Distributed event-triggered fixed-time formation tracking control for multi-spacecraft systems based on adaptive immersion and invariance technique

The problem of fixed-time formation tracking for multi-spacecraft systems without internal collisions is investigated in this paper. A novel adaptive immersion and invariance (I&I)-based control protocol is designed to solve this technical problem, with the goal of driving formation members to accurately realize and maintain the required configuration within the user-given time. The novelty here lies in two things. First and foremost, unlike the asymptotic convergence of the traditional I&I related works, the proposed protocol guarantees the fixed-time stability by integrating the prescribed performance control. Secondly, the event-triggered mechanism is adopted to alleviate the pressure of communication resources between formation members and reduce unnecessary information interaction. Lyapunov stability analysis shows that the proposed protocol can enable the defined implicit manifold to converge to the origin for most initial conditions. Also, benefiting from the prescribed performance techniques, the convergence time eliminates the dependence of designed controller parameters or initial system conditions, relying only on the actual mission requirements. In addition, we adopt a linear extended state observer to deal with the parameter uncertainties and external disturbances, and use the I&I adaption to estimate the observer errors to further improve the system performance. Moreover, a new exponential-type artificial potential function is designed to avoid close proximity between formation members and prevent internal collisions. Finally, numerical simulations are provided to verify the theoretical results.