Collision Avoidance in Formation Control Using Discontinuous Vector Fields

Abstract This paper presents a novel collision avoidance approach in formation control for Multi-agent Robots. The control strategy consists in the mix of attractive vector fields and repulsive vector fields based on a scaled unstable focus centered at the position of another robot, instead of the vector fields obtained from the negative gradient of repulsive potential functions. The analysis of the closed-loop system is presented for the case of two point robots. After that, a modification of the composite vector field is proposed adding a discontinuity in order to avoid the undesired equilibria of the system. Real-time experiments using unicycle-type robots show that the control strategy exhibits good performance.