Powered Descent Trajectory Optimization of Chandrayaan-3 using Radau Collocation and Controllable Sets

India achieved a significant milestone on August ${23}^{\text{rd}}$ 2023, becoming the fourth country to accomplish a soft landing on the Moon. This paper presents the powered descent trajectory design for the Chandrayaan-3 mission. The optimization framework is based on pseudospectral Radau collocation, and controllability-based waypoint refinement is employed to further enhance the robustness of the trajectory against state and control perturbations. Furthermore, the trade-off between fuel consumption and robustness is explicitly quantified, providing insights into the practical considerations of mission planning.