Kinematic Analysis and Control Algorithm for the Ballbot

The ballbot is a dynamically stable mobile robot designed to balance on a single ball, whose dynamic stability enables improved navigability in narrow, crowded, and dynamic environments. Through its single contact point with the ground, ballbot is omnidirectional and exceptionally agile, maneuverable, and organic in motion compared to other ground vehicles. For dealing with the challenging and imperative issues about ballbot, such as balancing, yaw, position control algorithms as well as the mathematical kinematic model, a novel model employing the Lagrange Equation is derived and control algorithm based on the similar principle as the second-order inverted pendulum is proposed, which is used for tackling the balancing, yaw, and position control. A cascade fuzzy proportional derivative (PD) controller and another controller with proportional integral (PI) control and PD feedback are designed for position and speed, respectively. Yaw control is presented, including head-hold mode and head-free mode. Some experiments are carried out to validate the effectiveness of the mathematical model and control algorithm.