A Control Barrier Function Composition Approach for Multi-Agent Systems in Marine Applications

TL;DR

This work addresses safe coordination of marine multi-agent systems under complex relative-pose constraints, including FOV, LOS, range, and collision avoidance. It develops a framework that encodes these constraints as nonsmooth control barrier functions (NCBFs) and combines them with Boolean composition into a single BNCBF, enabling unified safety guarantees. A dual-based approach handles the LOS min-distance constraint, and a quadratic program (BNCBF-QP) computes a safe control input that minimally alters the nominal reference. The method is validated through simulations and experiments with real maritime platforms, demonstrating reliable constraint satisfaction and scalable performance for large-scale marine MAS tasks.

Abstract

The agents within a multi-agent system (MAS) operating in marine environments often need to utilize task payloads and avoid collisions in coordination, necessitating adherence to a set of relative-pose constraints, which may include field-of-view, line-of-sight, collision-avoidance, and range constraints. A nominal controller designed for reference tracking may not guarantee the marine MAS stays safe w.r.t. these constraints. To modify the nominal input as one that enforces safety, we introduce a framework to systematically encode the relative-pose constraints as nonsmooth control barrier functions (NCBFs) and combine them as a single NCBF using Boolean composition, which enables a simplified verification process compared to using the NCBFs individually. While other relative-pose constraint functions have explicit derivatives, the challenging line-of-sight constraint is encoded with the minimum distance function between the line-of-sight set and other agents, whose derivative is not explicit. Hence, existing safe control design methods that consider composite NCBFs cannot be applied. To address this challenge, we propose a novel quadratic program formulation based on the dual of the minimum distance problem and develop a new theory to ensure the resulting control input guarantees constraint satisfaction. Lastly, we validate the effectiveness of our proposed framework on a simulated large-scale marine MAS and a real-world marine MAS comprising one Unmanned Surface Vehicle and two Unmanned Underwater Vehicles.

Figures (8)

• Figure 1: A marine MAS with optical communication.
• Figure 2: Simulated MAS: diamonds represent goal points; the blue and red tetrahedrons represent the follower and leader agents, respectively; the cyan tetrahedrons represent the obstacles; the dotted lines correspond to active LOS connections to the leader; the dotted curves in (b) are trajectories of the agents; (a) $t = 0$ secs and (b) $t = 20$ secs.
• Figure 3: Demonstration of the LOS constraint.
• Figure 4: Evolution of NCBF: solid blue line and dashed lines represent $h_g$ and the component functions, respectively; dashed red line represents the $0$-level.
• Figure 5: Experiment setup

Theorems & Definitions (11)

• Definition 1: magnus_tac
• Definition 2: Definition 1, magnus_ccta
• Definition 3: Definition 2, magnus_ccta
• Theorem 1: Theorem 3, magnus_lcs
• Definition 4
• Lemma 1: Lemma 10 dual_full (with reformed notations)
• Lemma 2
• proof
• Theorem 2
• proof