A ball balancing-robot is a non-minimum phase, omni-directional mobile robot that balances on a ball with shape accelerated dynamics. It possesses five degrees of freedom and it is driven by three actuators, yielding an under-actuated MIMO system.
This thesis covers the analysis of the dynamic model derived through Lagrangian mechanics and using quaternion representation, and it draws conclusions with regard to the implications of the unit quaternion operations.
Based on this model, two Unscented Kalman Filters (UKF) are implemented to deal with the measurement signals and are in charge of orientation and velocity estimation. The Quaternion UKF introduces a novel treatment of the quaternion to assure its unit norm.
Velocity and balance control are achieved through a cascade control structure. To deal properly with the MIMO system and quaternion algebra, a modification of the non-linear Feedback Linearization Controller is implemented. An adequate reference tracking, equivalent to a Sliding Mode Controller performance, is achieved.
Simulation results prove the ability of the algorithms to control the system, although further laboratory tests are to be conducted to justify the higher complexity