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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. Since this slipping motion causes increasing the acceleration of the mobile robot, then the slipping of one object leads to dangerous collapse of all carrying objects. Furthermore it interferes with accurate traveling motions. On the other hand, mobile robots are desired to transfer the carrying objects as fast as it can. On this view point of contradicted requirements, this paper purposes a controller to guide the mobile robot along a given course as fast as possible with acceleration restriction to avoid slipping of carrying objects during traveling.