Model Predictive Path Integral (MPPI) control has emerged as a powerful sampling-based optimal control method for complex, nonlinear, and high-dimensional systems. However, directly applying MPPI to legged robotic systems presents several challenges. This paper systematically investigates the role of sampling strategy design within the MPPI framework for legged robot locomotion. Based upon the idea of structured control parameterization, we explore and compare multiple sampling strategies within the framework, including both unstructured and spline-based approaches. Through extensive simulations on a quadruped robot platform, we evaluate how different sampling strategies affect control smoothness, task performance, robustness, and sample efficiency. The results provide new insights into the practical implications of sampling design for deploying MPPI on complex legged systems.

翻译：模型预测路径积分（MPPI）控制已成为处理复杂、非线性、高维系统的一种强大的基于采样的最优控制方法。然而，将MPPI直接应用于腿式机器人系统仍面临若干挑战。本文系统性地研究了在腿式机器人运动的MPPI框架中采样策略设计的作用。基于结构化控制参数化的思想，我们在该框架内探索并比较了多种采样策略，包括非结构化方法和基于样条的方法。通过在四足机器人平台上进行大量仿真，我们评估了不同采样策略如何影响控制平滑性、任务性能、鲁棒性和采样效率。研究结果为在复杂腿式系统上部署MPPI时采样设计的实际意义提供了新的见解。