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.

翻译：本文针对具有复杂非线性动力学的系统，提出了一种高效的模型预测路径积分（MPPI）控制框架。为在保持控制性能的同时提升经典MPPI的计算效率，我们采用学习的线性深度库普曼算子（DKO）模型替代用于轨迹传播的非线性动力学模型，从而实现更快的轨迹推演和更高效的轨迹采样。DKO动力学模型直接从交互数据中学习得到，无需解析系统模型。我们将所提出的控制器命名为MPPI-DK，在仿真环境中通过摆杆平衡与水面航行器导航任务进行评估，并在四足机器人上通过轨迹跟踪实验进行了硬件验证。实验结果表明，MPPI-DK在显著降低计算成本的同时，达到了接近使用真实动力学模型的MPPI的控制性能，从而能够在机器人平台上实现高效实时控制。