A tracking guidance method with funnel scheduling for Mars landing

Powered descent guidance is an enabling technology for extraterrestrial soft landing and reusable rocket recovery. Although the focus of guidance research has tilted towards trajectory optimization recently, feedback tracking control is still necessary to suppress the effects of flight perturbations and uncertainties. In this paper, for the Mars landing mission, the behavior of the powered descent closed-loop system is considered and a guidance method based on funnel (finite-time invariant set) scheduling is proposed. Firstly, the basic model of the powered descent problem is given and its state feedback closed-loop system is constructed. Subsequently, considering the thrust uncertainty as well as saturation constraints, the powered descent funnel model is established, and a point-by-point computation method based on Sum of Squares Programming (SOSP) is presented. On this basis, multiple nominal trajectories and their nearby funnels are solved. The guidance scheme based on funnel scheduling is formulated, which utilizes the funnels to provide a good basis for tracking different nominal trajectories, enhancing the adaptability to the initial state dispersions. The simulation results show that for the thrust deviation considered, the states within the funnel inlet can ensure convergence. The similar level of performance on fuel consumption and terminal accuracy of funnel scheduling guidance with convex programming guidance implies the bottleneck in feedback control performance.