Abstract: A navigational apparatus and method is provided for autonomous vehicles having digitally controlled drive means for driving the vehicle along a line in either forward or rearward direction and for turning the vehicle either clockwise or counterclockwise with zero turning radius. The navigational apparatus includes obstacle sensors connected to the vehicle for producing an obstacle signal in response to contact or other desired proximity between an obstacle and a vehicle as the vehicle is driven through a work area. The work area comprises a substantially horizontal planar work surface bounded on all sides by an obstacle. The navigational apparatus also includes a search memory storage device connected to the vehicle for storing a two-dimensional memory array comprising a sufficient number of array elements to represent the work area to a desired resolution and with each array element representing a unique work area increment within the work area.