Time-optimal trajectory planning for a rigid formation of nonholonomic mobile platforms

Abstract This paper presents a method for planning time-optimal trajectories for a formation of multiple nonholonomic (heavy duty) platforms (HDPs) to cooperatively transport an object to a specified pose. The first part addresses the mobile platforms themselves while the second part provides a trajectory planning approach derived from the well-known virtual leader approach . In order to ensure proper transport of the shared payload, the vehicles are modeled individually, resulting in a formation control problem. The goal of the optimization process is to minimize a cost function that balances time optimality, smooth control signals, and formation rigidity. The optimal control problem (OCP) takes into account the kinematics of the vehicles as well as their physical limitations. It is solved by using a multiple shooting method, which yields the desired trajectories for all vehicles while ensuring smooth control signals. The paper includes optimization results for several scenarios involving two and three HDPs together with various target poses, demonstrating the effectiveness of the proposed method.