Chance-Constrained Information-Theoretic Stochastic Model Predictive Control with Safety Shielding

TL;DR

The paper tackles safe planning for nonlinear systems under uncertainty by enforcing chance constraints in belief space. It introduces Belief-Space MPPI (BSS-MPPI), which combines Monte-Carlo propagation of state distributions with a CBF-inspired safety heuristic, integrated into Shield-MPPI. The method avoids explicit linearization and supports general nonlinear dynamics by solving the stochastic optimal control problem through forward simulation on an augmented belief-space, using a safety-aware objective. Simulation on a high-fidelity autonomous racing scenario shows reduced constraint violations with computation times comparable to existing MPPI approaches, indicating practical potential for real-time safety-critical tasks.

Abstract

This paper introduces a novel nonlinear stochastic model predictive control path integral (MPPI) method, which considers chance constraints on system states. The proposed belief-space stochastic MPPI (BSS-MPPI) applies Monte-Carlo sampling to evaluate state distributions resulting from underlying systematic disturbances, and utilizes a Control Barrier Function (CBF) inspired heuristic in belief space to fulfill the specified chance constraints. Compared to several previous stochastic predictive control methods, our approach applies to general nonlinear dynamics without requiring the computationally expensive system linearization step. Moreover, the BSS-MPPI controller can solve optimization problems without limiting the form of the objective function and chance constraints. By multi-threading the sampling process using a GPU, we can achieve fast real-time planning for time- and safety-critical tasks such as autonomous racing. Our results on a realistic race-car simulation study show significant reductions in constraint violation compared to some of the prior MPPI approaches, while being comparable in computation times.

Figures (6)

• Figure 1: BSS-MPPI control architecture.
• Figure 2: The planar single-track vehicle model used to model the AutoRally in Sec. \ref{['Sec:Results']}.
• Figure 3: s-mppi and bss-mppi trajectory visualization for a set of Monte-Carlo runs where the objective is to conclude a lap clock-wise. The trajectories generated by bss-mppi consider disturbances and are more conservative, resulting in lower speeds but fewer collisions
• Figure 4: Crash-rate comparison between bss-mppi and s-mppi as function of $q_{e_y}$, with a zoom-in in the lower plot. The curves represent average performance over 100 Monte-Carlo runs with the shaded tubes showing the 1-$\sigma$ confidence intervals.
• Figure 5: Collision-rate comparison between bss-mppi and s-mppi as function of $q_{e_y}$ corresponding to Fig. \ref{['fig:CrashRatePlot']}. Since there can be multiple collisions (i.e., constraint violations) during a lap, the ratio can be greater than one.

Theorems & Definitions (2)

• Remark 1
• Remark 2