Bounded controllers for formation stabilization of mobile agents with limited sensing ranges

A constructive method is presented to design bounded cooperative controllers that force a group of N mobile agents with limited sensing ranges to stabilize at a desired location, and guarantee no collisions between the agents. The control development is based on new general potential functions, which attain the minimum value when the desired formation is achieved, and are equal to infinity when a collision occurs. A p-times differential bump function is introduced and embedded into the potential functions to deal with the agent limited sensing ranges. An alternative to Barbalat's lemma is developed to analyze stability of the closed loop system. Extension to formation tracking is also addressed.