Close proximity formation flying via linear quadratic tracking controller and artificial potential function

•An LQR-based controller is designed for relative motion near eccentric orbits.•An APF-based guidance law is developed for collision avoidance.•The controller and guidance law effectively accomplish collision-free maneuvers of multiple spacecraft. A Riccati-based tracking controller with collision avoidance capabilities is presented for proximity operations of spacecraft formation flying near elliptic reference orbits. The proposed dynamical model incorporates nonlinear accelerations from an artificial potential field, in order to perform evasive maneuvers during proximity operations. In order to validate the design of the controller, test cases based on the physical and orbital features of the Prototype Research Instruments and Space Mission Technology Advancement (PRISMA) will be implemented, extending it to scenarios with multiple spacecraft performing reconfigurations and on-orbit position switching. The results show that the tracking controller is effective, even when nonlinear repelling accelerations are present in the dynamics to avoid collisions, and that the potential-based collision avoidance scheme is convenient for reducing collision threat.