This technical report presents a 3D model of a robot that balances on a ball. This new generation of robots, also called Ballbots, has recently been developed and described by several authors. Different from the conventional approach of generalizing 2D behavior to the 3D case, however, this report presents a full 3D model derived from geometrical, mechanical and energetical considerations; moreover, the motor dynamics is included. For control purposes, the model is linearized and analyzed with particular attention to controllability. The valid range of the linearized system is discussed based on a comparison with the original nonlinear model. Finally, the new model is validated using a 2D model from the literature.     «

This technical report presents a 3D model of a robot that balances on a ball. This new generation of robots, also called Ballbots, has recently been developed and described by several authors. Different from the conventional approach of generalizing 2D behavior to the 3D case, however, this report presents a full 3D model derived from geometrical, mechanical and energetical considerations; moreover, the motor dynamics is included. For control purposes, the model is linearized and analyzed with...     »