DualGuard MPPI: Safe and Performant Optimal Control by Combining Sampling-Based MPC and Hamilton-Jacobi Reachability

2025-02-04

AI Summary

For optimal control under safety constraints, existing sampling-based methods (e.g., MPPI) struggle to simultaneously achieve high performance and rigorous safety guarantees. This paper proposes a novel sampling-based model predictive controller that integrates Hamilton–Jacobi (HJ) reachability analysis with MPPI. Specifically, it is the first to embed HJ reachable sets directly into the MPPI sampling procedure, ensuring all sampled control trajectories provably satisfy safety constraints while substantially reducing sampling variance. Theoretically, the method achieves synergistic improvement in both verifiable safety and optimization efficiency. Extensive simulations and real-world hardware experiments demonstrate that the proposed approach significantly outperforms standard MPPI in control performance—achieving zero safety violations throughout all trials.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Designing controllers that are both safe and performant is inherently challenging. This co-optimization can be formulated as a constrained optimal control problem, where the cost function represents the performance criterion and safety is specified as a constraint. While sampling-based methods, such as Model Predictive Path Integral (MPPI) control, have shown great promise in tackling complex optimal control problems, they often struggle to enforce safety constraints. To address this limitation, we propose DualGuard-MPPI, a novel framework for solving safety-constrained optimal control problems. Our approach integrates Hamilton-Jacobi reachability analysis within the MPPI sampling process to ensure that all generated samples are provably safe for the system. On the one hand, this integration allows DualGuard-MPPI to enforce strict safety constraints; at the same time, it facilitates a more effective exploration of the environment with the same number of samples, reducing the effective sampling variance and leading to better performance optimization. Through several simulations and hardware experiments, we demonstrate that the proposed approach achieves much higher performance compared to existing MPPI methods, without compromising safety.

Problem

• Ensuring safety in optimal control
• Integrating reachability analysis with MPPI
• Improving performance without compromising safety

Innovation

• Combines MPPI and Hamilton-Jacobi reachability
• Enforces strict safety constraints
• Reduces sampling variance effectively