Motion planning for a pair of tethered robots

Considering an environment containing polygonal obstacles, we address the problem of planning motions for a pair planar robots connected to one another via cable limited length. Much like prior problems with single robot fixed base, straight line-of-sight visibility plays important role. The present paper shows how reduced graph provides natural discretization and captures essential topological considerations very effectively two case as well. Unlike case, however, bounded length introduces around coordination (or equivalently, when viewed from point view centralized planner, relative timing) that complicates matter. Indeed, has introduce rather more involved formalization than single-robot work in order establish core theoretical result -- theorem permitting be cast finding paths trajectories. Once affirmed, reduces straightforward search elegant representation connecting cable, demanding only few extra ancillary checks ensure sufficiency guarantee feasibility solution. We describe our implementation A${}^\star$ search, report experimental results. Lastly, prescribe optimal execution solutions provided by algorithm.