Really nice puzzle game with good level design.
The sphere of influence mechanic is really cool and the levels do make use of how it gets blocked. However, a lot of the puzzles require precise movement which is annoying(my game suffers from the same issue). On thing I do in my game is that I visually indicate objects that you can control. Perhaps you can make the robot sprites glow when they can be controlled. Otherwise, it is hard to know when I'm barely in range of the robot(which some puzzles require).
My game also has a very similar mechanic. I actually thought about using a sphere of influence around the player but ended up with a ray system for transferring controls to objects since it's much easier to code. If you don;t mind me asking, how are you checking if the sphere of influence is blocked by platforms?
Overall, great job!