What is difference between 2 wheels and 4 wheels and tracked differential mobile base kinematics?

Question

In generally I know that no difference between 2WD and 4WD mobile base control kinematics equations.

but is there really difference between two wheels differential mobile base and tracked/continuous tracks differential robot (Tank Treads) inverse kinematics equations?

I using this inverse kinematics of differential equation:

Which 'r' is wheel radius, 'd' is robot width, 'v' is linear velocity, 'w' is angular velocity, and thetaR and thetaL are left/right wheel RPM that you want them.

• For autonomous drive, I use DWA Planner that send v, w to my driver which inverse kinematics is here, and my driver calculate thetaR/thetaL of each posted v,w.
• For manualy driving, I use many of teleop node, that all of them sends v, w too.

Answer 1

The short answer is that the equations/models for these different vehicle should be different but there is no value in using more accurate equations.

All these equations are approximations that make assumptions about how the ground and wheels/tracks interact.

If there is 2 wheels and no slipping of the wheels on the ground, then the equation is reasonably close the reality. Otherwise the equation is equally bad for all cases.

However, if there is another feedback loop, a human driver or visual servoing or slam, then the equation is good enough.

If you are using this equation in an open loop manner, and your wheel-ground contact is very well behaved，then you can write more accurate equations. However you are unlikely to encounter such well behaved conditions outside of a lab.

Edit:

A tracked vehicle spends all its time slipping, except for when it is driving straight. For the equation to be an approximation during slipping, we are assuming the center of mass is in the middle of the vehicle and that the friction is uniform at all points under the track. If your conditions are different, then the actual motion will diverge from the prediction faster.

For some situations a small enough window or step size should work fine for those algorithms. I would not call them advanced; if they aren't working look for another approach, both in the model and in the navigation algorithms.