Swing-up and balancing control of underactuated robotic systems

Control algorithms for swing-up and balancing of underactuated robotic systems have been developed. Underactuated systems are defined as those that have fewer actuators than degrees of freedom and can arise in many applications. The swing-up and balancing control problem addressed within this thesis is to move an underactuated robot from its stable downward position to an unstable inverted position and balance it there. The control strategy is to design separate controllers for swing-up and balancing, then switch between these two controllers when the system enters the basin of attraction of the balancing controller. Underactuated two-link and three-link robots are studied. Three control algorithms are presented for swing-up. First, proportional plus derivative (PD) control design via partial feedback linearization is developed. Second, a control input design based on the energy of the system for the closed loop dynamics resulting from partial feedback linearization is studied. It is assumed that the parameters of the system are exactly known in the development of the above two control algorithms. Third, a robust control scheme using sliding mode concepts is developed to compensate for modeling uncertainties. In addition, three control algorithms are developed for balancing the underactuated robot at the unstable vertical position: a linear quadratic regulator, partial feedback linearization control, and sliding mode control. The reference trajectory used in the partial feedback linearization and sliding mode controller is designed from the linearized zero dynamics and selected to achieve locally asymptotic stability to the balancing configuration. To validate the control algorithms experimentally, a complete controller for swing-up and balancing has been designed and implemented on the Pendubot, a two-link underactuated robot. The parameters of the Pendubot were varied by up to 50% in order to test robustness to parameter errors. The robust control scheme using sliding mode concepts successfully compensated for modeling imprecision and disturbances inherent in the experimental demonstration.