We propose a contraction transformation algorithm to plan a complete coverage trajectory for a mobile robot to ac-complish specific types of missions based on the Aold dynamical system. First, we construct a chaotic mobile robot by com-bining the variable z of the Aold equation and the kinematic equation of the robot. Second, we construct the candidate sets including the initial points with a relatively high coverage rate of the constructed mobile robot. Then the trajectory is contracted to the current position of the robot based on the designed contraction transformation strategy, to form a continuous complete cov-erage trajectory to execute the specific types of missions. Compared with the traditional method, the designed algorithm requires no obstacle avoidance to the boundary of the given workplace, possesses a high coverage rate, and keeps the chaotic characteristics of the produced coverage trajectory relatively unchanged, which enables the robot to accomplish special missions with features of completeness, randomness, or unpredictability.