Car parking problem

Question

I want to park my car doing similar to the one in the image. But I want to define a curve such that I park the car at once (without going forward, always backward). Suppose that the place that I want to park is 1.5 times longer and 1.2 times wider than my car.Can you model such a curve?

Answer 1

If you could turn all four of your wheels to point left-right, , then parking is trivial -- pull up parallel to the space, turn your wheels, then roll in. The complexity of parking is that your rear wheels are fixed, and your front wheels don't turn all the way. This doesn't answer your question, but then again the question does not really model how cars move. An article about the relevant formula is here, and the actual paper is here.