In order to cover unknown workspace of mobile robots, an area-coverage path planning which is controlled by a novel memristor-based double-stroll chaotic system has been proposed in this paper. The motion path of the mobile robots is unpredictability, randomly, and evenly. The characteristics of unpredictability of motion path and the fast scanning have lots of usage, such as the surveillance of terrains, search or cleaning purposes and the patrolling for intrusion in military facilities. The novel memristor-based double-stroll chaotic system is given to generate higher unpredictability, more even and faster scanning path. Chaotic trajectories are executed using state variables of the new double-stroll chaotic system as input for a mobile robot through two independent active wheels. Simulation results and its analysis illustrate the usefulness and effectiveness of the proposed motion control strategy.