Capabilities of convex Powered-Descent Guidance algorithms for pinpoint and precision landing

The PDG (Powered Descent Guidance) algorithm provides a numerical method for onboard generation of guidance profiles for use during the powered-descent phase of Mars pinpoint or precision landing. The algorithm incorporates both state and control constraints, including minimum and maximum thrust limits, glideslope constraints to avoid impacting the surface, and speed and attitude constraints. These constraints are particularly important for powered-descent scenarios requiring large-divert capabilities to achieve pinpoint or precision landing. Additionally, the constraints ensure that guidance profiles are physically achievable. For instance, the thrust limits are particularly relevant for spacecraft that implement rocket engines that cannot be throttled off after ignition. The formulation of PDG poses the problem as a SoCP (Second-order Cone Program) that can be solved with numerically-efficient interior-point solvers in a finite time to within a prescribed accuracy. This feature is ideal for onboard implementation during powered descent where total flight time is short, thus guidance methods must guarantee convergence to an achievable solution within a short time. If a spacecraft can physically perform maneuvers to achieve pinpoint or precision landing (i.e., the problem is feasible), then the SoCP formulation of PDG will find the solution. Further, this solution will satisfy the prescribed constraints on position, fuel, thrust, speed and attitude.