Sampling-Based Control via Entropy-Regularized Optimal Transport

2026-05-03

AI Summary

This work addresses the issue of mode averaging and other artifacts in sampling-based model predictive control (MPC) arising from the neglect of geometric structure in complex cost landscapes. To overcome this limitation, the paper proposes OT-MPC, an algorithm that introduces entropy-regularized optimal transport into sampling-based control for the first time. By constructing an optimal coupling between candidate control sequences and low-cost proposals, OT-MPC jointly optimizes the entire sample set while preserving coverage of the solution space. The method employs Sinkhorn iterations to enable closed-form, gradient-free updates that balance local refinement with global diversity. Experimental results demonstrate that OT-MPC significantly outperforms existing approaches such as MPPI and CEM across navigation, manipulation, and locomotion tasks, substantially improving task success rates.

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.

Problem

• sampling-based control
• model predictive control
• optimal transport
• entropy regularization
• nonlinear robotic systems

Innovation

• optimal transport
• entropy regularization
• sampling-based MPC
• Sinkhorn algorithm
• model predictive control