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The paper describes a visual method for the navigation of autonomous floor-cleaning robots. The method constructs a topological map with metrical information where place nodes are characterized by panoramic images and by particle clouds representing position estimates. Current image and position estimate of the robot are interrelated to landmark images and position estimates stored in the map nodes through a holistic visual homing method which provides bearing and orientation estimates. Based on these estimates, a position estimate of the robot is updated by a particle filter. The robot's position estimates are used to guide the robot along parallel, meandering lanes and are also assigned to newly created map nodes which later serve as landmarks. Computer simulations and robot experiments confirm that the robot position estimate obtained by this method is sufficiently accurate to keep the robot on parallel lanes, even in the presence of large random and systematic odometry errors. This ensures an efficient cleaning behavior with almost complete coverage of a rectangular area and only small repeated coverage. Furthermore, the topological-metrical map can be used to completely cover rooms or apartments by multiple meander parts.