Path Following Using Gain Scheduled LQR Control : with applications to a labyrinth game

Abstract: This master's thesis aims to make the BRIO Labyrinth Game autonomous and the main focus is on the development of a path following controller. A test-bench system is built using a modern edition of the classic game with the addition of a Raspberry Pi, a camera and two servos. A mathematical model of the ball and plate system is derived to be used in model based controllers. A method of using path projection on a cubic spline interpolated path to derive the reference states is explained. After that, three path following controllers are presented, a modified LQR, a Gain Scheduled LQR and a Gain Scheduled LQR with obstacle avoidance. The performances of these controllers are compared on an easy and a hard labyrinth level, both with respect to the ability of following the reference path and with respect to success rate of controlling the ball from start to finish without falling into any hole. All three controllers achieved a success rate over 90 % on the easy level. On the hard level the Gain Scheduled LQR achieved the highest success rate, 78.7 %, while the modified LQR achieved the lowest deviation from the reference path. The Gain Scheduled LQR with obstacle avoidance performed the worst in both regards. Overall, the results are promising and some insights gained when designing the controllers can possibly be useful for development of controllers in other applications as well.