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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

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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).
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  • $\begingroup$ thank you very much as for the theta_dot ( my bad i just miss writen it in the post ) , but when i execute the simulation things are bit reversed , when i increase Vr the vehicle turne to the right insted of the left so when i inverse the sign of the y_dot or write theta_dot = (vr-vl )/w insted of (vl-vr) /w things seem to workout well , my only explanation for this is the frame change between the world and screen $\endgroup$ – zed_eln Nov 16 '20 at 14:36
  • $\begingroup$ the equations are written with x positive to the right, and y upwards. however the screen uses y- downwards as positive. That makes the two be reversed. $\endgroup$ – NMech Nov 16 '20 at 20:20

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