Topic: Kalman Filtering and Control Systems Design

Due: Monday, February 26

Three handouts are needed for this assignment.

1. Kalman Filter Design:
   
   Solve problem 1 in Chapter 3 of Dudek & Jenkin.
    
2. Control Systems Design:
   
   Using an inertia-free (i.e. mass-less) model of the differential-drive robot, design a second-order control system to solve the wall-following problem (without concern for inside or outside corners).  You may assume that the absolute value of the angle theta between the robot heading and the wall is small, and that the translational speed v is a known constant (otherwise we need to solve an under-constrained system of two unknown variables).
   
   Do this in the style of development as presented in Notes on Control Systems Design, except that you should add a differentiator instead of an integrator (see the PID Tutorial).  Also determine analytically the optimal gain to establish critical damping.
   
   Then, write a Frob program corresponding precisely to your design, and see how well it works.  What happens if mass is added to the analysis and simulation?