In order to improve the posture control and motion control ability of the single-ball robot

the single-ball robot with linear quadratic optimized controller based on fuzzy proportional-integral-differential（PID） control algorithm is designed

it is applied in robot self-balancing posture calculation and motion tracking control.In order to improve the real-time

accuracy and reliability of the single-ball robot posture control

complex kinematics model is simplified into two-dimensional inverted pendulum kinematics model

and forward kinematics and inverse kinematics are used to establish omnidirectional wheel and ball movement function of robot

then the Lagrangian dynamics model is built.Finally

posture balance and motion trajectory tracking process of robot are simulated.The simulation result shows that the ball balance robot with optimized controller has the advantages of fast response speed and strong anti-interference in posture control and motion control.