This paper briefly discuss the robot motion planning problem and some
of its solutions. It begins by some terminologies, and then presents an
O(n log n) algorithm, which is relatively fast but
does not find the optimal (shortest) path. It touches upon Minkowski sums,
a crucial mathematical tool in the motion planning problem. Visibility
graphs are then introduced, emphasizing its importance in finding the shortest
path. An O(n2 log n) algorithm which computes
the visibility graph is presented. Lastly, Dijkstra’s algorithm is described
to illustrate how visibility graphs are used to find the shortest path.