Motion Profiling Controllers

To solve these problems, you can profile the goal, accounting for the maximum accelerations and velocities of the drivetrain or other system you are modelling. You can also see that the only three values needed to calculate this cruising time is the maximum velocity, maximum acceleration, and the desired distance. This new maximum velocity can then be plugged into the two equations for time to acquire the constraints on time for the profile, and again you are able to calculate the velocity at any given point by following these constraints.

Source: steampunc.github.io