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Accelerating Sampling-Based Control via Learned Linear Koopman Dynamics

Wenjian Hao, Yuxuan Fang, Zehui Lu, Shaoshuai Mou

TL;DR

To improve the computational efficiency of classic MPPI while preserving control performance, the nonlinear dynamics used for trajectory propagation are replaced with a learned linear deep Koopman operator (DKO) model, enabling faster rollout and more efficient trajectory sampling.

Abstract

This paper presents an efficient model predictive path integral (MPPI) control framework for systems with complex nonlinear dynamics. To improve the computational efficiency of classic MPPI while preserving control performance, we replace the nonlinear dynamics used for trajectory propagation with a learned linear deep Koopman operator (DKO) model, enabling faster rollout and more efficient trajectory sampling. The DKO dynamics are learned directly from interaction data, eliminating the need for analytical system models. The resulting controller, termed MPPI-DK, is evaluated in simulation on pendulum balancing and surface vehicle navigation tasks, and validated on hardware through reference-tracking experiments on a quadruped robot. Experimental results demonstrate that MPPI-DK achieves control performance close to MPPI with true dynamics while substantially reducing computational cost, enabling efficient real-time control on robotic platforms.

Accelerating Sampling-Based Control via Learned Linear Koopman Dynamics

TL;DR

To improve the computational efficiency of classic MPPI while preserving control performance, the nonlinear dynamics used for trajectory propagation are replaced with a learned linear deep Koopman operator (DKO) model, enabling faster rollout and more efficient trajectory sampling.

Abstract

This paper presents an efficient model predictive path integral (MPPI) control framework for systems with complex nonlinear dynamics. To improve the computational efficiency of classic MPPI while preserving control performance, we replace the nonlinear dynamics used for trajectory propagation with a learned linear deep Koopman operator (DKO) model, enabling faster rollout and more efficient trajectory sampling. The DKO dynamics are learned directly from interaction data, eliminating the need for analytical system models. The resulting controller, termed MPPI-DK, is evaluated in simulation on pendulum balancing and surface vehicle navigation tasks, and validated on hardware through reference-tracking experiments on a quadruped robot. Experimental results demonstrate that MPPI-DK achieves control performance close to MPPI with true dynamics while substantially reducing computational cost, enabling efficient real-time control on robotic platforms.
Paper Structure (11 sections, 28 equations, 4 figures, 3 tables, 1 algorithm)

This paper contains 11 sections, 28 equations, 4 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. The Problem and Preliminaries
  3. Problem Formulation
  4. Dynamics Learning using DKO
  5. MPPI control
  6. Methodology
  7. Numerical Simulations
  8. Pendulum Balancing
  9. Surface Vehicle Navigation
  10. Experiments Results
  11. Concluding Remarks

Figures (4)

  • Figure 1: Average trajectory cost over $5$ independent trials for different lifting function architectures and training datasets.
  • Figure 2: Average trajectory cost over $5$ independent trials for different lifting dimensions and training datasets.
  • Figure 3: Tracking error over time. The solid line represents the mean over $4$ independent trials, and the shaded region indicates one standard deviation.
  • Figure 4: Representative trajectories generated by MPPI-DK and classic MPPI using true dynamics on a Unitree Go1 quadruped robot. In the experiment, the robot starts from the initial state $(x, y, \theta) = (-0.5 \text{m}, 0.4\text{m}, 0.3\text{rad})$ and navigates to the goal state $(x_{\mathrm{goal}}, y_{\mathrm{goal}}, \theta_{\mathrm{goal}}) = (1.5\text{m}, 0\text{m}, 0\text{rad})$.

Theorems & Definitions (1)

  • Remark 1