Accelerating and decelerating robot as it runs a certain distance

My team wants to make our robot drive a certain distance with a changing speed. For example to travel a distance, we want it to start with a growing speed and then smoothly becoming constant and finally, we want it to gradually decelerate until it stops.
We would like to do that to reduce the error margin due to sudden starts and stops.
Could you please help us out?

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What you are looking for is a motion profile. It sounds like you are describing a trapezoidal motion profile but there are other options, I usually use a cubic motion profile.

Tons of resources on these around