This paper considers a design problem for time synchronized coverage control of cooperative mobile robots. The derived algorithm provides a coverage control which not only considers the mobility characteristic of each mobile robot for task allocation but generates robot velocity profile for synchronized coverage completion within the constrained time. Since the environment for robot coverage work is modeled as a set of locations to visit by robots, the derived coverage algorithm and its control method are equally well suited to an unstructured working environment as to the structured work space. In determining the number of locations for each robot to visit during coverage operation, a time index derived from the minimum time velocity profile is used for the comparison of robot performance. Once the set of locations has been determined for each robot, the corresponding path tree and velocity profile are generated for synchronized execution of coverage work. The completeness of synchronized group coverage within the constrained time is proven through simulation for a group of mobile robots with different motor characteristics. An additional consideration by the derived coverage controller is collision avoidance of mobile robots in a crowded environment with the aid of finite potential function approach.