Distributed Safety Critical Control among Uncontrollable Agents using Reconstructed Control Barrier Functions

This paper investigates the distributed safety critical control for multi-agent systems (MASs) in the presence of uncontrollable agents with uncertain behaviors. To ensure system safety, the control barrier function (CBF) is employed in this paper. However, a key challenge is that the CBF constraints are coupled when MASs perform collaborative tasks, which depend on information from multiple agents and impede the design of a fully distributed safe control scheme. To overcome this, a novel reconstructed CBF approach is proposed. In this method, the coupled CBF is reconstructed by leveraging state estimates of other agents obtained from a distributed adaptive observer. Furthermore, a prescribed performance adaptive parameter is designed to modify this reconstruction, ensuring that satisfying the reconstructed CBF constraint is sufficient to meet the original coupled one. Based on the reconstructed CBF, we design a safety-critical quadratic programming (QP) controller and prove that the proposed distributed control scheme rigorously guarantees the safety of the MAS, even in the uncertain dynamic environments involving uncontrollable agents. The effectiveness of the proposed method is illustrated through a simulation.

💡 Research Summary

The paper addresses the problem of safety‑critical control for multi‑agent systems (MAS) when some agents are uncontrollable and exhibit uncertain behavior. Traditional control‑barrier‑function (CBF) methods enforce safety by imposing a single, globally coupled constraint that depends on the states of all agents. This coupling forces a centralized implementation and becomes infeasible when uncontrollable agents (e.g., pedestrians, human‑driven vehicles) are present, because their control inputs cannot be prescribed and therefore the coupled constraint cannot be satisfied locally.

To overcome these limitations, the authors propose a reconstructed CBF framework together with a distributed adaptive observer. The observer enables each controllable agent to estimate the states of all other agents (both controllable and uncontrollable) using only local communication over an undirected, connected graph. The observer dynamics (Eq. 7) include an adaptive gain ˆδ that is updated online; a Lyapunov‑based analysis shows that the estimation error is uniformly bounded and converges to a small residual set whose size depends on known Lipschitz constants, graph eigenvalues, and the adaptive gain parameters.

Using the estimated states, each agent builds a local reconstructed barrier function (\hat h_i) that approximates the original global barrier (h(x)). A prescribed‑performance adaptive parameter is introduced to tighten the reconstructed barrier so that satisfying (\hat h_i\ge 0) is a sufficient condition for the original safety condition (h(x)\ge 0). The authors prove this sufficiency by exploiting the positive‑definiteness of the matrix (H_j = L + B_j) (where (L) is the graph Laplacian) and by designing the adaptive parameter to dominate the coupling terms.

With the reconstructed barrier in hand, each controllable agent solves a local quadratic program (QP): \