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Sampling Strategy Design for Model Predictive Path Integral Control on Legged Robot Locomotion

Chuyuan Tao, Fanxin Wang, Haolong Jiang, Jia He, Yiyang Chen, Qinglei Bu

TL;DR

This work systematically analyzes how sampling strategy design affects Model Predictive Path Integral (MPPI) control for legged locomotion on a quadruped. It compares cubic spline, Bézier, and linear interpolation parameterizations, assessing their impact on control smoothness, robustness, and sample efficiency across flat-ground walking, stair climbing, and obstacle traversal. The results show that structured, low-dimensional spline parameterizations—especially CubicSpline with moderate dimensionality (k=4)—consistently provide favorable trade-offs between performance and computation, enabling more reliable whole-body MPPI in challenging contact-rich tasks. The findings offer practical guidelines for deploying MPPI on complex legged robots and motivate future work on adaptive sampling strategies to further improve real-time robustness and efficiency.

Abstract

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.

Sampling Strategy Design for Model Predictive Path Integral Control on Legged Robot Locomotion

TL;DR

This work systematically analyzes how sampling strategy design affects Model Predictive Path Integral (MPPI) control for legged locomotion on a quadruped. It compares cubic spline, Bézier, and linear interpolation parameterizations, assessing their impact on control smoothness, robustness, and sample efficiency across flat-ground walking, stair climbing, and obstacle traversal. The results show that structured, low-dimensional spline parameterizations—especially CubicSpline with moderate dimensionality (k=4)—consistently provide favorable trade-offs between performance and computation, enabling more reliable whole-body MPPI in challenging contact-rich tasks. The findings offer practical guidelines for deploying MPPI on complex legged robots and motivate future work on adaptive sampling strategies to further improve real-time robustness and efficiency.

Abstract

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.
Paper Structure (17 sections, 24 equations, 6 figures, 3 tables, 1 algorithm)

This paper contains 17 sections, 24 equations, 6 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Experimental Platform and Tasks
  5. Model Predictive Path Integral Control
  6. MPPI for Whole-Body Control of Legged Robots
  7. Different Sampling Strategy in MPPI algorithm
  8. Cubic Spline Sampling
  9. Bézier Curve Sampling
  10. Linear Interpolation--Based Sampling
  11. Simulation Results: Sampling Strategy Comparison
  12. Experimental Setup
  13. Flat-Ground Walking
  14. Stair Climbing
  15. Big Box Obstacle Traversal
  16. ...and 2 more sections

Figures (6)

  • Figure 1: Performance radar and efficiency trade-off for flat-ground walking.
  • Figure 2: Steps-to-goal and success-rate comparison for different sampling methods on flat-ground walking.
  • Figure 3: Performance radar and efficiency trade-off for the stair-climbing task.
  • Figure 4: Steps-to-goal and success-rate comparison for different sampling methods on the stair-climbing task.
  • Figure 5: Performance radar and efficiency trade-off for the big box obstacle traversal task.
  • ...and 1 more figures