Consider using calculus or rather derivatives.

You have stumbled upon the relationship between velocity and position. This can be extended to include acceleration. Simply put, velocity is the derivative of position. And taking the derivative of position gives acceleration. Instead of writing an equation and actually taking the derivative, computers simply takes samples and divide the samples by time. A good example might be an electronic bicycle speedometer.

For your project, you can get velocity by dividing the distance sensors position value by an arbitrary but consistent time interval. Then correcting the robot's velocity relative to the treadmill.

Consider using calculus or rather derivatives.

You have stumbled upon the relationship between velocity and position. This can be extended to include acceleration. Simply put, velocity is the derivative of position. And taking the derivative of position gives acceleration. Instead of writing an equation and actually taking the derivative, computers simply takes samples and divide the samples by time. A good example might be an electronic bicycle speedometer.

For your project, you can get velocity by dividing the change in the distance sensors position value by an arbitrary but consistent time interval. Then correcting the robot's velocity relative to the treadmill.