We introduce a novel strategy of designing a chaotic coverage path planner for the mobile robot based on the Che-byshev map for achieving special missions. The designed chaotic path planner consists of a two-dimensional Chebyshev map which is constructed by two one-dimensional Chebyshev maps. The performance of the time sequences which are generated by the planner is improved by arcsine transformation to enhance the chaotic characteristics and uniform distribution. Then the coverage rate and randomness for achieving the special missions of the robot are enhanced. The chaotic Chebyshev system is mapped into the feasible region of the robot workplace by affine transformation. Then a universal algorithm of coverage path planning is designed for environments with obstacles. Simulation results show that the constructed chaotic path planner can avoid detection of the obstacles and the workplace boundaries, and runs safely in the feasible areas. The designed strategy is able to satisfy the requirements of randomness, coverage, and high efficiency for special missions.