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An efficient, on-line terrain-covering algorithm is presented for a robot (AUV) moving in an unknown three-dimensional underwater environment. Such an algorithm is necessary for producing mosaicked images of the ocean floor. The basis of this three-dimensional motion planning algorithm is a new planar algorithm for nonsimply connected areas with boundaries of arbitrary shape. We show that this algorithm generalizes naturally to complex three-dimensional environments in which the terrain to be covered is projectively planar. This planar algorithm represents an improvement over previous algorithms because it results in a shorter path length for the robot and does not assume a polygonal environment. The path length of our algorithm is shown to be linear in the size of the area to be covered; the amount of memory required by the robot to implement the algorithm is linear in the size of the description of the boundary of the area. An example is provided that demonstrates the algorithm's performance in a nonsimply connected, nonplanar environment.

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