MDP robot grid-world example

Applies value iteration to learn a policy for a Markov Decision Process (MDP) -- a robot in a grid world.
The world is freespaces (0) or obstacles (1). Each turn the robot can move in 8 directions, or stay in place. A reward function gives one freespace, the goal location, a high reward. All other freespaces have a small penalty, and obstacles have a large negative reward. Value iteration is used to learn an optimal 'policy', a function that assigns a
control input to every possible location.
video at https://youtu.be/gThGerajccM

This function compares a deterministic robot, one that always executes movements perfectly, with a stochastic robot, that has a small probability of moving +/-45degrees from the commanded move. The optimal policy for a stochastic robot avoids narrow passages and tries to move to the center of corridors.

From Chapter 14 in 'Probabilistic Robotics', ISBN-13: 978-0262201629, http://www.probabilistic-robotics.org

Aaron Becker, March 11, 2015