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Skid-Steer turning analysis

Ether

By: Ether
New: 04-30-2014 03:02 PM
Updated: 09-20-2014 01:21 PM
Total downloads: 2731 times


Skid-steer turning analysis for non-cleated 4-wheel FRC robots, chained or independent drive



Turning analysis for non-cleated, non-omni, non-mec 4-wheel FRC robots with chained or independent drive

If the wheels are independently driven with equal torque, a simple model with an analytical solution is possible.

If the wheels are chained, it can be solved using nonlinear constrained optimization. This can be done in a spreadsheet such as Excel or Gnumeric, a CAS or Numerical computation package such as Maxima, Octave, SciLab, or Matlab, a general-purpose language such as Python (with an appropriate optimization library such as scipy), or a modeling language such as AMPL or GAMS.

See suggested reading order below.


Scenarios 1, 2, 3, & 5 are probably most applicable to FRC.

Scenario1
Simplest case: square drivebase; independently driven wheels (not chained) with same magnitude of torque applied to all wheels; all wheels identical; wheel CoF equal in all directions; center of mass located at center of wheel geometry. A very simplified analysis is possible with analytic solution.

Scenario2
Same as Scenario1 except rectangular drivebase.

Scenario3
Same as Scenario2 above, but the center of mass is located aft of the center of geometry.

Scenario5
Same as Scenario3, except front and rear wheels are chained together on each side


__________________________________________


Scenarios 4 and 6, with elliptical interpolation of mu, are presented mainly for pedagogical purposes. The elliptical interpolation model does not apply to wheels with cleats or rollers.


Scenario4
Same as Scenario3 above, but the coefficient of friction is different in forward/aft vs sideways directions.

Scenario6
4-wheel skid-steer with front and rear wheels chained together on each side. Maximum coefficient of friction occurs in the Y (fwd/rev) direction. Minimum coefficient of static friction occurs in the X direction. For any other direction, elliptical interpolation between uy and ux is used to compute the effective static coefficient in that direction. The static coefficients for the front wheels are not necessarily the same as for the rear. Center of Mass is located aft of Center of Geometry. An analytic solution for the free-body static force diagram is not possible, so contrained optimization is used.


Excel, Maxima, Python, and AMPL solvers are provided for Scenario5 and Scenario6


Suggested reading order:

1) Physics Quiz 5 Dec 20, 2011

2) Scenario1

3) Physics Quiz 6 Dec 21, 2011

4) Scenario2

5) Physics Quiz 7 Dec 27, 2011

6) Scenario3

7) Scenario5

... then if you're still interested:

8) Physics Quiz 4 Dec 18, 2011

9) Scenario4

A) Scenario6 PDF

B) Scenario6 Solvers:
........Solver help PDF
........Excel Solver
........Python Solver
........Maxima Solver
........AMPL Solver


Attached Files

  • pdf Scenario1

    Scenario1.pdf

    downloaddownload file

    uploaded: 04-30-2014 03:02 PM
    filetype: pdf
    filesize: 33.13kb
    downloads: 308


  • pdf Scenario2

    Scenario2.pdf

    downloaddownload file

    uploaded: 04-30-2014 03:02 PM
    filetype: pdf
    filesize: 41.67kb
    downloads: 225


  • pdf Scenario3

    Scenario3.pdf

    downloaddownload file

    uploaded: 04-30-2014 03:02 PM
    filetype: pdf
    filesize: 55.21kb
    downloads: 313


  • pdf Scenario4

    Scenario4 rev B.pdf

    downloaddownload file

    uploaded: 04-30-2014 03:02 PM
    filetype: pdf
    filesize: 61.57kb
    downloads: 339


  • pdf Scenario6

    Scenario6 analysis Rev B.pdf

    downloaddownload file

    uploaded: 04-30-2014 03:02 PM
    filetype: pdf
    filesize: 140.45kb
    downloads: 280


  • zip Scenario6 Excel solver

    Scenario6 Excel solver.zip

    downloaddownload file

    uploaded: 04-30-2014 03:02 PM
    filetype: zip
    filesize: 3.01kb
    downloads: 222


  • zip Scenario6 Maxima solver

    Scenario6 Maxima solver.zip

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    uploaded: 04-30-2014 03:02 PM
    filetype: zip
    filesize: 795bytes
    downloads: 170


  • pdf Scenario6 solver help

    Scenario6 solver help.pdf

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    uploaded: 04-30-2014 03:02 PM
    filetype: pdf
    filesize: 55.2kb
    downloads: 234


  • zip Scenario6 Python solver

    Scenario6 Python solver.zip

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    uploaded: 04-30-2014 08:11 PM
    filetype: zip
    filesize: 1.02kb
    downloads: 176


  • zip Scenario6 AMPL solver

    Scenario6 AMPL solver.zip

    downloaddownload file

    uploaded: 05-01-2014 02:47 PM
    filetype: zip
    filesize: 73.76kb
    downloads: 145


  • zip Scenario5 plus Excel, Maxima, Python, AMPL, & Octave solvers revB

    Scenario5 + solvers revB.zip

    downloaddownload file

    uploaded: 05-02-2014 09:27 PM
    filetype: zip
    filesize: 157.36kb
    downloads: 167


  • zip Instructions for Scenario5 Excel solver

    Scenario5 Excel solver (with instructions).zip

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    uploaded: 08-02-2014 12:25 PM
    filetype: zip
    filesize: 3.26kb
    downloads: 150



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