Trajectory design for landing on small celestial body with flexible lander

This paper investigates the trajectory design for landing on a small celestial body with a flexible lander. The flexible lander features a flexible structure that increases surface contact area and facilitates the dissipation of residual kinetic energy. Compared with rigid landing, flexible landing, which utilizes a flexible lander to execute the landing process, offers enhanced safety during the landing operation. However, the introduced nonlinear flexible force will degrade the convergence of landing trajectory optimization. To address this challenge, the homotopic approach is employed to smoothly connect the trajectory optimization problem from rigid landing to flexible landing. Then, the connection between the optimal solution of the rigid problem and the flexible problem is revealed in detail with the presented theorem. Based on this theorem, the flexible landing fuel optimal trajectory is generated by iteratively solving a sequence of convexified and discretized homotopic problems. The effectiveness of the proposed algorithm is demonstrated through 433 Eros flexible landing mission based numerical simulations.