LP-MPPI: Low-Pass Filtering for Efficient Model Predictive Path Integral Control

TL;DR

The paper tackles high-frequency perturbations in MPPI-based control, which cause chattering and actuator wear. It introduces LP-MPPI, which applies a low-pass Butterworth filter to control perturbations, biasing exploration toward low frequencies while preserving reactivity, and requires only two intuitive parameters ($f_c$ and $o_{LPF}$). Across Gymnasium tasks, simulated quadrupeds, and real F1TENTH racing, LP-MPPI outperforms state-of-the-art MPPI variants by up to ~32% and significantly reduces control signal chattering, all with negligible computational overhead. The approach is easy to integrate with existing MPPI-based methods and offers direct spectral shaping, making it practical for real-time robotic applications and adaptable to diverse dynamics and cost structures.

Abstract

Model Predictive Path Integral (MPPI) control is a widely used sampling-based approach for real-time control, valued for its flexibility in handling arbitrary dynamics and cost functions. However, it often suffers from high-frequency noise in the sampled control trajectories, which hinders the search for optimal controls and transfers to the applied controls, leading to actuator wear. In this work, we introduce Low-Pass Model Predictive Path Integral Control (LP-MPPI), which integrates low-pass filtering into the sampling process to eliminate detrimental high-frequency components and enhance the algorithm's efficiency. Unlike prior approaches, LP-MPPI provides direct and interpretable control over the frequency spectrum of sampled control trajectory perturbations, leading to more efficient sampling and smoother control. Through extensive evaluations in Gymnasium environments, simulated quadruped locomotion, and real-world F1TENTH autonomous racing, we demonstrate that LP-MPPI consistently outperforms state-of-the-art MPPI variants, achieving significant performance improvements while reducing control signal chattering.

Figures (8)

• Figure 1: The proposed Low-Pass Model Predictive Path Integral (LP-MPPI) control smooths out the controls via the low-pass filtering of control perturbations and increases the efficiency of the MPPI.
• Figure 2: Spectrograms of the actions drawn from the trained RL policy and the different sampling distributions. Both white and colored noise are unable to closely fit the spectrum of RL behaviors, while the low-pass filtered noise covers it quite accurately.
• Figure 3: Frequency response of the Butterworth filter used in the LP-MPPI algorithm (top row) and the control trajectories generated by it (bottom row) for a range of cutoff frequencies $f_{c}$ and filter orders $o_{\text{LPF}}$.
• Figure 4: Systems used in the experimental evaluation.
• Figure 5: Performance of the proposed LP-MPPI algorithm in Gymnasium environments (left), for a range of horizon lengths $H$ (y-axis) and numbers of rollouts $N$ (x-axis), and comparison to baselines (right). The green color represents the situation in which the LP-MPPI outperforms the baseline.