movement – Control how quickly 2D vehicle straightens out

I’m implementing vehicle movement in a 2D environment, where a vehicle consists of a front and a back “axle”, both represented as 2D points. When the front axle moves, the back axle should follow in that direction, mimicking the way vehicles move. The way I have it right now looks like this:

Sharp right

After moving the front point A (white), I place B on the line between A and B such that a constant distance (the vehicle length) is kept. More accurately, I use the vector from A to B, normalize it, multiply it with the vehicle length, and add it to A, to get the new B. When searching for similar issues, I found this question’s answer to come to the same technique.

As you can see, the resulting movement is quite recognizable as vehicle movement. The front also does not need to move as smoothly. Below I moved the front manually by dragging it around. As you can see, backwards movement also works perfectly:

Free movement

I want to use this movement system as the back bone of a puzzle game, so its stiffness is actually an asset, since it is also quite predictable.

The only issue that I have is that it takes a good while for the vehicle to straighten out, by which I mean have the back come in line with the travel direction of the front. I’m looking for a way to control how quick this happens.

I have already played around with biasing/weighing the back point onto the line on which the front appears to be traveling, but that resulted in weird moving behavior for any other scenario than moving in a perfectly straight line. I also haven’t been able to think of a different system that would inherently straighten out quicker.

So… I’m happy to try out any ideas that you might have!