Design of LQR-PI and MPC controllers for pitch control of a ballbot

A statically stable robot may or may not generally be dynamically stable. A multi-wheeled robot, although statically stable, dynamically may become unstable in highly inclined surfaces. Therefore, they need to have a low center of gravity and a wide base. Alternatively, a self-balancing 2-wheeled platform must yaw about its axis to travel in a desired direction. A single-wheeled robot however can move directly, without yawing, in any direction instantaneously. This paper presents a planar mathematical model and the controller design for a ball-bot system. Two controller techniques, viz., LQR-PI and MPC are designed to stabilize the Ball-bot. Comparison study based on the performance of the system with these two controllers are also done.