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An approach of dynamic path planning (DPP) was introduced elsewhere, and nonheuristic algorithms were described for planning collision-free paths for a point automaton moving in an environment filled with unknown obstacles of arbitrary shape. The DPP approach was further extended to a planar robot arm with revolute joints; in this case, every point of the robot body is subject to collision. Under the accepted model, the robot, using information about its immediate surroundings provided by the sensory feedback, continuously (dynamically) generates its path. Various kinematic configurations of planar arms with revolute and sliding joints are analyzed in this paper from the standpoint of applying the same strategy. It is shown that, depending on the arm kinematics, specific modifications must be introduced in the path planning algorithm to preserve convergence. The approach presents an attractive method for robot motion planning in unstructured environments with uncertainty.