Tread structures, wave motion navigational controls, and ramp up recovery controls are provided to an autonomous floor cleaner to reduce wheel slippage. The floor cleaner delivers liquid to the floor as part of the cleaning process. Wheels on the device are provided with relatively deep peripheral grooves to minimize the contact surfaces of a sprocket wheel and to accommodate the layer of liquid on the floor. In the event of wheel slippage, or to prevent wheel slippage, the device is designed to move forward with a slight side-to-side wave action caused by periodically altering the relative speeds of two drive wheels. There is also provided a slippage recovery mode where the drive wheels shut down or greatly slow when severe slippage is sensed, followed by a slow ramp up of speed.