Adaptive Deadlock Avoidance for Decentralized Multi-agent Systems via CBF-inspired Risk Measurement

TL;DR

This work tackles deadlock in decentralized multi-agent control by introducing a generalized CLF-CBF framework augmented with a deadlock indicator that adaptively activates a deadlock-resolution controller. A CBF-inspired risk metric $R_i$ gates activation through a sigmoid $zetai(R_i)$, and an extended CLF $V_q( extbf{x}_i, extbf{Q}_i)=V( extbf{Q}_i extbf{x}_i)$ with rotation dynamics enables transient deviation from task goals to avert deadlock. An auxiliary CBF $h_{ ext{D}_{ij}}$ and a unified QP synthesis over $( extbf{u}_i,oldsymbol{ extomega}_i,delta_i)$ balance task execution, safety, and deadlock avoidance, guaranteeing deadlock-free trajectories under adaptive activation. The approach demonstrates improved task efficiency and safety in both simulations and real-world experiments, highlighting its potential for scalable, robust decentralized multi-agent coordination.

Abstract

Decentralized safe control plays an important role in multi-agent systems given the scalability and robustness without reliance on a central authority. However, without an explicit global coordinator, the decentralized control methods are often prone to deadlock -- a state where the system reaches equilibrium, causing the robots to stall. In this paper, we propose a generalized decentralized framework that unifies the Control Lyapunov Function (CLF) and Control Barrier Function (CBF) to facilitate efficient task execution and ensure deadlock-free trajectories for the multi-agent systems. As the agents approach the deadlock-related undesirable equilibrium, the framework can detect the equilibrium and drive agents away before that happens. This is achieved by a secondary deadlock resolution design with an auxiliary CBF to prevent the multi-agent systems from converging to the undesirable equilibrium. To avoid dominating effects due to the deadlock resolution over the original task-related controllers, a deadlock indicator function using CBF-inspired risk measurement is proposed and encoded in the unified framework for the agents to adaptively determine when to activate the deadlock resolution. This allows the agents to follow their original control tasks and seamlessly unlock or deactivate deadlock resolution as necessary, effectively improving task efficiency. We demonstrate the effectiveness of the proposed method through theoretical analysis, numerical simulations, and real-world experiments.

Figures (5)

• Figure 1: Average distances from current time step positions to goal positions of four agents. Fig. \ref{['fig:comparison']} shows the performance of the CLF-CBF method, CLF-CBF with deadlock resolution method, and our method. Fig. \ref{['fig:zeta']} shows the average $\zeta$ value over the initial 300 time steps in Fig \ref{['fig:comparison']} with our method, where $\zeta = 0$ means the deadlock resolution is not activated and $\zeta \in (0,1)$ means the deadlock resolution is activated.
• Figure 2: The multi-agent position swapping game using four single-integrator agents with the CLF-CBF method (Fig. \ref{['fig:deadlock']}) and CLF-CBF with deadlock resolution method (Fig. \ref{['fig:baseline']}).
• Figure 3: The multi-agent position swapping game using four single-integrator agents with our method.
• Figure 4: Average distance to the target at $t = 500$, indicating the overall task efficiency. The figure is based on various scenarios, each involving a different number of agents starting from different initial positions. For each scenario, ten trials are conducted. The error bars represent the min and max values.
• Figure 5: Four Husarion ROSbot 2 PRO robots WinNT position swapping game with one static obstacle using our method. The filled circle with the same colored arrow represents the goal position of the corresponding robot. The curves are the corresponding real trajectories.

Theorems & Definitions (9)

• Lemma 1
• Lemma 2
• Lemma 3
• Remark 1
• Theorem 4
• proof
• Remark 2
• Remark 3
• Remark 4