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The fiber positioner plays an important role in carrying the fiber in the Fiber Multi-Object Spectrograph. Most spectrographs such as the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) and the Dark Energy Spectroscopic Instrument (DESI) have thousands of fiber positioners shared working space. However, the overlap of motion areas increases the possibility of collisions for fiber positioners within a confined space. The collision prevents fiber positioners from reaching the designated observation position, which reduces the observation accuracy of the telescope and the service life of fiber positioners. This study proposed a collision-free motion planning approach based on the collision risk function for the fiber positioner. By using this method, a collision-free trajectory can be planned before positioners run, avoiding the discontinuity of trajectory caused by collision avoidance while running. Simulated experiments validated that our method has the advantages of easy operation, complete avoidance of collision, and less accumulation of motion errors compared with the existing anti-collision motion trajectory planning methods.
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