MIRADAS is a near-infrared multiobject echelle spectrograph operating at spectral resolution R  =  20,000 over the 1 to 2.5  μm bandpass for Gran Telescopio Canarias. It possesses a multiplexing system with 12 cryogenic robotic probe arms, each capable of independently selecting a user-defined target in the instrument field of view. The arms are distributed around a circular bench, becoming a very packed workspace when all of them are in simultaneous operation. Therefore, their motions have to be carefully coordinated. We propose here a motion planning method for the MIRADAS probe arms. Our offline algorithm relies on roadmaps comprising alternative paths, which are discretized in a state-time space. The determination of collision-free trajectories in such space is achieved by means of a graph-search technique. The approach considers the constraints imposed by the particular architecture of the probe arms as well as the limitations of the commercial off-the-shelf motor controllers used in the mechanical design. We test our solution with real science targets and a typical MIRADAS scenario presenting some instances of the two identified collision conflicts that can arise between any pair of probe arms. Experiments show the method is versatile enough to compute trajectories fulfilling the requirements.