Application of Discrete Time High Order Control Barrier Functions for a prototype multi-spacecraft inspection of the ISS

Sammanfattning: In the past few years, the application of Control Barrier Functions (CBF) and High Order Control Barrier Functions (HOCBF) as a suitable framework to ensure safety for autonomous systems has attracted increasing interest. In particular, autonomous space systems are frequently subject to safety-critical constraints due to the high costs involved in manufacturing and launching. In the present work, the application of a sample data MPC controller subject to CBF and HOCBF constraints is explored as a suitable solution for spacecraft formation flight operations. Specifically, a prototype inspection mission of the International Space Station through a multi-agent formation of CubeSats is explored. Each CubeSat is assumed to be injected in a passive relative orbit around the ISS and controlled such that the state of each agent is maintained within a prescribed safe corridor from its reference relative orbit. Moreover, appropriate conditions on the minimum control authority required to guarantee the constraints satisfaction within the MPC scheme formulation are derived and a numerical procedure to assess the recursive feasibility of the designed controller is presented. Moreover, suitable analytical modifications of the classical CBF and HOCBF constraints definitions are introduced such that the presented sample data MPC control scheme is guaranteed to ensure safety for the state of each agent in between sampling intervals. Lastly, the final control strategy is validated numerically by means of computer simulation.