Fail-safe Rendezvous Control on Elliptic Orbits using Reachable Sets

In this paper, a fail-safe control policy is developed for rendezvous on generic elliptic orbits using backwards reachable sets and model predictive control (MPC). The backwards reachable sets are computed as unsafe regions of state space that, in the event of total thruster failure, would lead to a collision between the chaser spacecraft and the rendezvous target. The backwards reachable sets are incorporated as passive safety constraints in the MPC online trajectory generation in order to guide the chaser to rendezvous with its target through an inherently safe approach. Simulations demonstrate the effectiveness of the passive safety constraints in altering a nominally unsafe rendezvous to one that is passively safe.