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BYQ-III is a spherical mobile robot. This paper deals with the problem of its simple motion control in a fixed motion mode. The robot BYQ-III is designed to be partially self-contained. A simplified dynamic model of the rotation motion in the median sagital plane is derived under some assumptions. A full-state linear feedback controller for the dynamic model and a PI controller are designed to implement the motion control in the median coronal plane and the sagital plane respectively. The model and the controllers were validated through a set of experiments. Experimental trajectories for a circle of the robot on the plane were found to agree to a reasonable accuracy. The overall design, actuator mechanism, control system, and initial results are presented in this paper.