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This work continues the approach to sensor-based robot motion planning in an unknown environment first studied in 2,3 and further developed for various configurations of planar robot arms in 4,10. The main idea of the approach is to reduce the problem to the analysis of simple closed curves on an appropriate two-dimensional (2d) manifold. We extend the same ideas to simple 3d arms with two revolute joints whose endpoints travel along 2d manifolds whereas their bodies operate in a "normal" 3d space. For such an arm, a path planning algorithm is described, its convergence is shown, and an example of the algorithm performance is given.
Lumelsky et al. (Wed,) studied this question.