Almost-Global Formation Tracking Control for Multiple Vehicles With Disturbance Rejection

This paper studies the anti-disturbance control scheme for multiple vehicles formation tracking a specified trajectory. By communicating connections, these vehicles form a vehicle network. The communication topology of the network is a directed acyclic graph. Each node vehicle is modeled as a fully actuated rigid body on SE(3)(a Special Euclidean group) with an unknown constant disturbance, except the root node, which is used to specify the trajectory to be tracked. By means of Euclidean group operation and the convex combination theory on Euclidean group, the problem is first converted to the leader-follower tracking control for two vehicles. Then, without using local coordinates, an almost-globally exponential anti-disturbance tracking control law with the knowledge of the leader's acceleration is designed by using Lyapunov stability theory which achieves formation tracking a given trajectory. To overcome the difficulties in practical obtaining acceleration information of the vehicle being tracked, a dynamic acceleration estimator is designed by using singular perturbation method, thereafter the formation tracking control law based on the acceleration estimator is constructed. For demonstration of the result, some numerical examples have been included.