Reduced order motion planning for nonlinear symmetric distributed robotic systems

This paper develops a motion planning algorithm which exploits symmetry in distributed systems to reduce complexity and motion planning design time. The motion planning computations are carried out on a reduced order system, then extended to larger-order equivalent systems in such a way that the objectives of the larger system are satisfied and collision avoidance is guaranteed. The algorithm maintains a rigid body formation as a group robots follows a specified trajectory at the beginning and end of the trajectory. At this point, our algorithm is open loop. A simulation of four robots maintaining a square formation is presented to demonstrate the utility of the algorithm.