Uncertainty analysis of reachable set for planetary entry using polynomial chaos

Reachable set (RS) is a useful tool in assessing the flight capability of the entry vehicle with the given initial entry state and the required control and path constraints. The evolution of the RS under the effects of uncertainties of some important entry parameters is also beneficial to the mission design and analysis. The objective of this paper is to investigate the RS evolution under parameter uncertainties. It would be computationally intensive to compute all the elements of the RS, and therefore only the RS boundary (RSB) extreme points, which well characterize the RS, are considered. The method of tracking drag profile is employed to generate each point of the RSB. By parameterizing the random uncertainties and introducing random parameters in uncertainties, the uncertainty analysis problem of the RSB is converted to a stochastic trajectory approximation problem, which can be solved by the polynomial chaos expansion-based method. The evolutions of the RSB under uncertainties of initial flight path angle, lift-to-drag ratio and atmospheric density are illustrated by a specific Mars entry mission. With uncertainty analysis of the RSB, the robustness of deployment site selection and the satisfaction of path constraints under uncertainties can be quantified in the entry mission design, thus enhancing the safety, reliability and accuracy of entry missions.