Hierarchic Controllability Analysis in High-Dynamic Guidance for Autonomous Vehicle Landing

Abstract

Controllability analysis is significant for guidance law optimization and control system synthesis during atmospheric landing of hypersonic flight vehicles. This article concerns the problem of quantifying the controllability and developing a novel controllability measure, i.e., the degree of controllability (DOC), for linear (or linearized) time-varying systems, and conducts the hierarchically quantitative controllability analysis in high-dynamic guidance for autonomous vehicle landing. In particular, a novel DOC criterion is derived via analyzing the characteristics of singular values and the condition number of the controllability Gramian. The proposed DOC criterion can offer a deep insight into the controllability of both the system and each state subspace, and thus, it possesses a clear physical meaning in practice. Furthermore, a certain normalization and modification method is designed to make the criterion more applicable in aerospace engineering. To validate the derived criterion, the scenario of 3-DOF Mars entry guidance is simulated based on a reference-trajectory tracking scheme with active disturbance rejection control algorithm. According to the simulation results, the optimality of different reference trajectories can be evaluated and compared via the DOC criterion. Therefore, the DOC criterion can function as an indicator to analyze the influence of trajectory parameters on the landing process from the perspective of controllability analysis.