FixTheRobot Explore Robotics / Guidance, Navigation and Control / M9 / M9-L1

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

Guidance, Navigation and Control · Trajectory Optimization and Predictive Guidance · M9-L1 · Advanced

Find the Switch Time

Bench log · Hopper on the test range

16:00. Hopper's engine cannot be throttled during the drop test: it is off or at full thrust. The test engineer wants it to light as late as possible to save propellant and to arrive at the ground at rest.

You will find the altitude by hand, compute it for any start, and find out how much margin the burn has.

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 minimum-fuel full-thrust burn is the last possible one; there is a single ignition altitude that stops the vehicle at the ground, and its window is a few tenths of a metre wide. Stage 2: the altitude from the free-fall and braking equations, with the mean mass of the burn. Stage 3: the sensitivity: a few hundredths of a second of delay or a per cent of thrust is a large landing speed.

    Grading evaluates the touchdown speed of your altitude, compares your computed altitude with the exact optimum to 0.5 m, and checks your tolerated errors against the simulation.

    Theory for this lab

    Trajectory Optimization and Predictive Guidance labs

    1. M9-L1: Find the Switch Time: this lab.
    2. M9-L2: Solve the Landing as a Convex Program

    Educational simplification: a vertical drop, instantaneous thrust, a fixed mass flow, and an engine shut down for good when the speed reaches zero; module 9 treats the general problem with the minimum principle and then the convex formulation.

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