System Modeling And Research On Self-Balancing Control Of A Single-Ball Self-Balancing Mobile Robot

The Single-ball self-balancing mobile robot which originates from inverted pendulum model is a typical multivariable,nonlinear,high order,strong coupling and static instability system.The control theory of the single-ball self-balancing mobile robot model is also widely used in robot and artificial intelligence control,missile interception and space station docking control,rocket launch and spacecraft flight attitude control and other fields.In this paper,a physical prototype was developed for the self-balancing control of single-ball self-balancing mobile robot system,and the mechanics modeling and control algorithm were studied of the prototype.The main contributions were follows:Firstly,through the study of the mechanical structure and motion characteristics of the singleball self-balancing mobile robot,the physical prototype of the single-ball self-balancing mobile robot was established on the based of the design of "Rezero" robot.The physical prototype had a smaller angle between the three omnidirectional wheel and the vertical line,so that the effective friction between the omnidirectional wheel and the drive sphere was greater,and the transmission efficiency was higher.In addition,the main controller which was used by the single-ball selfbalancing mobile robot control system was the United States TI company model TMS320FC28335high-speed DSP(Digital Signal Processing)development board,while a high-performance nine-axis attitude sensor as a detection device was introduced,so that the entire single-ball self-balancing mobile robot control system response faster,accuracy and efficiency were higher.Secondly,based on the systematic analysis and study of the mechanical structure of the single-ball self-balancing mobile robot,the single-ball self-balancing mobile robot model was equivalent to the principle of simple,theoretical maturity of one-stage inverted pendulum model and IASMP(Inverse Atlas Spherical Motion Platform)model,so that the accuracy and reliability of the modeling of the single spherical self-balancing mobile robot improved a lot.At the same time,the dynamics and kinematics modeling of single-ball self-balancing mobile robot were build up by using the Euler-Lagrangian equation and Jacobian matrix and the established kinetic equation was linearized in the vicinity of the system state zero to obtain the linearization model.Finally,controllability,observability and stability of the linearized model were analyzed.Then,aiming at the problem of self-balancing control(including position control and inclination angle control)for single-ball self-balancing mobile robot,two kinds of control algorithms of PID and LQR which were simple in structure and widely used were designed.Andthe position of the single-ball self-balancing mobile robot was mainly controlled by the PID control algorithm.The LQR control algorithm mainly controlled the inclination of the single-ball selfbalancing mobile robot.And the control effect of two control algorithms of PID and LQR was simulated and analyzed by using MATLAB/SIMULINK software.Finally,according to the demand of self-balancing and position control of single-ball selfbalancing mobile robot,the self-balancing and position control program and motion conversion program of single-ball self-balancing mobile robot were designed.At the same time,the hardware and software of the control system were debugged,and the control algorithm was written into the CCS(DSP programming software)program code then it would be inserted into the DSP main controller to experiment and analyze of the single-ball self-balancing mobile robot physical prototype,indicating the effectiveness of the designed control algorithm.