  A novel mechanism to derive self-entanglement-free (SEF) path for tethered
differential-driven robots is proposed in this work. The problem is tailored to
the deployment of tethered differential-driven robots in situations where an
omni-directional tether re-tractor is not available. This is frequently
encountered when it is impractical to concurrently equip an omni-directional
tether retracting mechanism with other geometrically intricate devices, such as
a manipulator, which is notably relevant in applications like disaster
recovery, spatial exploration, etc. Without specific attention to the spatial
relation between the shape of the tether and the pose of the mobile unit, the
issue of self-entanglement arises when the robot moves, resulting in unsafe
robot movements and the risk of damaging the tether. In this paper, the SEF
constraint is first formulated as the boundedness of a relative angle function
which characterises the angular difference between the tether stretching
direction and the robot's heading direction. Then, a constrained
searching-based path planning algorithm is proposed which produces a path that
is sub-optimal whilst ensuring the avoidance of tether self-entanglement.
Finally, the algorithmic efficiency of the proposed path planner is further
enhanced by proving the conditioned sparsity of the primitive path validity
checking module. The effectiveness of the proposed algorithm is assessed
through case studies, comparing its performance against untethered
differential-driven planners in challenging planning scenarios. A comparative
analysis is further conducted between the normal node expansion module and the
improved node expansion module which incorporates sparse waypoint validity
checking. Real-world tests are also conducted to validate the algorithm's
performance. An open-source implementation has also made available for the
benefit of the robotics community.
