Control barrier functions enable the design of controllers capable of guaranteeing safe maneuvers. The possibility of including constraints of high relative degree was recently studied in the literature. These contributions are pertinent to tackle collision avoidance of satellites because the constraint can be formulated as a function of the relative position of the satellites, while controls are on their relative accelerations (hence, the constraint is of relative degree 2). The stage is devoted to the numerical implementation of these techniques. To this end, a simplified problem will first be considered, namely a double integrator with bounds on the maximum control action will be used to model the relative dynamics. If time permits, a linearized dynamical model for the relative motion between two satellites will be considered. In view of a perspective onboard implementation of the algorithms, special care will be devoted to the computational efficiency of the controller.
Breeden, J.; Panagou, D. High Relative Degree Control Barrier Functions Under Input Constraints. Proceedings of 60th IEEE Conference on Decision and Control (2021).