Real-Time, Fuel-Optimal, Powered Descent Guidance Using Interpolated Time-of-Flight and Propellant Mass

Soft landing using rockets requires a trajectory to be planned for the lander from rocket ignition — typically several kilometers in altitude and moving at up to 200 m/s — to the point near the surface with near-zero velocity. The exact initial and possibly final points are not known beforehand, so the trajectory must be found onboard a landing spacecraft in near real time. An algorithm to find such a trajectory is called powered descent guidance (PDG). The previous state-of-the-art had been the computationally fast but suboptimal Polynomial PDG of Apollo heritage. In the last decade, a previous technology advance that transforms the PDG problem into a convex optimization problem that can be solved efficiently formed the basis of the Guidance for Fuel Optimal Large Diverts (G-FOLD) PDG algorithm. While G-FOLD finds the constrained optimal PDG trajectory, it still requires a search to find the optimal time-of-flight, which in turn can typically require 10 trajectory optimizations. While a PDG trajectory for a single time-of-flight can be found in near real time, having to evaluate 10 trajectories while running in the background on a 200-MHz flight processor would take too long.