This paper proposes a new, robust method to solve the inverse kinematics (IK) of multi-segment continuum manipulators. Conventional Jacobian-based solvers, especially when initialized from neutral/rest configurations, often exhibit slow convergence and, in certain conditions, may fail to converge (deadlock). The Virtual-Variable-Length (VVL) method proposed here introduces fictitious variations of segments' length during the solution iteration, conferring virtual axial degrees of freedom that alleviate adverse behaviors and constraints, thus enabling or accelerating convergence. Comprehensive numerical experiments were conducted to compare the VVL method against benchmark Jacobian-based and Damped Least Square IK solvers. Across more than $1.8\times 10^6$ randomized trials covering manipulators with two to seven segments, the proposed approach achieved up to a 20$\%$ increase in convergence success rate over the benchmark and a 40-80$\%$ reduction in average iteration count under equivalent accuracy thresholds ($10^{-4}-10^{-8}$). While deadlocks are not restricted to workspace boundaries and may occur at arbitrary poses, our empirical study identifies boundary-proximal configurations as a frequent cause of failed convergence and the VVL method mitigates such occurrences over a statistical sample of test cases.

翻译：本文提出了一种新的鲁棒方法，用于求解多段连续体机械臂的逆运动学（IK）。传统的基于雅可比矩阵的求解器，尤其是在从中性/静止构型初始化时，通常收敛缓慢，且在特定条件下可能无法收敛（死锁）。本文提出的虚拟变长度（VVL）方法在求解迭代过程中引入了段长度的虚拟变化，赋予虚拟轴向自由度以缓解不利行为和约束，从而促进或加速收敛。通过全面的数值实验，将VVL方法与基准的基于雅可比矩阵和阻尼最小二乘IK求解器进行了比较。在覆盖两段至七段机械臂的超过1.8×10⁶次随机试验中，所提方法在等效精度阈值（10⁻⁴-10⁻⁸）下，相比基准方法实现了高达20%的收敛成功率提升，并将平均迭代次数减少了40-80%。尽管死锁并非局限于工作空间边界，可能发生在任意位姿，但我们的实证研究发现，靠近边界的构型是收敛失败的常见原因，而VVL方法在统计样本测试案例中缓解了此类情况的发生。