A mobile robot configured to travel across a residential floor or other surface while cleaning the surface with a cleaning pad and cleaning solvent is disclosed. The robot includes a controller for managing the movement of the robot as well as the treatment of the surface with a cleaning solvent. The movement of the robot can be characterized by a class of trajectories that achieve effective cleaning. The trajectories include sequences of steps that are repeated, the sequences including forward and backward motion and optional left and right motion along arcuate paths.