FixTheRobot Explore Robotics / Guidance, Navigation and Control / M8 / M8-L2

This lab works on phones, but writing code is much easier on a laptop.

Guidance, Navigation and Control · Guidance Laws · M8-L2 · Advanced

Fly the Polynomial Descent

Bench log · Hopper on the test range

11:15. Hopper's descent was programmed on the ground: a smooth acceleration history from 200 m to a stop. On the first flight the engine gave 8% less than commanded and the vehicle reached the ground at 19 m/s. The operator also wants the descent shortened to save time, and the engineers do not know how short it can be.

You will see why a programme fails and a recomputed law does not, write the law, and compute the shortest descent the engine allows.

Your task

    Simulation
    solution.pyLoading Python…
    Ctrl+Enter runs
    What Python can I use?

    Plain Python 3 with the standard library and the course library gnckit (import gnckit as g: transfer functions and margins, state space and LQR, the Hopper model, quaternions, a convex solver). NumPy is not available in the browser. Your code runs in a background worker: an endless loop is stopped after a few seconds and the page stays usable. It runs in your browser and is never sent anywhere.

    Hints

    What this lab teaches

    Stage 1: the same polynomial acceleration, computed once (feedforward) or recomputed from the present state and the remaining time (feedback); only the second survives a wrong start state or a weak engine. Stage 2: the law itself, a = 6 (rf − r)/T² − 2 (2v + vf)/T. Stage 3: the demanded thrust rises as the time-to-go shortens, and bisection finds the shortest descent within the engine limit.

    Grading flies three disturbed descents with your choice, compares your law with the exact one on hidden states, and your shortest time-to-go with the reference to 0.02 s.

    Theory for this lab

    Guidance Laws labs

    1. M8-L1: Hold the Survey Line in Wind
    2. M8-L2: Fly the Polynomial Descent: this lab.

    Educational simplification: a vertical descent with a known mass flow, instantaneous thrust and no gimbal; module 8 treats the lateral axes and the terminal conditions of position and velocity together, and module 9 adds the thrust and glide-slope limits properly.

    Get the next lab

    Get notified when new robotics labs are released. One email per new lab, nothing else.