Non-Gaussian Chance-Constrained Trajectory Control Using Gaussian Mixtures and Risk Allocation

Standard chance-constrained trajectory control algorithms typically rely on the assumption that the vehicle state uncertainties obey Gaussian distributions. While this is a valid assumption for many systems, this paper considers the class of real-life systems for which this assumption does not hold - for example, systems with highly nonlinear dynamics such as spacecraft maneuver planning problems. This paper extends the chance-constrained control formulation to consider a non-Gaussian distribution by approximating the distribution as a mixture of Gaussian distributions. The original chance constraint is then approximated as a conjunction of weighted individual chance constraints on each of the distributions in the mixture. Iterative risk allocation is used in a two-stage op-timization procedure to minimize the degree of conservatism in this approximation. The method is applied to a simple impulsive stochastic spacecraft maneuver targeting problem in two-body dynamics. The resulting algorithm accurately computes control parameters that satisfy the probabilistic bounds on the non-Gaussian distribution.