  Tendon-driven continuum robots (TDCRs), with their flexible backbones, offer
the advantage of being used for navigating complex, cluttered environments.
However, to do so, they typically require multiple segments, often leading to
complex actuation and control challenges. To this end, we propose a novel
approach to navigate cluttered spaces effectively for a single-segment long
TDCR which is the simplest topology from a mechanical point of view. Our key
insight is that by leveraging contact with the environment we can achieve
multiple curvatures without mechanical alterations to the robot. Specifically,
we propose a search-based motion planner for a single-segment TDCR. This
planner, guided by a specially designed heuristic, discretizes the
configuration space and employs a best-first search. The heuristic, crucial for
efficient navigation, provides an effective cost-to-go estimation while
respecting the kinematic constraints of the TDCR and environmental
interactions. We empirically demonstrate the efficiency of our planner-testing
over 525 queries in environments with both convex and non-convex obstacles, our
planner is demonstrated to have a success rate of about 80% while baselines
were not able to obtain a success rate higher than 30%. The difference is
attributed to our novel heuristic which is shown to significantly reduce the
required search space.
