Control of Multi-Agent Systems with Finite Time Control Barrier Certificates and Temporal Logic

TL;DR

This paper introduces a novel control synthesis method for multi-agent systems that guarantees finite-time convergence and task satisfaction based on control barrier functions and temporal logic, validated through robotic experiments.

Contribution

It presents a new framework combining finite time control barrier functions with temporal logic for multi-agent control synthesis, enhancing flexibility and feasibility.

Findings

Guarantees finite-time convergence to desired states.

Ensures forward invariance after convergence.

Successfully applied in robotic experiments on multi-robot testbed.

Abstract

In this paper, a method to synthesize controllers using finite time convergence control barrier functions guided by linear temporal logic specifications for continuous time multi-agent dynamical systems is proposed. Finite time convergence to a desired set in the state space is guaranteed under the existence of a suitable finite time convergence control barrier function. In addition, these barrier functions also guarantee forward invariance once the system converges to the desired set. This allows us to formulate a theoretical framework which synthesizes controllers for the multi-agent system. These properties also enable us to solve the reachability problem in continuous time by formulating a theorem on the composition of multiple finite time convergence control barrier functions. This approach is more flexible than existing methods and also allows for a greater set of feasible control laws. Linear temporal logic is used to specify complex task specifications that need to be satisfied by the multi-agent system. With this solution methodology, a control law is synthesized that satisfies the given temporal logic task specification. Robotic experiments are provided which were performed on the Robotarium multi-robot testbed at Georgia Tech.