Stochastic Safety in Space Conjunctions

The stochastic reach-avoid problem termed p-safety is further examined in the context of space debris and short-term orbital encounters. We define the collision probability problem, and reformulate it as a strong p-safety problem, which offers a computable solution. Enabling computation comes at the cost of a more restrictive formulation which requires several relaxation schemes. To this end, Bernstein forms are employed as polynomial approximation of the nonlinear dynamics, and sum-of-squares as bases to attain certificates of positivity. Finally, a stochastic version of the unperturbed planetary equations is used to model the dynamics.