Abstract:

We develop a guidance policy for lunar landing under navigational uncertainty with feasible divert in the event a hazard is detected. Offline, we compute stochastic controllable sets under convexified dynamics and constraints that characterize the set of noisy state estimates from which the lander can be driven to a landing site with a pre-specified, sufficiently high probability. We establish that the sets computed for the convexified problem are inner-approximations of the true stochastic controllable sets. The controllable sets are parameterized by available fuel mass and length of trajectory, and provide a tractable method to quickly assess online whether a landing site is reachable. Numerical simulations demonstrate the efficacy of the approach.