Landing Footprint Computation and Simulation for Spacecraft of Reentry Phase

Flexible and rapid computation of landing footprints for spacecraft of reentry phase is the crucial capability required for on-board options of possible landing sites. Mathematically, the problem is formulated as maximizing the crossrange for any downranges. Since solving the necessary optimality for the 3DOF model with Earth’s rotation proves to be a difficult task, some simplifications were made. Using energy-state approximations, the equations of motion are simplified. Based on the quasi-equilibrium glide condition (QEGC), the typical inequality constraints are enforced with velocity-dependent boundary constraints about the bank angle. Using Gauss pseudospectral method (GPM), the maximum crossrange optimization problem is converted to a nonlinear programming (NP) problem, which is solved by the sequential quadratic programming (SQP) algorithm. The approach is tested using the Apollo 11 model, and the simulation results prove the proposed algorithm could determinate landing footprints for the spacecraft of reentry phase reliably and simultaneously satisfy all the path constraints.