Finite-time Formation Tracking Control for Vehicles Based on Motion Planning Approach

This paper addresses the finite-time formation tracking problem for vehicles with dynamics model on SE(3) (the specific Euclidean group of rigid body motions), under the condition that the tracking time is given according to task requirements in advance. By using Pontryagin's maximum principle (PMP) on Lie groups, a finite-time optimal tracking control law is designed for vehicles to track a desired trajectory at the given time. Simultaneously, the corresponding cost function is guaranteed to be optimal. To demonstrate the effectiveness of the proposed control law, an illustrative example is provided.