Quasi-Spectral Unscented MPSP Guidance for Robust Soft-Landing on Asteroid

A new quasi-spectral version of unscented model predictive static programming is proposed, which is a fusion of two philosophies, namely the unscented optimal control formulation (which in turn is inspired from the unscented Kalman filter philosophy) as well as the model predictive static programming, which is known for its computational efficiency. The proposed technique greatly diminishes the impact of uncertainties in the system parameters and the initial condition of the state. In this design, a much lesser number of free variables is used in the process than the existing unscented optimal control methods. As the optimization problem eventually leads to the optimal selection of coefficients of the basis functions, the overall dimension of the optimization process is significantly reduced. The significance of the proposed technique is demonstrated by successfully solving the soft-landing problem on asteroid Vesta. For emphasizing the importance of the proposed technique, the numerical analysis of the powered descent phase of the lander is presented in detail while comparing with the existing methods.