There can be M obstacles presented in the N dimensional space. Yes, the example objects given were 2 3 dimensional rectangles.
Distance of the path may also be taken into consideration.
One of the most trivial applications of this would be making a robot go from (x1, y1) to (x2, y2). It would be a 2 dimensional space.
I had not considered motors with this problem. The scope I viewed this problem was an advanced robotic arm trying to go from one position to another by stepping through positions that would arrive at the goal position.
State space was the wrong term. What I am asking for is an N dimensional *kinodynamic motion planning algorithm. There will be limitations as to how far in space the robot may move each iteration, but I have yet to decide on the exact restrictions
*The most famous problem is the
piano mover's problem