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.

In addition, Multi-X is emerging as promising architecture for next-generation missions. In Multi-X, a lander first selects from pre-specified safe sites and then plans a trajectory to the selected site. Multi-X enables going to landing ellipses with large hazards that can be pre-determined from orbital imagery.

It was determined through extensive simulation studies that the optimal time-of-flight and optimal propellant mass as calculated by G-FOLD can be accurately interpolated from a coarse seven-dimensional grid of initial position, velocity, and mass of the lander. As a result, instead of G-FOLD performing a time-of-flight search with approximately 10 trajectory optimizations, the optimal time-of-flight is simply interpolated from a small table (e.g., 40 KB). Then a single trajectory optimization is performed for this interpolated time-of-flight, thereby reducing the G-FOLD runtime by a factor of 10.

The new technology reported here consists of five elements that extend G-FOLD and that derive from the engineering-level interpolability of the optimal time-of-flight and propellant mass. First, as described, the time-of-flight line search in G-FOLD can be replaced with interpolation from a small table, immediately reducing the runtime by a factor of 10. Second, for G-FOLD to trigger powered descent while a lander is descending on chute or a deorbit trajectory, the optimal propellant mass to reach the target can be looked up over a finite horizon. If the propellant to reach the target starting a divert now is a local minimum and/or viable, then start powered descent. Third, when using G-FOLD for Multi-X, the optimal target can be selected quickly from hundreds of possibilities by simply looking up the propellant mass for each target and selecting the lowest. For Multi-H, in which hazardous regions are specified instead, a grid of safe targets can be generated and, again, the lowest-propellant target can be selected. Importantly, non-convex constraints on the landing site can be handled in this manner. Additional criteria can be included, such as distance to the landing target. Fourth, if there is insufficient propellant to reach a specific target — for example, for pinpoint landing — G-FOLD can find the point closest to the target that is reachable by interpolating propellant masses for candidate targets between the lander and the original target, and taking the point closest to the target with propellant equal to what the lander has available. Fifth and finally, G-FOLD can also approximate the farthest possible divert by searching over discrete directions and distances and finding the largest propellant-feasible distance.

This work was done by Scott R. Ploen and Daniel P. Scharf of Caltech, and Behcet Acikmese of the University of Texas at Austin for NASA's Jet Propulsion Laboratory. This software is available for license through the Jet Propulsion Laboratory, and you may request a license here. NPO-49545