Subtle rotations on a motion path

My solution is a little it more complicated and requires a few triggers.

The only method I could find to create a nice curve was to make your shape follow a circle path. But clearly you don't want it animating the entire 360. So what I had to do was create the motion path, extend the animation timing so it doesn't zip around the circle quickly. What I did next was the fiddly stuff.

First of all I needed a reference point of where I wanted the object to stop. That reference coming in the form of a screen recording of the motion path animation (I used quicktime), and then I slowly moved through the frames of the video capture to find the frame of where I wanted the object to stop, and screen captured that single frame. I brought that new screen shot into the project and reduced its opacity. You'll notice in the project file I had a visible circle so I could align the screen capture up with that.

From there I duplicated the original shape, removed it's motion path and then rotated and lined that up with the screen shot. Then I made a rectangular shape, and made that 100% transparent and rotated and positioned that to the left of that new shape "the end of the animation".

From there I just used a trigger to hide the duplicated shape at the start of the timeline, and then showed it once the animated shape had left interacting with the hidden rectangle. I also then hid the animated shape at the same time.

It's a little bit of work and this would need to be done for every stop point I'd assume. But you will end up with a smooth animations.

Best I could come up with sorry.