Formation Stabilization of Multiple Agents Using Decentralized Navigation Functions

We develop decentralized cooperative controllers, which are based on local navigation functions and yield (almost) global asymptotic stability of a group of mobile agents to a desired formation and simultaneous collision avoidance. The formation could be achieved anywhere in the free space; there are no pre-specified final positions for the agents and is rendered stable both in terms of shape and in terms of orientation. Shape and orientation stabilization is possible because the agents regulate relative positions rather than distances with respect to their network neighbors. Asymptotic stability is provable and guaranteed, once the parameters in the local navigation functions are tuned based on the geometry of the environment and the degree of the interconnection network. Feedback controllers steer the agents away from stationary point-obstacles and into the desired formation using information that can be obtained within their sensing neighborhood and through communication with their network neighbors. The methodology is tested in simulation where groups of three and four mobile agents come into formations of triangles and diamonds, navigating amongst obstacles.