Force and torque induced by traveling motion of a mobile robot effect dynamically to the objects being carried on it. If the induced force and torque should be bigger than the static friction force and torque exerting between the carrying objects and the mobile robot, the carrying objects start to slip on it. Since this slipping motion causes increasing the acceleration of the mobile robot, then the slipping of one object leads a dangerous collapse of all carrying objects. Furthermore it interferes with accurate traveling motions. From these influence again safe transportation without fixations of the objects to the mobile robot to save time and to increase production efficiency in factories, this paper purposes a controller to guide the mobile robot along a given course as fast as possible with acceleration restriction not to slip the carrying objects during traveling.