Definition
The Guidance for Fuel-Optimal Large Divert (G-FOLD) algorithm is a mathematical framework used to calculate the most fuel-efficient trajectory for a spacecraft or rocket to reach a specific landing target from its current position.
Why It Matters
G-FOLD is the mathematical breakthrough that made vertical rocket landing possible; it provides the real-time ‘convex optimization’ needed to ensure a booster always finds the most fuel-efficient path to a landing pad, turning an impossible balancing act into a predictable engineering feat.
Core Concepts
- Inventor: Co-invented by Lars Blackmore and Behcet Acikmese while at NASA’s Jet Propulsion Laboratory (JPL).
- Function: Solves the “Fuel-Optimal Control Problem” in real-time, accounting for physical constraints like maximum thrust, engine gimbal limits, and fuel mass.
- Divert Capability: Allows for large “diverts” (lateral movements), which is essential if the vehicle is off-course or if the landing target moves.
- SpaceX Adaptation: Originally designed for setting robotic landers on Mars, Blackmore adapted it for the vertical landing of Falcon 9 boosters on Earth.
- Fuel-Optimal Objective Function
- How to read: “Minimize the integral from t zero to t f of the absolute value of thrust as a function of t with respect to t.”
- Meaning: Find the trajectory that uses the least total thrust (hence least fuel) while still reaching the landing target — the convex objective G-FOLD solves in real time.