Question bank — Autonomous GNC for reusable rockets — SpaceX approach overview

False — a nearly-empty booster's minimum thrust exceeds its weight (TWR $>1$), so the smallest possible push still accelerates it upward. It literally cannot balance at constant altitude, which is why it must do a timed hoverslam instead.

False — the constraint is that even the lowest usable throttle gives $T/m>g$ (TWR $>1$). If it could throttle down to TWR $=1$ it could hover; the whole problem exists precisely because it cannot.

False — Guidance decides where to go (the desired trajectory/target state), while Control decides how to move the actuators to close the gap to that trajectory. Navigation is the third: where am I now?

False — it fuses two complementary flaws: the Kalman Filter blends a fast-but-drifting IMU with slow-but-drift-free GPS/radar, trusting each according to its uncertainty. Removing either source degrades the estimate.

False — it is recomputed many times per second (closed-loop). Winds, exact mass, and engine performance are never known exactly, so the trajectory is re-solved live from fresh state estimates.

False — a pure proportional term needs a nonzero error to produce a correction, so it settles with a residual offset against a steady wind. The integral term $K_i\int edt$ accumulates that offset and drives the steady-state error to zero.

False — it is used because convex problems have a guaranteed global optimum found in bounded time. That determinism is essential when a mission-critical decision must be produced every cycle; see Convex Optimization and Lossless Convexification.

False — during any powered burn the engine gimbal dominates the steering torque. Grid fins provide aerodynamic steering during the atmospheric coast/descent, not when the engine is doing the work.

False — even with a perfect feed, signal latency plus plasma blackout plus a ~250 ms human reaction time exceed the ~10 ms control loop the vehicle needs. The decision must be made onboard.

The error: lighting early makes you reach zero velocity above the ground. Since TWR $>1$ you can't then hover, so you rise again or dump fuel — the ignition altitude $h_{ign}=v_0^2/(2a_{net})$ (with $a_{net}=T/m-g$) is a precise target, not a floor.

The error: position is the double integral of acceleration, so a constant acceleration bias $b$ contributes $\frac{1}{2}b{t}^2$ to position — a small offset that balloons with time. GPS/radar is required to bound that drift, not as a luxury.

The error: that relation contains no time — that is exactly why it is chosen. It links speed to distance directly, answering where speed hits zero; burn time comes separately from $t=v_0/a_{net}$. See Kinematics — v²=v0²+2as.

The error: the boostback burn cancels or reverses horizontal velocity to aim back at the landing site. Vertical descent speed is bled off later by the entry and landing burns.

The error: cold-gas thrusters are weak; they are used only in vacuum/coast when there is no air for fins and the engine is off. Torque authority is chosen by environment, not raw strength — gimbal for burns, fins for atmosphere.

The error: $h$ is the remaining stopping distance at the moment we evaluate it, not total altitude. The controller continuously recomputes with the current $v$ and current $h$ each cycle.

A parachute gives no lateral steering precision and no way to hit a barge-sized target through wind, and a heavy booster needs enormous chutes. Propulsive landing lets the same engine that launched it also steer and brake to a pinpoint.

Because there is no margin: with TWR $>1$ you cannot pause to correct, so ignition must be timed so velocity hits zero exactly at zero altitude. A moment's error means stopping mid-air (then falling) or hitting the ground.

Because the required deceleration is $v^2/(2h)$: braking harder is needed when speed $v$ is high or remaining height $h$ is small, and both change every instant. The $+g$ cancels gravity so the engine's net effect equals that required value; a fixed thrust would over- or under-brake as $v$ and $h$ evolve.

Quaternions avoid the gimbal-lock singularities and discontinuities that Euler angles suffer near vertical orientations, which matters when the booster flips through large attitude changes; see Attitude Dynamics & Quaternions.

Because each has authority only in its regime: gimbal needs the engine lit, grid fins need air, cold-gas needs neither but is weak. GNC schedules them by flight phase so some control is always available.

It responds to how fast the error is changing, damping the motion so the rocket doesn't overshoot the target attitude and oscillate. Without it, the proportional term alone tends to ring.

It gives $h_{ign}=0$: with no speed to kill you never need to ignite for braking. The formula degenerates sensibly to "no burn required."

The demanded thrust diverges to infinity — physically impossible. This is why ignition must happen early enough that $h$ is never squeezed toward zero while still moving fast.

With $T/m=g$ its net acceleration $a_{net}=0$, so it could truly hover, descending as slowly and gently as it liked and easing onto the pad. Real boosters sit above this hovering threshold (TWR $>1$), which is the whole reason the precisely-timed hoverslam is forced.

A smaller $a_{net}$ means the needed ignition altitude was higher than assumed, so the vehicle is now behind — it will command maximum available thrust, and if that still can't stop it in the remaining $h$, no control law can recover. This is why margin is designed into the trajectory, not improvised.

Only the cold-gas thrusters — there is no air for grid fins and no exhaust to gimbal. This is exactly the regime they exist for, such as the post-separation flip.

Yes: even with zero lateral error it holds attitude against disturbances (wind gusts, thrust misalignment). A PID controller with $e=0$ still counters any $\dot{e}$ that appears, keeping the correction ready.

No — net upward acceleration is still $a_{net}=T/m-g>0$ because TWR $>1$. That's why the engine must cut off precisely at touchdown; leaving it lit would push the booster back up.