Constraint-oriented formation control of multi-robot system in leaderless consensus under confined conditions

In this paper, constraint-oriented coordination control of a first-order multi-robot system has been considered in a leaderless consensus where rectangular velocity components of participating robots are subject to constraints while also avoiding inter-robots collisions. The desired formation control of different robots and their inter-robots collision avoidance in a team of robots are achieved by solving an optimization problem based on control barrier functions whereas graph theory concepts are used to represent the interaction relations among robots. A devised quadratic programme subject to the velocity and safety conditions, minimizes the desired cost function encoded in the control barrier function and generates separate control inputs for each robot. The rectangular components of the velocity against each robot are kept constrained during the entire operation of the formation control. The optimization-technique-based decentralized controllers were simulated in MATLAB and the corresponding results were recorded. The robots in the team successfully attained the desired formation in a leaderless consensus, deploying themselves in a plane under constrained rectangular velocities without colliding with each other. Several simulation examples with different values of velocity constraints have been shown to illustrate the operation of constrained controllers while ensuring that the desired leaderless-consensus-based formation remains attainable in a safe manner.