A ball-balancing robot (BBR) is a robot that balances itself on top of a ball, typically using three omni-directional wheels. This class of robot features a highly coupled 3D nonlinear dynamics that is capable of natural and holonomic motion. This dissertation presents a new mechanical design, a tractable dynamic model that is accurate at high yaw rates, and an effective estimation and control strategy for a micro ball-balancing robot (MBBR). The miniaturization and the low-cost components used in this design add significant control challenges, which manifest in the form of reduced durability and high amounts of noise, friction, and vibration, making the design of effective state estimation and control strategies for it very difficult, especially under high yaw rates. This motivates the design and use of a reduced nonlinear model which captures the important high yaw-rate dynamics well, and the design of an effective model-based observer and controller based on this reduced nonlinear model. The primary contributions of this dissertation in the general area of ball-balancing robotics include: (1) the novel (and, now, patented) midlatitude and orthogonal-omniwheel orientation of the design, (2) a reduced (minimum complexity) nonlinear BBR dynamic model which well captures its high yaw-rate behavior, and (3) the development of an effective model-based estimator (Extended Kalman Filter) and controller which are capable of achieving remarkable performance of this delicate system under high yaw rates.

The novel omniwheel placement minimizes coupling and increases the normal force acting on the omniwheels, which helps to reduce the slipping caused by its very light body. Another contribution of this dissertation is: (4) the modeling and real-time implementation of drive/coast motor drivers, which is also used in the MBBR. Drive/coast motor drivers exhibit highly nonlinear behavior, which makes using them in a model-based controller difficult, but they allow for zero torque dynamics which can be quite useful for many wheeled robots. The drive/coast motor model has been implemented in our linear feedback controller, and has achieved remarkably good position tracking even under high yaw-rates. The performance of the observer and controller were verified with a motion capture system.