A robotic focal plane system using robotic fiber positioners enables multi-object spectroscopy for hundreds to thousands ofgalaxies by utilizing a dense array of positioners that are closely packed at the focal plane of a telescope. While this densearrangement increases the number of observations, it also introduces the potential for collisions between adjacentpositioners. A fiber positioner is designed similarly to a SCARA robot. It is driven by two series of BLDC motors. Eachpositioner is manufactured with an outer diameter of 16 mm. It operates within an annular workspace with an outerdiameter of 33.6 mm and an inner diameter of 12.8 mm. As these positioners are arranged with a spacing of 16.8 mm,target assignment and motion planning are critical to avoid collisions caused by overlapping workspaces. To address this,we proposed an optimized step choice algorithm using a motion planning method based on optimization with the sequentialquadratic programming algorithm. Simulation results demonstrated that paths for all positioners within a tile weresuccessfully generated with a success rate of up to 93.75% across 80 tiles.
