Path planning among unknown obstacles: the case of a three-dimensional Cartesian arm

A generalization to the 3-D manipulator of a 2-D approach to sensor-based robot motion planning in an unknown environment with arbitrary obstacles is considered. For the approach to guarantee convergence, it is vital that the number of options that the arm has for passing around an obstacle be limited. A three-link arm has an infinite number of directions for passing around an obstacle, but, by making use of the natural constraints imposed by the arm kinematics, the 2-D approach is extended to a three-link 3-D arm manipulator with sliding joints (a Cartesian robot arm). The technique exploits certain properties, called anisotropy and monotonicity, of the arm configuration space. The resulting algorithm is the first nonheuristic algorithm for online motion planning in three dimensions, with no prior knowledge of the obstacles. Collision-free motion is guaranteed for every point of the robot body; in no case does the generated path amount to an exhaustive search of the work space