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A spatial sampling criterion for sonar systems that allows all obstacles within a given radius from the sensor to be detected is described. The environment considered is a two-dimensional floor plan that is extended into the third dimension, in which the scanning is performed in the horizontal plane. In this environment, edgelike reflectors, such as edges of doors or doorways, and oblique surfaces are the most difficult to detect. By considering the physics of sound propagation, the sonar scanning density required to detect these objects is determined. An experimental verification is included. The limitations of detecting objects with sonar in a more general environment are discussed. These results can be used to determine the necessary spacing in a transducer ring array and the maximum step size that a mobile robot can translate without danger of collision.>
Roman Kuc (Sun,) studied this question.