Online Safety under Multiple Constraints and Input Bounds using gatekeeper: Theory and Applications

2025-08-13

AI Summary

This paper addresses the online safety-critical control problem for cyber-physical systems subject to multiple state and input constraints. We propose the Gatekeeper framework, which recursively verifies—via a backup controller—the existence of infinitely-horizon feasible trajectories, thereby ensuring real-time satisfaction of system dynamics and nonconvex, nonlinear constraints (e.g., obstacles, engagement zones). Theoretical contributions include: (i) establishing a complete Gatekeeper theory; (ii) deriving the first provable suboptimality bound relative to nonlinear trajectory optimization; (iii) enabling joint runtime verification of safety and performance; and (iv) reducing controller synthesis to optimizing a single scalar variable under minimal, verifiable assumptions. We validate the approach on multi-agent Dubins vehicle formations, demonstrating low computational overhead, high scalability, and real-time safety guarantees.

Technology Category

Planning, Routing, and Scheduling: Optimization of Spatio-temporal SystemsConstraint Satisfaction and Optimization: Satisfiability Modulo TheoriesSearch and Optimization: Mixed Discrete/Continuous Search

Application Category

Security and Privacy: Large-scale security measurementsSystems and Infrastructure for Web, Mobile and WoT: Novel mobile and WoT systems, and system-of-systemsEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

This letter presents an approach to guarantee online safety of a cyber-physical system under multiple state and input constraints. Our proposed framework, called gatekeeper, recursively guarantees the existence of an infinite-horizon trajectory that satisfies all constraints and system dynamics. Such trajectory is constructed using a backup controller, which we define formally in this paper. gatekeeper relies on a small number of verifiable assumptions, and is computationally efficient since it requires optimization over a single scalar variable. We make two primary contributions in this letter. (A) First, we develop the theory of gatekeeper: we derive a sub-optimality bound relative to a full nonlinear trajectory optimization problem, and show how this can be used in runtime to validate performance. This also informs the design of the backup controllers and sets. (B) Second, we demonstrate in detail an application of gatekeeper for multi-agent formation flight, where each Dubins agent must avoid multiple obstacles and weapons engagement zones, both of which are nonlinear, nonconvex constraints.

Problem

• Ensures cyber-physical system safety under multiple constraints
• Guarantees infinite-horizon trajectory satisfying dynamics and limits
• Applies to multi-agent flight with nonlinear obstacle avoidance

Innovation

• Recursive infinite-horizon trajectory guarantee
• Scalar variable optimization for efficiency
• Backup controller for constraint satisfaction