Dynamic analysis and control synthesis of a spherical wheeled robot (Ballbot)

Ballbot is a mobile robot consists of a body mounting on a spherical wheel. The spherical wheel can make the robot move in any directions. This robot is an unstable underactuated system with nonholonomic velocity constraints. In this paper, first, a 3D dynamic model of the robot is derived while taking the nonholonomic constraints into considerations. Since Ballbot is an underactuated system, finding a normal form for the equations could be helpful in the control point of view. Therefore, the equations of motion are examined to find whether there is a simple normal form or not. To enforce the robot to track any given trajectory on the ground, an online fuzzy logic trajectory planning is suggested. A computed torque method and a sliding mode controller are used along the fuzzy trajectory planning to perform the tracking goal. To consider uncertainties and disturbances, some simulations are performed. The results show that the sliding mode controller demonstrate much better performance compared to the computed torque controller. When there is no uncertainty, the computed torque method is candidate showing less tracking error than the sliding controller.