Navigation-Optimal-Guidance for Precision Planetary Landing by Convexification of Estimated-Error-Variance of Navigation

Abstract

This paper presents a navigation optimal powered descent landing guidance for autonomous precision planetary landing. High precision navigation is required for precision landing and use of terrain relative navigation (TRN) is being studied. Since the navigation accuracy of the TRN depends on the landing trajectory, we propose the navigation optimal trajectory to improve landing accuracy. This paper defines the optimal control problem which minimizes the navigation error at landing by using the estimated error covariance of the Kalman filter of the navigation algorithm. By assumption and approximation, around reference trajectory, trace of covariance matrix is linearized with respect to the landing trajectory, and the trajectory is discrete linearized with respect to the dynamics and non-convex constraints. The problem is convexified by these discrete-linearizations and formulated to sub-problem of Second-order cone programming (SOCP). Therefore, this problem is solved by iterative convexification and convex-optimization. The effectiveness of the algorithm is confirmed by Monte Carlo simulation on Mars landing problem. In this simulation, the accuracy of TRN depends on the line of sight distance of the image sensor. The proposed guidance algorithm by using convex programming can potentially be implemented in spacecraft as onboard real-time applications.