Feasibility-guaranteed analytical mars landing guidance in hazardous terrains with disturbances

This paper investigates the Mars landing guidance problem in hazardous terrains. Disturbances during landing, including parameter uncertainties and external forces, may cause the guidance problem infeasible, preventing the lander from avoiding the terrains. To ensure a safe landing, it is crucial, though challenging, to maintain the recursive feasibility of the guidance problem in each guidance cycle. To this end, we propose a two-phase guidance framework, where recursive feasibility is considered only in the first phase and the terminal constraints in this phase are significantly relaxed. This turns the recursive feasibility requirement into the assured satisfaction of the terrain avoidance constraint under disturbances in each guidance cycle. The main contribution of this work lies in analytically deriving a feasible control set and proving that, as long as the control command is within this set, the state at the next guidance cycle must be able to reach the required terminal state while satisfying the terrain avoidance constraint. This guarantees the recursive feasibility of the guidance problem, provided it is feasible in the initial time. As a result, guidance commands in the first phase can be generated by the well-known ZEM/ZEV guidance law, and then simply saturated by the derived feasible control set. In the second phase, the terrain avoidance constraint no longer needs to be considered and the ZEM/ZEV guidance law is applied to drive the lander to the desired location with a safe touchdown velocity. Numerical examples demonstrate that the proposed method can ensure recursive feasibility of the guidance problem under disturbances and is capable of achieving meter-level landing accuracy.