Model Predictive Path Integral (MPPI) control is a sampling-based optimization method that has recently attracted attention, particularly in the robotics and reinforcement learning communities. MPPI has been widely applied as a GPU-accelerated random search method to deterministic direct single-shooting optimal control problems arising in model predictive control (MPC) formulations. MPPI offers several key advantages, including flexibility, robustness, ease of implementation, and inherent parallelizability. However, its performance can deteriorate in high-dimensional settings since the optimal control problem is solved via Monte Carlo sampling. To address this limitation, this paper proposes an enhanced MPPI method that incorporates a Jacobian reconstruction technique and the second-order Generalized Gauss-Newton method. This novel approach is called \textit{Gauss-Newton accelerated MPPI}. The numerical results show that the Gauss-Newton accelerated MPPI approach substantially improves MPPI scalability and computational efficiency while preserving the key benefits of the classical MPPI framework, making it a promising approach even for high-dimensional problems.

翻译：模型预测路径积分（MPPI）控制是一种基于采样的优化方法，近年来在机器人学和强化学习领域受到广泛关注。MPPI作为一种GPU加速的随机搜索方法，已被广泛应用于模型预测控制（MPC）框架中出现的确定性直接单次打靶最优控制问题。MPPI具有若干关键优势，包括灵活性、鲁棒性、易于实现以及固有的可并行性。然而，由于最优控制问题通过蒙特卡洛采样求解，其在高维场景下的性能可能下降。为克服这一局限，本文提出一种增强型MPPI方法，该方法融合了雅可比矩阵重构技术与二阶广义高斯-牛顿法。这一创新方法被称为\textit{高斯-牛顿加速MPPI}。数值实验表明，高斯-牛顿加速MPPI方法在保持经典MPPI框架核心优势的同时，显著提升了MPPI的可扩展性与计算效率，使其即使在高维问题中也能成为极具前景的解决方案。