Adaptive appointed-time formation tracking control for multiple spacecraft with collision avoidance under a dynamic event-triggered mechanism

This paper focuses on the appointed-time formation control problem for multiple spacecraft with limited communication and control resources. The control objective is to make each spacecraft move along its reference trajectory with guaranteed tracking performance while avoiding collision with each other. To this end, we attempt to propose an event-triggered formation tracking control protocol to achieve this objective. Firstly, a sliding mode manifold containing formation tracking and velocity errors is designed. Then, a group of prescribed performance constraints are imposed on the transient and steady-state behaviors of the newly defined sliding mode manifold, to derive a formation controller with performance guarantees and appointed-time convergence. By integrating the artificial potential function, a collision-free control term is devised, which is plus after the foregoing formation tracking controller to avoid the collision between the neighboring spacecraft. Furthermore, to reduce unnecessary data transmission and improve resource utilization, a dynamic event-triggered strategy is proposed to determine when the developed controller updates. In this case, the threshold parameter in triggering condition is dynamically changed over time rather than being fixed, in order to achieve a desired balance between communication frequency and system performance. Compared with the existing works, the major advantage of the proposed control protocol is that the formation tracking performance, the collision avoidance and the communication transmission preservation can be assured simultaneously. Finally, comparative simulations illustrate the effectiveness of the proposed protocol.