Single Spherical Wheel Mobile Robot And Its Self-balancing Control

As a typical multivariable and under-actuated system of high nonlinearity, self-balancing robot has always been a challenge for modern control theories. The work of this paper mainly focuses on the balancing control of a single spherical wheeled mobile robot which is called ballbot. Unlike the two-wheeled robot, the ballbot can balance upright on a sphere which is the only contact to the ground. Therefore, the ballbot becomes the ideal platform for validation of control algorithms.The work of this paper mainly focuses on the balancing control of the ballbot. First, the mathematical model of the ballbot is established. Next, the linear quadratic regulator and the hierarchical sliding mode controller are used in the balancing control. Finally, simulations and experiments are implemented to validate the control algorithms proposed in this paper. The main work is as follows:1. System design. The driving mechanism of the ballbot is designed. Hardware system of the ballbot is designed based on an embedded system of ARM. A data fusion algorithm is used to get the attitude information of the ballbot.2. Kinematics analysis and dynamic modeling. This paper presents a 3D model derived from geometrical, mechanical considerations which references to the modeling method of Carnegie Mellon University (CMU). Lagrange equation is introduced in the modeling and the properties of the system are analyzed.3. Controller design of the ballbot. A controller is designed to keep balance of the ballbot, employing the linear quadratic regulator and the hierarchical sliding mode controller. Simulations are implemented to analyze the control effect.4. Validation of control algorithms. The experiments of the control algorithms proposed in this paper are implemented to validate the control effect. The performances are analyzed and conclusions are received.