Modelling and Control of a Robotic Hula-hoop System without Velocity Measurements

摘要

The contact kinematics of a robotic hoop and a pole system is obtained by using the Montana's equations, considering the case of contact without slipping. The resulting kinematic model is completely nonholonomic. After some mild assumptions, a set of Pfaffian constraints is established. Then, a dynamic model of the system is developed by employing the Lagrange-d'Alembert formulation. This dynamic model, which represents an underactuated mechanical system, is later used to design a controller which does not need velocity measurements. The proposed method, and its robustness against model uncertainties, is validated through numeric simulations.