Stochastic Powered Descent Guidance with Atmospheric Drag and Control Chance Constraint

This paper presents a convex programming approach for random disturbed fuel-optimal powered descent landing in the presence of aerodynamic drag, which is modeled as a chance-constrained covariance control problem. The main challenges for the problem include the nonlinear stochastic dynamics and the nonconvex chance constraints. For stochastic dynamics, successive linearization is applied to eliminate the influence of nonlinearities, and the propagation of the first two moments of stochasticity is obtained by linear covariance analysis. For the nonconvex chance constraints, a conservative approximation is applied to convert chance constraints into deterministic form, and the lossless convexification approach for the deterministic system is employed to convexify the constraints. An iterative covariance steering algorithm is summarized to handle the stochastic fuel-optimal trajectory. In numerical simulation, a Mars' powered descent guidance is exhibited as an example, which shows that the proposed optimal closed loop guidance can achieve the desired landing site with predefined accuracy and satisfy the related control constraint.