Multiagent Navigation Functions Revisited

This paper presents a methodology to design a control law that can provably steer a group of mobile agents to a free-floating formation of specific shape, while avoiding collisions. We indicate why existing multiagent solutions have a theoretical limitation due to one of the working assumptions of the single-agent potential function approach being violated. A new nonsmooth type of multiagent potential functions is, thus, developed. It is shown how this extension of the navigation function concept to multiagent systems ensures the nondegeneracy of the critical points of the potential function.