Accelerating Sampling-Based Control via Learned Linear Koopman Dynamics

2026-03-05

AI Summary

This work addresses the high computational cost of Model Predictive Path Integral (MPPI) control in complex nonlinear systems by embedding a data-driven Deep Koopman Operator (DKO) into the MPPI framework. By replacing the original nonlinear dynamics with linear Koopman dynamics learned from data, the proposed method enables efficient trajectory propagation and sampling without requiring an explicit analytical system model. To the best of our knowledge, this is the first end-to-end integration of learned linear dynamics into MPPI. Experimental evaluations on benchmark tasks—including the inverted pendulum, surface vessel, and quadrupedal robot—demonstrate that the resulting MPPI-DK approach substantially reduces computational overhead while maintaining control performance comparable to that of conventional MPPI based on ground-truth dynamics.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: State Estimation
• Machine Learning: Mixture of Experts (MoE)

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• sampling-based control
• computational efficiency
• nonlinear dynamics
• real-time control
• model predictive control

Innovation

• Koopman operator
• model predictive path integral control
• data-driven dynamics
• nonlinear systems
• real-time robotic control