Dynamic modeling and trajectory planning for a mobile spherical robot with a 3Dof inner mechanism

A spherical robot consists of a spherical shell and an inner mechanism. In this paper, a new inner mechanism with three independent actuators is presented. The robot motion is based on angular momentum conservation principle and the system is nonholonomic. The kinematic and dynamic equations of the whole system are derived by using Euler parameters and Kaneʹs method. The singularity does not occur in the equations of inverse dynamic because of using Euler parameters instead of Euler angles. By adding one degree of freedom to the inner mechanism, the trajectory planning of the mobile spherical robot is possible for every desired trajectory. The trajectory planning is done for linear and circular arc trajectories. The robot starts its motion from first point with zero velocity to the end point on the desired trajectory and stops at the end point. The computer simulation of robot motion is done. The comparison of the numerical solution with computer simulation shows good agreement.