The biggest source of difficulty with this assignment was deriving the dynamics. People either took the Lagrange approach, or went with free-body diagrams. The problem was with how to apply the torque from the motor to the wheel and the rider. By Newton's Third Law, the torque acting on the rider must be equal and opposite to the torque acting on the pendulum. Some people applied the force just to the wheel. This corresponds to balancing a broomstick on your fingertip. It is also a challenging problem, but it is not equivalent to the segway.
In part 4, minimizing the sum of squared torques can potentially induce a higher peak torque to get the job over with, depending on the problem. I didn't see people reason that if we're trying to use small motors, that we should be trying to minimize the maximum torque ever applied, not the average torque.
Some notable examples:- The code with this assignment has an instructive use of classes in Matlab, and a concise use of symbolic math functions to derive the dynamic equations and linearize them.
- This assignment used genetic algorithms in the planner of part 4.
- Free body diagram approach to deriving the dynamics.
- Attempts at dynamic programming were not successful.
- The most robust solutions to the planning part transferred control between different LQR controllers to speed up, slow down, and move steadily.
Remarks on grading: Some people whose work was interesting got penalized for sloppy or incomplete writeups. I want to see thorough writeups that clearly document the decisions made and the details of the approaches taken. Don't be shy to include lots of plots, but say something about each of them. I graded on a narrower scale for this assignment.
