Multi-agent formation control with collision avoidance based on discontinuous vector fields

A novel formation control strategy with collision avoidance is presented for the case of two point robots moving in the plane. The control law is based on the design of attractive and repulsive vector fields which guarantee the non-existence of undesired equilibria. The strategy falls in a variable structure control approach which guarantees convergence to the desired formation and non-collision for all initial conditions. The results are extended to the case of formation of unicycles. The performance of the proposed strategy is evaluated over an experimental set-up consisting of two unicycle-type robots.