By: Ether
New: 30-04-2014 16:02
Updated: 20-09-2014 14:21
Total downloads: 2137 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

• Scenario1

  Scenario1.pdf

  download file

  uploaded: 30-04-2014 16:02
  filetype: pdf
  filesize: 33.13kb
  downloads: 255

  
  

• Scenario2

  Scenario2.pdf

  download file

  uploaded: 30-04-2014 16:02
  filetype: pdf
  filesize: 41.67kb
  downloads: 187

  
  

• Scenario3

  Scenario3.pdf

  download file

  uploaded: 30-04-2014 16:02
  filetype: pdf
  filesize: 55.21kb
  downloads: 195

  
  

• Scenario4

  Scenario4 rev B.pdf

  download file

  uploaded: 30-04-2014 16:02
  filetype: pdf
  filesize: 61.57kb
  downloads: 201

  
  

• Scenario6

  Scenario6 analysis Rev B.pdf

  download file

  uploaded: 30-04-2014 16:02
  filetype: pdf
  filesize: 140.45kb
  downloads: 235

  
  

• Scenario6 Excel solver

  Scenario6 Excel solver.zip

  download file

  uploaded: 30-04-2014 16:02
  filetype: zip
  filesize: 3.01kb
  downloads: 189

  
  

• Scenario6 Maxima solver

  Scenario6 Maxima solver.zip

  download file

  uploaded: 30-04-2014 16:02
  filetype: zip
  filesize: 795bytes
  downloads: 151

  
  

• Scenario6 solver help

  Scenario6 solver help.pdf

  download file

  uploaded: 30-04-2014 16:02
  filetype: pdf
  filesize: 55.2kb
  downloads: 188

  
  

• Scenario6 Python solver

  Scenario6 Python solver.zip

  download file

  uploaded: 30-04-2014 21:11
  filetype: zip
  filesize: 1.02kb
  downloads: 149

  
  

• Scenario6 AMPL solver

  Scenario6 AMPL solver.zip

  download file

  uploaded: 01-05-2014 15:47
  filetype: zip
  filesize: 73.76kb
  downloads: 125

  
  

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

  Scenario5 + solvers revB.zip

  download file

  uploaded: 02-05-2014 22:27
  filetype: zip
  filesize: 157.36kb
  downloads: 133

  
  

• Instructions for Scenario5 Excel solver

  Scenario5 Excel solver (with instructions).zip

  download file

  uploaded: 02-08-2014 13:25
  filetype: zip
  filesize: 3.26kb
  downloads: 127

  
  

Recent Downloaders

• Guest

Tags

Add Tags