Terminal altitude maximization for Mars entry considering uncertainties

Uncertainties present in the Mars atmospheric entry process may cause state deviations from the nominal designed values, which will lead to unexpected performance degradation if the trajectory is designed merely based on the deterministic dynamic model. In this paper, a linear covariance based entry trajectory optimization method is proposed considering the uncertainties presenting in the initial states and parameters. By extending the elements of the state covariance matrix as augmented states, the statistical behavior of the trajectory is captured to reformulate the performance metrics and path constraints. The optimization problem is solved by the GPOPS-II toolbox in MATLAB environment. Monte Carlo simulations are also conducted to demonstrate the capability of the proposed method. Primary trading performances between the nominal deployment altitude and its dispersion can be observed by modulating the weights on the dispersion penalty, and a compromised result referring to maximizing the 3σ lower bound of the terminal altitude is achieved. The resulting path constraints also show better satisfaction in a disturbed environment compared with the nominal situation.