The TAIAPAN instrument, being developed by the Australian Astronomical Optics (AAO) - Macquarie University, deploys 159 Starbug robots to position optical fibers on a 32 cm glass field plate on the focal plane of the 1.2 m UK-Schmidt telescope. The Starbug Routing algorithm created for the instrument allows the autonomous robots to reach accuracies of 0.5 arcsec of the assigned target. It employs a 3 stage tiered approach to find a collision-free path for Starbugs of increasing complexity and computational cost. For each Starbug a path is attempted using a direct simultaneous movement. If unsuccessful, subsequently more complex (and expensive) methods are tried until a valid path is found or the target is discarded. The system uses a MongoDB database to record and retrieve starbug locations and properties which allow in-situ re-routing to take place as well.