  This paper considers the motion planning problem for multiple tethered planar
mobile robots. Each robot is attached to a fixed base by a flexible cable.
Since the robots share a common workspace, the interactions amongst the robots,
cables, and obstacles pose significant difficulties for planning. Previous
works have studied the problem of detecting whether a target cable
configuration is intersecting (or entangled). Here, we are interested in the
motion planning problem: how to plan and coordinate the robot motions to
realize a given non-intersecting target cable configuration. We identify four
possible modes of motion, depending on whether (i) the robots move in straight
lines or following their cable lines; (ii) the robots move sequentially or
concurrently. We present an in-depth analysis of Straight & Concurrent, which
is the most practically-interesting mode of motion. In particular, we propose
algorithms that (a) detect whether a given target cable configuration is
realizable by a Straight & Concurrent motion, and (b) return a valid
coordinated motion plan. The algorithms are analyzed in detail and validated in
simulations and in a hardware experiment.
