How SpaceX Lands Rockets with Astonishing Accuracy

From David Ogawa:

Landing Accuracy Explained The booster contains high precision GPS, gyroscopes, and accelerometers at both top and bottom ends to precisely interpolate the booster orientation, position, and velocity. The booster also contains a huge number of strain gauges that monitor forces on the structure at crucial locations, especially engine thrust. (Strain gauges are exquisitely sensitive thin films that are bonded to surfaces to electrically measure the stretching and compression of structures.)

All of these data inputs are timestamped so the three-way redundant computers can calculate where the booster was microseconds ago. By comparing the past position and vector to the desired course, the latest navigation error is calculated. The computers run many physics equations on graphics cards. These are used to optimize the flight path, calculate errors, and control thrust vectoring, grid fin positions, and cold gas thruster durations.

The booster has three opportunities to correct course using the main engines. Each burn is typically done with the center engine alone or with 3 in-a-row engines. The booster is much lighter after consuming propellant and detaching from the second stage, so the first burn is surprisingly short. In a boost-back burn, the booster is flipped end-for-end. The burn reverses horizontal velocity to return to land near the launch site or, for a drone-ship landing, the horizontal velocity is nearly zeroed.

In some rare cases, when fuel will be scarce, the first burn is just a minor course correction that may even briefly boost downrange before the flip maneuver occurs. This fuel-starved booster will reenter the atmosphere at a rather shallow angle. The reentry burn is primarily used to reduce air velocity so that the booster is not damaged by reentry heat, but is also the second opportunity to correct any reentry path error.

In between the reentry burn and the landing burn, there is a relatively long time spent falling through increasingly thick air. The waffle-shaped grid-fins, around the top, can force the booster to be oriented rather broadside in the air stream, while conserving the maneuvering thruster gas. The broadside orientation primarily bleeds off velocity, but any tilt also changes horizontal velocity.

During this period, the booster slows from hypersonic to trans-sonic. Up to 10% of the altitude drop can be exploited to make horizontal adjustments while falling. The landing burn is the final opportunity to correct the horizontal error. Although the concrete landing zones have over 30 meters radius, the drone ship decks allow only 10 meters error.

As the booster slows and approaches the landing pad, the top priority shifts to zeroing out the horizontal and vertical velocities as the landing legs touch down. At this time, any residual horizontal error under 10 meters is nominal.

To minimize fuel consumption, the landing burn is sequenced with 1, then 3, then 1 engine(s) running. The three-engine burn interval ends with a velocity & altitude that allows the single center engine to operate in the middle of its throttle-range. This throttling and center engine tilting (gimbal) are both part of "thrust vector control", which can provide significant sideways force at the bottom of the booster.

As the booster slows during this last burn, the grid-fins loose efficacy. The cold gas thrusters are used to compensate. Since these are also located at the top, they have little effect on the base. Since the throttle range of one engine does not include a level where hovering is possible, the booster must decelerate all the way down to the landing surface, and shut-off with microsecond accuracy before the touch-down.

Excess error will either lift the booster away again, or consume the landing leg crush material (or both). The landing zone has stationary GPS receivers that provide continuous reference corrections for the booster's onboard GPS. (The raw data from both receivers are combined, improving the GPS precision from three meters to about one centimeter, relative to the landing site.)

Of course this implies a landing zone data channel transmitting to the booster. The onboard landing radar provides precise data on altitude and doppler velocity. (During planning for the first Falcon Heavy dual-booster landing spectacle, there was concern about possible interference between the two landing radars, so the booster landings were intentionally staggered in time to minimize this possibility.)

When landing on a drone-ship, the landing is further complicated by the ocean waves moving the landing surface. Waves are not completely predictable from analysis of past events, so this tends to consume the crush material in the landing legs. At some point, Lunar and Mars landings will need realtime optical recognition of terrain, landmarks and landing hazards - such as bolders. I expect the Tesla autopilot AI is being configured for this task.