Control how quickly 2D vehicle straightens out

Question

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:

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:

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!

Thanks!

Update 1: I've implemented the idea from @GaleRazorwind. This results in the back point moving away from the front point:

Answer 1

Ok, I put in a bit of thought on how to increase the speed of straightening out. Let's start with a basic image showing what you have right now:

The car starts with its front at A1 and its rear at B1. During the update, the front moves to A2, so you calculate the normal from A2 to B1 and use that to find B2.

Now, you are trying to get the vector from A2 to B2 to line up with the vector from A2 to A1 more quickly. So, take a vector from B2 to A1, normalize it, and then multiply it by a scaling value ("artist defined"). You will then offset B2 by this new scaled vector to get B3.

However, now we are no longer at the proper distance from A2, so create a vector from A2 to B3, normalize it, scale it by the vehicle length, and add it to A2 to get B4, which is the final position.

Notes: This will cause issues as you approach moving in a straight line, so you can check the Dot Product between A2A1 and A2B2 before performing these extra steps. If the dot product is close to 1/-1, don't do the extra steps. You could also multiply your scaling factor by the inverse of the dot product (1 - Dot). This will make your scaling more aggressive at sharper angles and less aggressive at shallow angles.