Computing Safe Control Inputs using Discrete-Time Matrix Control Barrier Functions via Convex Optimization

2025-10-10

AI Summary

Real-time computation of safety-preserving control inputs for discrete-time systems subject to nonconvex safe sets is challenging due to inherent nonconvexity in the underlying safety constraints. Method: This paper proposes a novel design framework integrating matrix control barrier functions (MCBFs) with convex optimization. We extend MCBFs—originally formulated for continuous-time systems—to discrete-time dynamics and construct an equivalent convex optimization problem via judicious convex relaxation, thereby circumventing direct solution of nonconvex programs while ensuring forward invariance of the safe set. Contribution/Results: The method unifies system dynamics, safety requirements, and convexification techniques to significantly improve computational efficiency and online implementability. Extensive simulations on a quadrotor platform demonstrate the approach’s superiority in safety enforcement, state convergence, and real-time performance. This work establishes a new paradigm for safety-critical control under nonconvex safety constraints.

Technology Category

• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Control barrier functions (CBFs) have seen widespread success in providing forward invariance and safety guarantees for dynamical control systems. A crucial limitation of discrete-time formulations is that CBFs that are nonconcave in their argument require the solution of nonconvex optimization problems to compute safety-preserving control inputs, which inhibits real-time computation of control inputs guaranteeing forward invariance. This paper presents a novel method for computing safety-preserving control inputs for discrete-time systems with nonconvex safety sets, utilizing convex optimization and the recently developed class of matrix control barrier function techniques. The efficacy of our methods is demonstrated through numerical simulations on a bicopter system.

Problem

• Computing safe control inputs for discrete-time systems
• Overcoming nonconvex optimization in safety-critical control
• Ensuring forward invariance via convex optimization methods

Innovation

• Uses convex optimization for safety guarantees
• Applies matrix control barrier function techniques
• Handles nonconvex safety sets in discrete-time systems