Design, modeling, and control of a two degree of freedom pendulum on an omnidirectional robot

In this thesis a dynamical model for a two degree of freedom inverted pendulum on an omnidirectional cart is developed. This system is actuated not only by the wheels on the cart but also by a quadrotor system used to stabilize the inverted pendulum. The dynamic model is designed to be modular allowing for the substitution of different actuators, electrics, and control algorithms without the need to re-derive the model. The parameters of this system are identified with procedures and background where necessary. This thesis presents two controller methods: PID and LQG controllers. The PID controllers were designed using both hand tuning and model based tuning. The LQG controllers were designed using a systematic procedure to initially choose good weights and adjust the weights based off of systems performance in order to get the most out of the system. All sets of controllers are presented along with a comparison of their behavior and plots comparing the real system to that of the non-linear simulation. The results of this design are discussed along with issues that shaped the design decisions, future work and systems improvements are discussed.