Feedback Confused Movement, chess

I have a chess board and I need to move objects from Vector3 to Vector3 slowly on it, Sometimes they need to be shown as jumping from Vector3 to Vector3 at random, I would rather not use animation to do this, please tell me how a quatuernim rotate then jump animation could be used ?

Ok, very vague, chess board, player can move x or z when he moves he turns and leaves a ball behind him (animation) he's also allowed to jump, if he does he looses a jump but can affect (spray can) change the color of everything around him x8 spray. how do I 1) move from exact position A to exact position B and 2) a perfect jump from a-b

 

I would recommend using a spline plugin such as Curvy on the Asset Store.