Formula for controlling the movement of a tank-like vehicle?

Question

Anyone know the formula used to control the movement of a simple tank-like vehicle?

To \'steer\' it, you need to alter the force applied the left and right \"wheels\

Answer 1

For a skid steered vehicle that is required to turn in radius 'r' at a given speed 'Si' of the Inner Wheel/Track, the Outer track must be driven at speed 'So' :

So = Si * ((r+d)/r)

Details:

In Skid Steering, a turn is performed by the outer wheels/track traveling further distance than the inner wheels/track.

Furthermore, the extra distance traveled is completed in the same time as the inner track, meaning that the outer wheels/track must run faster.

Circle circumference circumscribed by "Inner" track:

c1 = 2*PI*r
'r' is radius of circle origin to track/wheel

Circle circumference circumscribed by "Outer" track:

c2 = 2*PI*(r+d)
'r' is radius of circle origin to inner track/wheel
'd' is the distance between the Inner and Outer wheels/track.

Furthermore, c2 = X * c1, which says that c2 is proportionally bigger than c1

X = c2 / c1
X = 2*PI*(r+d) / 2*PI*r
X = (r+d)/r

Therefore for a skid steered vehicle that is required to turn in radius 'r' at a given speed 's' of the Inner Wheel/Track, the Outer track must be driven at :

So = Si * ((r+d)/r)

Where:

'So' = Speed of outer track
'Si' = Speed of inner track
'r'  = turn radius from inner track
'd'  = distance between vehicle tracks.


               ********* <---------------- Outer Track
           ****    |    ****                     
        **         |<--------**----------- 'd' Distance between tracks
       *        *******<-------*---------- Inner Track
      *      ***   ^   ***      *  
     *      *      |<-----*------*-------- 'r' Radius of Turn
     *     *       |       *     * 
     *     *       O       *     * 
     *     *               *     * 
     *      *             *      * 
      *      ***       ***      *  
       *        *******        *   
        **                   **    
           ****         ****       
               *********