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An automatic system for planning safe trajectories for a computer controlled manipulator among obstacles is a key component of robot assembly operations. This paper describes an algorithm transforming cartesian obstacles into obstacles in the space of the first three joints of a manipulator with six revolute joints (e.g. a ACMA-CRIBIER V80), and giving a hierarchical description of the free space by mean of an octree. Such a description is very useful in testing for collision between the arm of the manipulator end obstacles since it is represented by a point in this space.