Time-Correlated Model Predictive Path Integral: Smooth Action Generation for Sampling-Based Control

In this paper, we introduce time-correlated model predictive path integral (TC-MPPI), a novel approach to mitigate action noise in sampling-based control methods. Unlike conventional smoothing techniques that rely on post-processing or additional state variables, TC-MPPI directly incorporates temporal correlation of actions into stochastic optimal control, effectively enforcing quadratic costs on action derivatives. This reformulation enables us to generate smooth action sequences without extra modifications, using a time-correlated and conditional Gaussian sampling distribution. We demonstrate the effectiveness of our approach through simulations on various robotic platforms, including a pendulum, cart-pole, 2D bicopter, 3D quadcopter, and autonomous vehicle. Simulation videos are available at https://youtu.be/nWfJ2MAV2JI.

Authors

• Minhyeong Lee
• Dongjun Lee

Keywords

• Solid modeling
• Correlation
• Three-dimensional displays
• Costs
• Noise
• Stochastic processes
• Optimal control
• Predictive models
• Autonomous vehicles
• Quadrotors
• Smooth Action
• Normal Distribution
• Smoothing
• Sample Distribution
• State Variables
• Sequence Of Actions
• Conditional Distribution
• Pendulum
• Quadratic Cost
• Stochastic Control
• Sampling-based Methods
• Stochastic Optimal Control
• Root Mean Square Error
• Diagonal Matrix
• Probability Density Function
• Control Problem
• Sample Covariance
• Joint Angles
• Optimal Distribution
• Block Diagonal Matrix
• Sampling Efficiency
• Optimal Control Problem
• Extensive Dynamics
• Model Predictive Control
• Savitzky-Golay Filter
• Thrust Force
• Gradient Operator
• Angular Speed