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Issues with the Carvallo-Whipple Bicycle Model #446

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moorepants opened this issue Oct 23, 2020 · 4 comments
Open

Issues with the Carvallo-Whipple Bicycle Model #446

moorepants opened this issue Oct 23, 2020 · 4 comments
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@moorepants
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moorepants commented Oct 23, 2020 •
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This example is live: https://pydy.readthedocs.io/en/latest/examples/carvallo-whipple.html. It mostly works but there are some hanging issues that should be addressed in that example and are related to the issues in #122

  • There is a divide-by-zero if q7 (steer angle) initial condition is set to zero. This returns nan from the underlying c-code.
  • The simulation is very sensitive to the epsilon value of the initial condition q7. It runs on some machines and not on others. Gives different results with a change in decimal place, 1e-7 instead of 1e-8.
  • It isn't clear the simulation results are reproducible across machines with q7 set to an epsilon that works on one machine.
  • There are some uses of 0.0 in the symbolic derivation (setting velocities to zero and inertia scalars to zero). If I change these to 0 or sympy.S(0) I get different simulation results (stable to unstable for example). I'm not sure why these would change the behavior.
  • Make sure that the dependent speed initial conditions are properly set. If u4 is nonzero, then u3, u5, and u8 are very likely to be non-zero because they depend on u4.
@moorepants
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Here is some code to get the initial dependent u's:

eval_nonholonomic = sm.lambdify((u3, u5, u8, u4, u6, u7, q4, q5, q7, d1, d2, d3, rf, rr), nonholonomic)
def eval_nonholonomic_vector(u_dep, u4, u6, u7, q4, q5, q7, d1, d2, d3, rf, rr):
    u3 = u_dep[0]
    u5 = u_dep[1]
    u8 = u_dep[2]
    return eval_nonholonomic(u3, u5, u8, u4, u6, u7, q4, q5, q7, d1, d2, d3, rf, rr)
res = fsolve(eval_nonholonomic_vector,
       [0.0, 0.0, -initial_speed/sys.constants[rf]],  # guess
       args=(initial_roll_rate,
             -initial_speed/sys.constants[rr],
             0.0,
             0.0,
             initial_pitch_angle,
             initial_steer_angle,
             sys.constants[d1],
             sys.constants[d2],
             sys.constants[d3],
             sys.constants[rf],
             sys.constants[rr]))
initial_yaw_rate = res[0]
initial_pitch_rate = res[1]
initial_front_wheel_rate = res[2]

Quick an dirty way. For only setting an initial roll rate and rear wheel rate this doesn't change the results. Only u8 is non-zero and it can be calculated as I have it in the notebook.

@moorepants moorepants mentioned this issue Jun 23, 2021
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@oliverlee
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I'm getting very different results across two machines - which are also differing from the example.

@moorepants
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I'm not surprised. You can see more lengthy explorations of issues here: #122 (which you helped on years ago). I think we should get the idea in PR #462 working to see if that solves things. If it does, then I need to rework PyDy's internals to match for the general case.

@moorepants
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moorepants commented Feb 7, 2022 •
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Also, the model gives the correct answers if Symengine is used to evaluate to arbitrary precision. So it is some kind of numerical rounding error.

Edit: see this comment #122 (comment)

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@moorepants @oliverlee