PYTHON · NUMPY

Close the Loop

Add a PD controller on altitude that drives the quad from the ground to a target height and holds it with no steady-state drift.

01Challenge

Start the quad at 0 m, command it to 5 m. Open-loop hover thrust holds altitude but can't correct error. Add a controller that adjusts thrust from the height and climb-rate error so it reaches 5 m and stays.

02Model

Hover thrust is a guess — the instant a gust or a modeling error nudges the aircraft, open-loop flight drifts. A controller closes the gap: measure how far you are from the target (position error) and how fast you're approaching (velocity), and push thrust up or down in proportion. That is PD control — the P term pulls toward the target, the D term damps the approach so you settle instead of overshoot. It is the same loop, from this altitude hold to a full six-degree-of-freedom aircraft.

03Guided practice

Worked: simulate vertical dynamics with semi-implicit Euler. Faded: add thrust = mg + Kp(z_target - z) - Kd*v. Independent: tune Kp, Kd for no overshoot and settle by 4 s.

04Feedback

PASS WHEN The PD loop drives altitude error to zero with no overshoot and holds the target.

If your run fails, check:

FAIL: never reaches 5 m — Kp too small; the proportional term isn't pulling hard enough.
FAIL: overshoots and oscillates — Kd too small; add damping on the velocity term.

05Retrieve & space

What does the D term do physically? (Damps the approach velocity so the quad eases into the target instead of overshooting.)
Why keep the m·g feed-forward? (So the PD terms only correct error, not fight gravity from scratch.)
Same loop, harder axis: which is harder to control, altitude or horizontal position? (Horizontal — it requires tilting the aircraft first.)

06Mastery & project

Implements and tunes a PD altitude controller that reaches the setpoint with no overshoot and zero steady-state error (L2: close a stable feedback loop on a dynamic plant).

This PD loop is the inner controller the planning and multi-agent modules command with position setpoints.

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PYTHON · NUMPY

Close the Loop

Close a PD altitude loop and fly the quad to 5 m.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you