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