Online feedback motion planning for spacecraft obstacle avoidance using positively invariant sets

This paper investigates a novel reliable feedback motion planning algorithm for steering a spacecraft to the desired position while satisfying dynamics and environmental constraints, such as actuator constraints, unexpected state constraints, bounded disturbances, etc. The proposed algorithm, termed safeRRT∗, applies positively invariant (PI) set transitions to an online sampling approach based on the asymptotically optimal rapidly-exploring random tree (RRT∗). A time-varying safe corridor is generated which consists of a sequence of PI sets under the instantaneous constraints. A spacecraft is guaranteed to remain within the corridor when the feedback controllers corresponding to the PI set transitions are executed. Simulations of the spacecraft avoiding obstacles validate the feasibility and effectiveness of the proposed safeRRT∗ algorithm.