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The navigation of autonomous mobile machines, which are referred to as robots, through terrains whose models are not known a priori is considered. The authors deal with point-sized robots in 2-D and 3-D (two- and three-dimensional) terrains and circular robots in 2-D terrains. The 2-D (or 3-D) terrains are finite-sized and populated by an unknown, but finite, number of simple polygonal (or polyhedral) obstacles. The robot is equipped with a sensor system that detects all vertices and edges that are visible from its present location. Two basic navigational problems are considered. In the visit problem, the robot is required to visit a sequence of destination points in a specified order, using the sensor system. In the terrain model acquisition problem, the robot is required to acquire the complete model of the terrain by exploring the terrain with the sensor. A framework that yields solutions to both the visit problem and the terrain model acquisition problem using a single approach is presented, and the algorithms are described. The approach consists of incrementally constructing, in an algorithmic manner, an appropriate geometric graph structure (1-skeleton), called the navigational course. A point robot employs the restricted visibility graph and the visibility graph as the navigational course in 2-D and 3-D cases, respectively. A circular robot uses the modified visibility graph.>
Rao et al. (Mon,) studied this question.