A new mobile ball robot-dynamic modeling and simulation

In this paper the construction and dynamic modeling of a mobile ball robot is represented. The unique mechanical structure of this robot results more reliable and stable motion with respect to previous similar robots. Driving mechanism is placed within a hollow spherical case, and consists of three sets of actuated omni–wheels for omni-directional motion of the robot. This mechanism decreases relative slip between the inner actuation system and outer ball case, and results more precise control of the robot in different paths and places. At first, the mechanical structure, actuation and control system, and process of different components assembling to work as a robot is explained. Then, based on the Newton–Euler formulation, mathematical model of motion is derived and dynamic equations of the robot are evaluated. These equations have differential algebraic equations (DAEs) formation. Consequently, a computational method to solve ADEs has been developed. Finally, in a case study, the robot performance in passing through a linear path with two perpendicular segments is studied. Simulation and experimental results demonstrate that robot moves through the desired and predefined trajectory.