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\title{An Open-Source Snake Hole-Digging Inspired Safety-Critical
Insertion~Planning and Replanning Framework for Continuum Robots~~~~}



\author[1]{Guanglin Ji}%
\author[1]{Zhenglong Sun}%
\affil[1]{Affiliation not available}%


\vspace{-1em}



  
  \date{April 26, 2026}


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\begin{abstract}
Continuum robots, with their slender, flexible structures, are
increasingly utilized in delicate tasks. These robots must navigate
confined spaces with high precision, often employing follow-the-leader
(FTL) motion to ensure minimal trauma. The baseline FTL motion planning
algorithm can not adjust the continuum robot's configuration using all
the segments, especially the tail of the robot. Furthermore, it has
limitations in dynamic, obstacle-rich environments, where real-time
re-planning and obstacle avoidance are essential but often not
sufficiently addressed. To address the above gaps, we propose a novel
FTL motion planning framework inspired by snake hole-digging motions
that can configure its optimal shape during the insertion task. Our
approach outperforms the baseline FTL by 75.36\%. The framework
incorporates real-time obstacle avoidance by integrating Control Barrier
Functions (CBF) and Quadratic Programming (QP) into the motion
re-planning process. To avoid deviations caused by obstacle avoidance,
the Control Lyapunov Function (CLF) is also integrated, forming a
CLF-CBF-QP framework for online motion re-planning. The target reaching
error of using CLF-CBF-QP decreases by 69.15\% compared to using only
CBF-QP. We also provide the open-source code of this work online.%
\end{abstract}%



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