An approach to the planning of optimal robotic motions in the pres ence of obstacles is proposed. It is based on the use of nonclassical formulation of Pontryagin's maximum principle, which makes it possible to handle efficiently the state constraints resulting from the robotic tasks to be performed. The convergence properties of the algorithm are examined. A computer example involving a pla nar redundant manipulator of three revolute kinematic pairs, which performs two tasks in a two-dimensional work space including ob stacles, is given. A comparison of the proposed approach with the well-known method of penalty function is made.
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