Semi-analytical and extremal solutions for design and synthesis of powered descent and landing trajectories

摘要

Semi-analytical solutions to the optimal control problem for 3-dimensional fuel-efficient planetary landing trajectories with constant exhaust velocity and limited mass-flow rate in a drag-existing central Newtonian field are presented. The first-order optimality conditions reduce the problem to a Hamiltonian canonical system for the design and synthesis of feasible and extremal planetary entry, descent, and landing trajectories. The proposed solutions allow us to describe the state vector and Lagrange multipliers in terms of time and switching function's characteristics to determine the number and sequence of thrust arcs. These solutions can be adjusted for manoeuvres near other celestial bodies for which a central gravitational acceleration can be dominant. The paper describes new extremal trajectories, which are based on the analysis of first- and second-order optimality conditions. The results of this work can be used to support mission design analysis and synthesis of fuel-efficient trajectories.