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trajectory generation via parametric optimal control

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trajectory

trajectory generation via parametric optimal control

#function of different parts test_case.py: generate a set of final state values using curvature function

trajectory.py: initial a set of curvature parameters supposing a parabolic model, then fine-tune the initial parameters to get the trajectory

plot.py: plot and compare the trajectories of accurate parameters and calculated parameters or just plot an single calculated trajectory

main.py: interface of the algorithm

#some tricky part

  1. the integration among sin, cos function uses Simpson's rule

  2. gradient shooting method works only in fine-tune period

  3. Initial the parameters via:

    s = s = d * (theta_f ** 2 / 5 + 1) + 2 * abs(theta_f) / 5

    b = 6 * theta_f / (s ** 2) - 2 * k_0 / s + 4 * k_f / s

    c = 3 * (k_0 + k_f) / (s ** 2) + 6 * theta_f / (s ** 3)

    d = 0

  4. changes of parameters need to be scaled down to preserve the stability

    current scalability factor is (# of iteration) / 5

  5. due to the effect of scalability, the number of epics need to increase from 3 to 5

    which leads to less efficiency.

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