Cell mathematical game whith semi-phisics like Kula World

Hi everybody! =) So, one more strange think I want to ask you today. I am extremely new to Unity and C# programming, but trying hard to catch everything fast. My learning progress of new thing always based on solving self-tasks. I tried many solutions, but no one work as needed. I found two themes on this forum with the same question, but all of them are unsolved.

I tried to program the core game mechanic of very old roll-a-ball game Kula-World. Here is a game play video: http://www.youtube.com/watch?v=umjdNlQ6Ik8

Core: this is not a fully physical based game. That is kind off cell mathematical game whith semi-phisics. The ball rolls on connected cubes puzzle.

- This is 3rd person camera game. Camera moves with player and it is always behind.

- Ball gravity always pointed down.

- This is a cell-like world. Player moves from one cube (cell) to another and he cannot stop in between of cubes or move slowly. Only one-step roll.

- He can roll over his horizontal plane step by step (one step = one cube) forward. To turn right or left we need to press right or left button, ball will turn 90gre and then he can move forward if it’s possible.

- The ball can jump in every direction for three steps. If he jumps to empty place, he will fall down.

- The ball can change horizontal plane and gravity vector on the age of some cubes.

Here is some more ideas in photos about this game: DROPBOX

The main question: is it possible to program ball movement using riggetbody for moving in a cell-like world and keep ball gravity always down to player? Or step-by step. Does anybody know where to find any information about this or help somehow? ) Thank You!!!