Reduction and nonlinear controllability of symmetric distributed systems with robotic applications

The purpose of this paper is to develop methods to reduce the complexity of nonlinear distributed systems by using symmetry properties within the system. A method for contracting and expanding controllable nonlinear systems is developed which maintains the controllability of the original system. In fact, it is shown that an entire equivalence class of symmetric nonlinear distributed control systems can be determined by checking the controllability of only one of its members. A group of mobile robots is used to demonstrate the utility of methods presented.