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Skid-Steer turning analysis
Skid-steer turning analysis for non-cleated 4-wheel FRC robots, chained or independent drive
[/i]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.
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.
Same as Scenario1 except rectangular drivebase.
Same as Scenario2 above, but the center of mass is located aft of the center of geometry.
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.
Same as Scenario3 above, but the coefficient of friction is different in forward/aft vs sideways directions.
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:
… then if you’re still interested:
Scenario1.pdf (33.1 KB)
Scenario2.pdf (41.7 KB)
Scenario3.pdf (55.2 KB)
Scenario4 rev B.pdf (61.6 KB)
Scenario6 analysis Rev B.pdf (140 KB)
Scenario6 Excel solver.zip (3.01 KB)
Scenario6 Maxima solver.zip (795 Bytes)
Scenario6 solver help.pdf (55.2 KB)
Scenario6 Python solver.zip (1.02 KB)
Scenario6 AMPL solver.zip (73.8 KB)
Scenario5 + solvers revB.zip (157 KB)
Scenario5 Excel solver (with instructions).zip (3.26 KB)