Stochastic Reachability for Control of Spacecraft Relative Motion

The concept of stochastic reachability allows for the assessment, before any maneuvers are initiated, of the probability of successfully implementing a rendezvous or docking procedure for spacecraft. The so-called reach-avoid problem lets us find the probability of reaching a target set while avoiding some unsafe or undesired set, despite uncertainty due to nonlinearity and disturbances. This paper examines two novel methods for the calculation of stochastic reachable sets, and specifically for rendezvous and docking problems. In particular, we examine a) particle (or scenario) approximations to expected values, and b) conversion of the reach-avoid probability to a chance-constrained convex optimization problem. Both methods allow for computation of the reach-avoid set in higher dimensions, as compared to other existing methods for computing stochastic reachable sets. We describe in detail both of these methods, and then apply them to spacecraft relative motion, a four-dimensional problem.