Prescribed-time collision-free formation tracking control for multiple spacecraft using control barrier functions

Abstract:

To significantly enhance the response speed of spacecraft formation coordination and meet strict time-window requirements for formation missions, this paper develops a novel prescribed-time performance-guaranteed control framework. This framework effectively addresses three critical challenges prevalent in formation systems: limited perception range, actuator saturation constraints, and inter-agent collision avoidance requirements. First, by integrating error transformation technique with sliding mode control, a control Lyapunov function condition is constructed. This design not only ensures the system meets strict timing requirements for formation tasks, but also guarantees prescribed transient response characteristics and steady-state performance metrics. Second, through the establishment of high-order control barrier functions, precise regulation of relative distances between adjacent spacecraft is achieved, maintaining formation communication topology connectivity while effectively preventing collision risks. Furthermore, this study employs quadratic programming to solve for optimal control inputs, realizing multi-objective coordinated optimization of prescribed-time convergence, topology connectivity maintenance, and collision avoidance control under actuator saturation constraints. To validate the effectiveness of the proposed control framework, systematic performance verification is conducted through numerical simulations. The simulation results fully demonstrate the reliability and superiority of the proposed control scheme in satisfying all specified constraints.