FixTheRobot Explore Robotics / Guidance, Navigation and Control / M11 / M11-L2

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Guidance, Navigation and Control · Spacecraft and Rocket GNC · M11-L2 · Advanced

Approach Along the Velocity Bar

Bench log · Hopper on the test range

23:10. A small servicing vehicle waits 1000 m behind a station on its velocity bar. The flight director wants it at a hold point 20 m behind the station within an hour and a quarter, never more than 200 m above or below the station's orbit, and with as little propellant as possible.

You will choose the transfer time, write the relative-motion equations, and compute the two burns.

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: in relative orbit motion a longer transfer needs a smaller velocity change, but the schedule and the corridor limit the time; half an orbit swings too far, a whole orbit is too slow. Stage 2: the Clohessy-Wiltshire solution, with the drift term whose sign says that a chaser above the station falls behind. Stage 3: the two impulses, from the position block of the state transition matrix, and the second burn that cancels the arrival velocity.

    Grading evaluates the schedule, the corridor and the cost of your transfer time, and compares your propagation and impulses with the exact values on hidden states, distances and times.

    Theory for this lab

    Spacecraft and Rocket GNC labs

    1. M11-L1: Detumble and Point
    2. M11-L2: Approach Along the Velocity Bar: this lab.

    Educational simplification: in-plane motion about a circular orbit, instantaneous impulses and the linearized equations, accurate to metres for a few kilometres; module 11 treats the out-of-plane motion, the nonlinear check and the corridor of a real approach.

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