Reciprocal collision avoidance for a group of second order agents

This paper focuses in the design of a formation control strategy for a group of second order agents while they avoid collisions against each other and possible obstacles, either static or dynamic. The control strategy is based on artificial potential functions. For the collision avoidance, the main novelty is the adaptation of the known results about repulsive vector fields for single integrator dynamics applied to the second order dynamics. The repulsive vector fields are based on a scaled counter clockwise unstable focus centered at the position of the other agents or obstacles. The control strategy is implemented on two different systems: second order dynamics and quadrotor dynamics. The theoretical results are verified by numerical simulations.