Euler-Lagrangian modeling and exact trajectory following controlling of Ballbot-like robot

Sphere-based spherical inverted pendulum (SSIP) robot, the first prototype of SSIP robot being Ballbot by CMU, consists of a pendulum-like upper body and a supporting spherelike rolling body and moves in human environment without falling. Motion control of Ballbot-like robot is a key factor determining whether Ballbot-like robot can safely exist in human environment. In this paper, modeling and trajectory following controller of Ballbot-like robot are investigated in detailed. Using Euler-Lagrangian equation method, we formulate the dynamics of the Ballbot-like robots, which is a nonholonomic mechanical system, combining the characteristics of nonholonomic rolling of sphere without sliding and the strong nonlinearity of spherical inverted pendulum. Further, the exact trajectory following controller approach is employed to the Ballbot-like robot to follow trajectory. Numerical simulations are implemented to demonstrate the controller's effectiveness. To the best knowledge of the authors, it is the first time for Ballbot-like robot to obtain the explicit dynamics and to realize exact trajectory following.