Smooth Model Predictive Path Integral Control without Smoothing

TL;DR

The paper tackles chattering in sampling-based MPPI controls under rapidly changing environments by introducing SMPPI, which performs input lifting to a higher-order action space and adds a derivative-action-based smoothing term with an extra cost $\Omega$. This preserves the information-theoretic MPPI interpretation while enabling smoothing along both the iteration-axis (i-axis) and the trajectory-axis (t-axis), via updates $a_t^{i+1} = a_t^{i} + u_t^{i+1} \Delta t$ and $C(V^k,A) = S(V^k) + \Omega(A + V^k\Delta t) + \lambda \sum_t {\bf u}_t^{\mathrm{T}} \bm{\Sigma}^{-1} \bm{\epsilon}_t^k$. The framework is validated on an inverted pendulum with neural-network dynamics and on a high-fidelity CarMaker-based vehicle task, where SMPPI outperforms MPPI and SGF-smoothed baselines, stabilizing nonlinear systems and enabling faster, safer aggressive driving. The results demonstrate that derivative-action smoothing reduces chattering without sacrificing responsiveness to environmental changes, suggesting broad applicability to nonlinear robotics and autonomous driving under model uncertainty.

Abstract

We present a sampling-based control approach that can generate smooth actions for general nonlinear systems without external smoothing algorithms. Model Predictive Path Integral (MPPI) control has been utilized in numerous robotic applications due to its appealing characteristics to solve non-convex optimization problems. However, the stochastic nature of sampling-based methods can cause significant chattering in the resulting commands. Chattering becomes more prominent in cases where the environment changes rapidly, possibly even causing the MPPI to diverge. To address this issue, we propose a method that seamlessly combines MPPI with an input-lifting strategy. In addition, we introduce a new action cost to smooth control sequence during trajectory rollouts while preserving the information theoretic interpretation of MPPI, which was derived from non-affine dynamics. We validate our method in two nonlinear control tasks with neural network dynamics: a pendulum swing-up task and a challenging autonomous driving task. The experimental results demonstrate that our method outperforms the MPPI baselines with additionally applied smoothing algorithms.

Figures (6)

• Figure 1: A simplified representation of the MPPI algorithm during each optimization iteration. For clarity, we only visualize one sampled trajectory (in green). (a) Amount of changes between previously computed control sequence and the next control sequence (along the "i-axis"). (b) Amount of changes in control values during MPPI rollouts (along the "t-axis"), which are hard to be minimized by the MPPI baseline.
• Figure 2: Average state costs during optimization procedures with different control methods. Each iteration consists of $20$ time steps. Note that we apply logarithmic scaling to the y-axis and that the costs are clamped to a minimum of $0.01$.
• Figure 3: Trajectory of our proposed method with a reference speed of $60$ km/h.
• Figure 4: Estimation results on the validation dataset.
• Figure 5: Visualization of trajectories of the compared controllers. The friction coefficient of corner #2 (in gray) is 0.85 and that of corner #3 (in brown) is 0.75.