Finite-time formation tracking control for multiple vehicles: A motion planning approach

This paper addresses the finite‐time formation tracking problem for multiple vehicles with dynamics model on SE(3) (the specific Euclidean group of rigid body motions), under the condition that the tracking time is preassigned according to the task requirements. By using Pontryagin's maximum principle on Lie groups, a class of finite‐time optimal tracking control laws are designed for vehicles to track a desired trajectory within a given finite time. Meanwhile, the corresponding cost function is minimized. Furthermore, a tracking‐time lower bound is derived for multi‐vehicle systems with control constraints. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed control laws