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Inspired by infant development theories, a robotic developmental model combined with game elements is proposed in this paper. This model does not require the definition of specific developmental goals for the robot, but the developmental goals are implied in the goals of a series of game tasks. The games are characterized into a sequence of game modes based on the complexity of the game tasks from simple to complex, and the task complexity is determined by the applications of developmental constraints. Given a current mode, the robot switches to play in a more complicated game mode when it cannot find any new salient stimuli in the current mode. By doing so, the robot gradually achieves it developmental goals by playing different modes of games. In the experiment, the game was instantiated into a mobile robot with the playing task of picking up toys, and the game is designed with a simple game mode and a complex game mode. A developmental algorithm, “Lift-Constraint, Act and Saturate,” is employed to drive the mobile robot move from the simple mode to the complex one. The experimental results show that the mobile manipulator is able to successfully learn the mobile grasping ability after playing simple and complex games, which is promising in developing robotic abilities to solve complex tasks using games.