1. Show how you would compute the Minkowski sum of two given unit squares (i.e., with unit length sides).
2. Given a set of obstacles and a collision free path, draw the shortest collision free path homotopic to the given path.
3. A robot arm consists of two rigid pieces: fore-arm and upper-arm. Upper-arm has a full ball and socket joint and the lower has an elbow joint. The arm can fly in all three directions. Describe the arm's configuration space.
4. If A is a robot and B be a static obstacle in a 3-D workspace W. Suppose A is made of a single rigid body that can only translate. Also suppose A (at any configuration) and B are convex subsets of W. Prove that the C-obstacle corresponding to B is a convex region of the C-space of A.