The continuum robot has attracted more attention for its flexibility. Continuum robot kinematics models are the basis for further perception, planning, and control. The design and research of continuum robots are usually based on the assumption of piecewise constant curvature (PCC). However, due to the influence of friction, etc., the actual motion of the continuum robot is approximate piecewise constant curvature (APCC). To address this, we present a kinematic equivalent model for continuum robots, i.e. APCC 2L-5R. Using classical rigid linkages to replace the original model in kinematic, the APCC 2L-5R model effectively reduces complexity and improves numerical stability. Furthermore, based on the model, the configuration self-estimation of the continuum robot is realized by monocular cameras installed at the end of each approximate constant curvature segment. The potential of APCC 2L-5R in perception, planning, and control of continuum robots remains to be explored.

中文翻译：

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近似分段恒定曲率等效模型及其在连续体机器人构型估计中的应用

连续体机器人因其灵活性而受到更多关注。连续统机器人运动学模型是进一步感知、规划和控制的基础。连续体机器人的设计和研究通常基于分段恒定曲率（PCC）的假设。但是，由于摩擦等因素的影响，连续体机器人的实际运动是近似分段常曲率（APCC）。为了解决这个问题，我们提出了连续体机器人的运动学等效模型，即 APCC 2L-5R。APCC 2L-5R模型在运动学上采用经典刚性连杆代替原有模型，有效降低复杂度，提高数值稳定性。此外，基于模型，连续体机器人的构型自估计是通过安装在每个近似恒定曲率段末端的单目相机实现的。APCC 2L-5R 在连续体机器人的感知、规划和控制方面的潜力仍有待探索。