Optimal Wheel Placement for 4-wheel drive

[Ether]

Originally Posted by lior9999

Given a generic "box" robot being driven by 4 CIMs on 4 standard, rubber tread wheels, what are the optimal positions for the 4 wheels to be in to allow for maximum driving power while still being able to easily turn in place? Or could someone point me to a set of equations/graphs to determine the optimal distance?

Are each of the 4 wheels independently driven or are the front and rear wheels on each side chained (or belted) together?

It makes a difference in the analysis of turning forces.

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 Excel or a CAS such as Maxima, Octave, SciLab, Matlab, etc.

Scenario2:
In the case of independently driven wheels with equal coefficient of friction in all directions and center of mass located at center of geometry, a very simplified analysis is possible. PDF.

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

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

Scenario6:
4-wheel skid-steer with front and rear wheels chained together on each side. Maximum coefficient of friction occurs in the Y 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. PDF. . . Excel solver. . . Maxima solver. . . Solver help file.