differential drive vehicle in screen coords

Question

differential drive vehicle in world frame
what would change in the kinematic model of the differential drive vehicle if i  wanted to simulate it
using pygame module in python ( pygame or opencv or any other one )
x_dot = (vl+vr)/2*cos(theta)
y_dot = (vl+vr)/2*sin(theta)
theta_dot = (vr-vl)/w
vr is the velocity of the right wheel
vl is the velocity of the left wheel
theta is the heading angle
it uses a screen coords system which start at the top left corner of the screen insted of the lower left
my initial guess is since only the y axis is inverted then i should invert the sign of the y_dot
i hope i explained my question clearly the picture is in the link above

NMech · Accepted Answer

The kinematics equation should remain the same. The only problem I see is with the third equation which should be
theta_dot = (vr-vl)/W
What you need to consider on top of those equations since you are working with screen pixels is:

relationship of x and y with screen pixels (units should be $frac{text{x units}}{pixel}$, $frac{text{y units}}{pixel}$ or the inverse).
you'd need to add variables for monitoring the position (preferably floats). e.g:

x = 0.0 
y = 0.0

you'd need to integrate in time with respect to the position

x = x+ x_dot*dt
y = y+ y_dot*dt
theta = theta+ theta_dot*dt

where dt is the timestep you want to use.

then you'd just need to redraw the vehicle at the orientation of theta (after you cast x, y to integers).

differential drive vehicle in screen coords

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