Model and Definitions of Robotic Sensor

The space to be filled by the sensors is a simply connected to orthogonal region S that is partitioned into square cells each of size roughly equal to the area occupied by a sensor. Simply connected means, it is possible to reach any cell in the space from any other cell and there are no obstacle surrounded completely by cell belonging to the space.

The system is composed of simple entities, called sensors, having locomotion and sensory capabilities. The entities can move and turn in any direction. The sensory devices on the entity allow it to have a vision of its surrounding: we assume the sensors to have restricted vision up to a fixed radius around it. They do not have any explicit means of communicating with each other even if two sensors see each other. Each sensor functions according to preprogrammed algorithm into it. The sensors have a (1) bits of working memory, and they have the orientation of local sense.

If two sensors are in the same cell at the same time then there is a collision. The algorithms executed by the sensor have to avoid collisions. The sensors enter the space through special cell that is called doors. A door is simply a cell in the space which always has sensors. Whenever the sensors in the door move to the neighboring cell, a new sensor appears instantaneously in the door.

The sensor first look s at its surrounding and then based on the rules of the algorithm during each step taken by a sensor, the sensor either chooses one of the neighboring cells to move to, or decides to remain stationary. Each step is atomic and during one step of sensor can only move to a cell of neighboring. However since the sensors are asynchronous, an arbitrary amount of time may lapse between two steps that taken by a sensor.

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