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SpaceX: just optimal control or something else?
SpaceX uses a particular set of control laws, called Guidance for Fuel Optimal Large Divert (G-FOLD). This is an algorithm that is developed to compute, onboard in real-time, fuel optimal trajectories for large divert maneuvers necessary for planetary pinpoint or precision landing. It uses loseless convexification for converging into a globally optimal solution that incorporates all relevant mission constraints. But, what does it mean?
Trajectory optimization is the process of designing a trajectory that minimizes (or maximizes) some measure of performance while satisfying a set of constraints. In general terms, trajectory optimization is a technique for computing an open-loop solution to an optimal control problem.
On the other hand, lossless convexification refers to the process of obtaining a convex relaxation of an optimization problem, where an optimal solution of the relaxed problem also defines an optimal solution for the original non-convex problem. The main issue with this approach lies on the original problem boundaries and its approximation with a convex problem.
In this application, lossless convexification is used to assesses planetary soft landing, which is gaining renewed interest due to the increased focus on the exploration of planets in the solar system. The soft landing problem with all…
