Computing from words via rough mereology in mobile robot navigation

In this paper a method of mobile robot navigation based on rough mereology is presented, that can be useful in translating spatial expressions in natural language into low level spatial descriptions. In our paper we apply a geometry of solids, that takes disks as a geometrical primitive and the relation "to be a part in degree", as a basis to build more complicated geometrical notions. In specifying to which degree one region is the part of another the rough membership function is applied. To determine regions we use a sonar system, that consists of one omni-directional ultrasonic transmitter located on the robot and a set of receivers located in the robot space\´. By measuring time of flight of pulse from the transmitter to a receiver we determine the distance between them, as well as receiver regions-disks with centers in receiver positions and radii equal to measured distances. The reflected pulse determines the distance to the nearest wall or obstacle and defines the non-collision region-a disk with radius equal to measured distance. In navigation tasks we do not treat the robot as a point, but we replace it with a non-collision region. We propose a scheme for converting natural language control into physical descriptions. This scheme can be used in dynamical systems (e.g., mobile robot navigation). Finally, we present results of simulation and real world experiments.