Controllable set analysis for planetary landing under model uncertainties

Controllable set analysis is a beneficial method in planetary landing mission design by feasible entry state selection in order to achieve landing accuracy and satisfy entry path constraints. In view of the severe impact of model uncertainties on planetary landing safety and accuracy, the purpose of this paper is to investigate the controllable set under uncertainties between on-board model and the real situation. Controllable set analysis under model uncertainties is composed of controllable union set (CUS) analysis and controllable intersection set (CIS) analysis. Definitions of CUS and CIS are demonstrated and computational method of them based on Gauss pseudospectral method is presented. Their applications on entry states distribution analysis under uncertainties and robustness of nominal entry state selection to uncertainties are illustrated by situations with ballistic coefficient, lift-to-drag ratio and atmospheric uncertainty in Mars entry. With analysis of CUS and CIS, the robustness of entry state selection and entry trajectory to model uncertainties can be guaranteed, thus enhancing the safety, reliability and accuracy under model uncertainties during planetary entry and landing.