Object follow irregular path 2D

Hello everyone. I am making a 2d game endless runner. I want to make a cart follow the path of an irregular rail as shown in the image below, but without taking off the rail, without rail swinging. I'm not able to do this, the way I'm doing the cart sometimes falls back and shakes a lot. Is there a way to do that while the cart is in contact with the rail, do the same path clinging to the rail? My rail is a 2d sprite with polygoncollider and my cart is a sprite with a rigidbody with a 2d boxcollider