Cooptimizing Safety and Performance Using Safety Value-Constrained Model Predictive Control

2026-04-26

AI Summary

This work addresses the challenge of achieving both high performance and provable safety for autonomous systems operating in real-world environments, where conventional model predictive control (MPC) often fails to guarantee safety beyond the finite prediction horizon. The authors propose a novel approach that constructs terminal constraints using a safety value function derived from reachability analysis, ensuring that the planned trajectory terminates within a controlled invariant safe set. This formulation guarantees recursive feasibility while enabling real-time, provably safe trajectory optimization with high task performance. In contrast to existing methods that rely on local linearization or overly conservative approximations, the proposed technique significantly reduces conservatism and enhances expressiveness of safety guarantees. Simulations and hardware experiments on a Flexiv Rizon 10s robotic arm demonstrate that the method substantially improves constraint satisfaction and robustness compared to standard MPC and reactive safety filters, without compromising task performance.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Natural Language Processing: Safety and Robustness
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Autonomous systems are increasingly deployed in real-world environments, where they must achieve high performance while maintaining safety under state and input constraints. Although Model Predictive Control (MPC) provides a principled framework for constrained optimal control, guaranteeing safety beyond its finite planning horizon remains a fundamental challenge. In this work, we augment MPC with a safety value function-based terminal constraint that enforces membership in a control-invariant safe set at the end of each planning horizon. This formulation enables real-time synthesis of trajectories that are both high-performing and provably safe. We show that, under an exact safety value function and a feasible initialization, the proposed MPC scheme is recursively feasible, thereby ensuring persistent safety. In contrast to traditional terminal set constructions that rely on local linearizations or conservative approximations, our approach incorporates a reachability-based safety value function for terminal constraints, yielding less conservative and more expressive safety guarantees. We validate the proposed framework through simulation and hardware experiments on a Flexiv Rizon 10s manipulator. Results demonstrate improved constraint satisfaction and robustness compared to standard state-constrained MPC and reactive safety filtering, while maintaining competitive task performance. The full implementation and experiments are available on the project website.

Problem

• Safety
• Model Predictive Control
• Autonomous Systems
• Control Invariance
• Constraint Satisfaction

Innovation

• Safety Value Function
• Model Predictive Control
• Control-Invariant Set
• Recursive Feasibility
• Reachability Analysis