The Powered Descent Guidance (PDG) software provides a computationally efficient guidance algorithm for powered descent that ensures satisfaction of the governing dynamics, along with adherence to physical control and state constraints, such as avoid the surface, limit thrust magnitude and pointing, and divert based on available fuel. The software can generate guidance profiles for precision landing (or pinpoint landing when feasible) and also incorporate smart diverts to avoid the backshell landing corridor.
The PDG enhancements allow enforcing thrust-pointing constraints (e.g., avoid profiles with downward thrust directions) and limiting maximum speed (e.g., avoid excessive drag or reaching supersonic speeds on Mars). These constraints result in the PDG optimization trading required fuel and flight time to limit the maximum speed or thrust direction in the guidance solution. For example, the lower the allowable maximum speed, the larger the required fuel to reach the target, and the longer the flight time.
The computational efficiency of the PDG algorithm comes from a lossless convexification of the dynamics and constraint equations in the soft landing guidance problem. Specifically, the formulation casts the problem as a SoCP (Second-order Cone Program) that can be solved with numerically efficient interior-point solvers that converge within a desired accuracy in a specified number of steps. The convexification is lossless in the sense that the global optimal solution of the relaxed, convexified problem is theoretically proven to also be the global optimal solution for the original, non-convex problem. This formulation is conducive for onboard, real-time implementation and is the basis for the onboard G-FOLD (Guidance for Fuel Optimal Large Diverts) software.
This work was done by John M. Carson, Behcet Acikmese, and James C. Blackmore of Caltech for NASA’s Jet Propulsion Laboratory.