Finite-time optimal formation tracking control of vehicles in horizontal plane

This paper studies the problem of finite-time optimal formation tracking for planar vehicles which are considered as rigid bodies, under the condition that the tracking time is given according to task requirements in advance. By using Pontryagin's maximum principle (PMP) on a Lie group, an optimal control law is designed for vehicles with holonomic dynamics to track a desired reference trajectory at the given tracking time in the manner of rigid formation which is also specified by task requirements. Simultaneously, a corresponding cost function is considered and guaranteed to be optimal. Then, the above mentioned result of tracking is extended to the case of multi-vehicle systems with a directed-tree communication topology. Furthermore, some conditions are proposed to ensure the adjoint orbits of vehicles to be non-holonomic. Finally, the numerical simulations are provided to illustrate the effectiveness of the theoretical results.