Task	Controller	Success (%)	Avg. Steps
Car Obstacle Easy	OT-MPC	99.00	76.1 ± 21.6
	MPPI	95.00	57.2 ± 5.7
	CEM	70.00	79.5 ± 15.2
	SV-MPC	93.00	84.8 ± 22.4
Car Obstacle Hard	OT-MPC	93.50	89.5 ± 33.8
	MPPI	88.50	61.7 ± 24.4
	CEM	56.00	82.8 ± 14.5
	SV-MPC	78.50	105.0 ± 46.2
2D Push-T	OT-MPC	76.00	33.08 ± 11.35
	MPPI	4.00	83.0 ± 1.0
	CEM	46.00	47.26 ± 19.95
	SV-MPC	0.00	—
Franka Push-T	OT-MPC	66.00	52.67 ± 35.03
Franka Push-T	MPPI	64.00	46.69 ± 17.87
Quad. Obstacle Easy	OT-MPC	100.00	119.7 ± 19.9
Quad. Obstacle Easy	MPPI	100.00	93.6 ± 9.3
Quad. Obstacle Medium	OT-MPC	100.00	159.6 ± 33.3
Quad. Obstacle Medium	MPPI	60.00	127.4 ± 23.3
Quad. Obstacle Hard	OT-MPC	92.00	217.8 ± 56.6
Quad. Obstacle Hard	MPPI	19.00	147.4 ± 13.6
Two Quad. Carry Normal	OT-MPC	91.00	143.93 ± 27.28
Two Quad. Carry Normal	MPPI	22.00	371.45 ± 44.65
Two Quad. Carry Hard	OT-MPC	75.00	202.13 ± 89.75
Two Quad. Carry Hard	MPPI	10.00	369.2 ± 42.22

Table I: Benchmark results comparing OT-MPC with various control schemes on a variety of robotics control tasks.

Task	Controller	Avg. Steps	Median Goal Dist.
Go2 Locomotion	OT-MPC	427.8 ± 89.06	0.205
Go2 Locomotion	MPPI	799.2 ± 150.72	0.249
Go2 Box Pushing	OT-MPC	101.0 ± 23.0	0.084
Go2 Box Pushing	MPPI	124.9 ± 65.4	0.16

Table II: Results of Go2 quadruped locomotion tasks.

Environment	Time / Iter. (milliseconds)		Wall Clock (milliseconds)
Environment	MPPI	OT-MPC	MPPI	OT-MPC
Car	3.07	4.73	24.57	27.81
2D Push-T	1.44	0.95	5.75	15.12
Quadrotor	67.6	26.6	338.0	133.0
Two Quad Carry	23.1	12.4	230.7	99.1

Table III: Computation times for JAX-vectorized environments. Each method uses its Optuna-tuned sample count (e.g., Quadrotor: MPPI uses 2000 proposals; OT-MPC uses 200).

Environment	OT-MPC Overhead (milliseconds)
Franka Push-T	1.6
Go2	0.2

Table IV: Per-iteration OT-MPC overhead over MPPI for MuJoCo environments (Sinkhorn solve + barycentric update).

Citation

If you find this work useful, please cite our paper:

@article{pacelli2026otmpc, title={Sampling-Based Control via Entropy-Regularized Optimal Transport}, author={Vincent Pacelli, Akash Ratheesh, and Evangelos A. Theodorou}, journal={arXiv preprint arXiv:2605.02147}, year={2026} }