3D Modeling and Control Design for a Ballbot

• Main Authors: Chia-Lung Hsu, 徐嘉隆
• Other Authors: 林麗章
• Format: Others
• Language: zh-TW
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/38171380037779164263

碩士 === 國立中興大學 === 機械工程學系所 === 96 === In this thesis, we consider the modeling and control for a ballbot that can freely move in any direction within range. The whole complex analytical dynamic equations are derived and then used for synthesizing a nonlinear tracking control law for arbitrary trajectory following. Based on the assumption of no slippage between the three rollers and the ball, forward and inverse velocity kinematics equations are derived. After building the complex kinetic energy and potential energy expressions, the analytical 3D dynamic equations are derived via Lagrange’s equations. The dynamics model of a ballbot is input-output feedback linearizable. Thus, by choosing an appropriate Lyapunov function candidate, a stable nonlinear control law is derived, based on the linearizable part model, using the backstepping method. Finally, computer simulations are used to illustrate the effectiveness of the suggested control strategy using a desired motion trajectory generated by the cubic spline interpolation method.