# Robot differential drive wheel speed

I would like to build a small robot. The robot will have 4 independent motors, one for each wheel. It will have a rear axle fixed and the front axle will be freely pivoting around its center, somewhat like in the image below.

Source:https://www.ri.cmu.edu/pub_files/pub3/shamah_benjamin_2001_1/shamah_benjamin_2001_1.pdf When I tried calculating the speed of the wheels using the formulas in the image, I did not get the expected result (if as input I choose 1.5708 radiant as "Rsteer", the resulting speed for the rear wheels are both positive, while I was expecting one wheel to have opposite speed of the other, to permit the robot to rotate around the center of the rear axle.

I am not sure the formulas are correct or complete. Is there a way to calculate te speed for all four the wheels at different speed and angle of turn for this configuration of wheels? Could you please me point me in the right direction to understand the math involved in this calculation?