So, we have a mobile that behaves very much like a car, with some rules simplified.

The mobile has a maximum turning speed and a turning acceleration, this goes to both directions of the car relative to its forward vector.

It also has a top forward speed, which is limited to a linear interpolation between the maximum in straight line and the maximum while using top turning speed.

In order to reach this top speed and to stop it has an acceleration as well, considered to be constant.

Unlike a car, we are not meant to move backwards.

For the purposes of this task we are in a wide open empty parking lot, so room to move and manouver is plenty, we start in a given position facing a given angle and we are given the goal of arriving at another specific spot at another specific orientation.

This goal may very well be to end up standing in the same spot but facing the opposite direction.

Acceleration and speeds for both translation and rotation will make the beggining of our movement process look very nice, but arrival is more complicated, we need to arrive from a specific direction in order to end up looking in the angle we were given.

My first instinct is to try to extrapolate the arrival turn from the goal backwards, but I have no idea how to do this mathematically. Formulas? hints? alternative solutions? it needs to look soft and obey the rules stated above.

Acceleration and deceleration may have different magnitudes.