Reachability-Guided Sequential Quadratic Programming-Guarded Model Predictive Path Integral for Safe Nonlinear Predictive Control

2026-10-03

AI Summary

This study addresses the limitations of sampling-based methods violating constraints, the initial-value dependence of deterministic model predictive control (MPC), and the computational expense of reachability analysis in nonlinear safe control. To overcome these challenges, this work proposes the ReSQ-MPPI architecture, introducing a novel "generate-and-refine" paradigm that integrates Hamilton–Jacobi reachability analysis, Model Predictive Path Integral (MPPI) control, and Sequential Quadratic Programming (SQP). Specifically, offline-computed reachability functions guide MPPI sampling to generate candidate trajectories, after which unconstrained updates are reformulated as constrained mixed complementarity problems (MCPs) and iteratively refined via SQP to satisfy strict safety constraints. Experimental evaluations in complex obstacle navigation and autonomous driving scenarios demonstrate that the proposed framework significantly enhances both control safety and performance, comprehensively outperforming existing baseline methods.

Abstract

Safe robot control often requires combining long-horizon performance optimization with hard state and input constraints, but existing approaches tend to address this tradeoff partially. Sampling-based model predictive control (MPC) methods such as model predictive path integral (MPPI) are effective in handling nonlinear and nonconvex environments, yet their finite-sample rollouts and unconstrained weighted-average update can return an unsafe control. Deterministic nonlinear MPC can explicitly incorporate constraints, but its real-time safety and performance depends strongly on warm starts and local convergence. Hamilton--Jacobi reachability (HJR) provides rigorous safety certificates, but offline value-function computation remains practical only for reduced-order models. We propose ReSQ-MPPI, a reachability-informed generation--refinement architecture that combines these complementary strengths. An HJR value function computed offline for a reduced-order model guides online MPPI sampling toward safe, promising trajectory candidates. The MPPI solution is then refined by a small number of sequential quadratic programming (SQP) iterations in a full-order MPC problem. A key observation is that the standard MPPI inference step is an unconstrained weighted least-squares problem; ReSQ-MPPI replaces it with a constrained MPC refinement that recovers the MPPI update when it is feasible and minimally modifies it otherwise. Simulations in cluttered navigation and autonomous racing environments demonstrate that ReSQ-MPPI improves safety and performance over standalone MPPI, MPC, and reachability-filtered sampling-based control baselines.

Problem

• safe robot control
• nonlinear model predictive control
• model predictive path integral
• Hamilton-Jacobi reachability
• constrained optimization

Innovation

• Model Predictive Path Integral (MPPI)
• Hamilton-Jacobi Reachability (HJR)
• Sequential Quadratic Programming (SQP)
• Safe Nonlinear Predictive Control
• Generation-Refinement Architecture