Distributed Hierarchical Control for Collaborative Signal Temporal Logic Tasks via Reconstructed Control Barrier Functions

This paper investigates distributed cooperative control for multi-agent systems (MASs) subject to signal temporal logic (STL) specifications. We begin by encoding the STL formulas into control barrier functions (CBFs) to connect high-level task specifications with low-level system constraints. A key challenge is that collaborative tasks generate coupled CBF constraints, which depend on the states of multiple agents and prevent a distributed control solution. To overcome this, we introduce a novel method that reconstructs these coupled CBFs into decoupled, local constraints. This is achieved using distributed adaptive observers to estimate the states of other agents. We further modify the reconstructed CBFs with a prescribed performance adaptive parameter, which guarantees that satisfying the local constraint ensures the satisfaction of the original, global one. This framework is particularly robust as it remains effective even when collaborative tasks involve uncontrollable agents with uncertain behaviors. Furthermore, to manage multiple STL tasks with a predefined priority hierarchy, we develop a two-step quadratic programming (QP) controller. This controller uses a half-space projection method based on the reconstructed CBFs to ensure that the execution of lower-priority tasks never interferes with higher-priority ones. We demonstrate that our proposed distributed control scheme enables MASs to achieve complex collaborative STL tasks, as supported by physical simulations. Note to Practitioners—The tasks faced by robotic systems, such as cooperative transportation for warehouse robots and cooperative navigation for autonomous vehicles, are growing in complexity. Traditional control objectives, like trajectory tracking and stabilization, are often insufficient to capture these complex tasks. Consequently, temporal logic, as a formal language, is employed to specify these complex tasks. In this work, we begin by using signal temporal logic (STL) specifications to precisely define these complex tasks. These specifications are then translated into system constraints using control barrier function (CBF) techniques. When multiple autonomous systems are required to collaborate on a task, it results in “coupled” CBF constraints, which impede the implementation of a distributed control scheme. To solve this, our main contribution is a novel method to reconstruct these coupled constraints into local ones that each system can follow on its own. Furthermore, since these systems usually need to handle multiple tasks simultaneously, we developed a hierarchical task control scheme. This allows the system to handle tasks according to a predefined priority hierarchy. The proposed distributed control scheme is robust enough to function reliably even in uncertain dynamic environments. The proposed method is applicable to solving complex collaborative tasks for multiple autonomous systems and its efficacy is demonstrated through physical simulations.