提出虚拟变长法，解决多段连续机器人的逆运动学收敛难题。
A virtual-variable-length method for robust inverse kinematics of multi-segment continuum robots
- 通过虚构段长变化引入虚拟轴向自由度
- 在超180万次测试中成功率提升20%，迭代次数减少40%-80%
- 特别适合易卡死的靠近工作空间边界的情况
本文提出一种新型鲁棒方法，用于求解多段连续机械臂的逆运动学问题。传统基于雅可比矩阵的求解器在从初始中立构型开始时，常出现收敛缓慢甚至无法收敛（死锁）的问题。所提出的虚拟变长（VVL）方法在求解迭代过程中引入虚构的段长变化，赋予虚拟轴向自由度，从而缓解不良行为与约束，实现或加速收敛。通过大规模数值实验，将VVL方法与基准雅可比法及阻尼最小二乘逆运动学求解器进行对比。在覆盖2至7段机械臂、超过1.8×10⁶次随机测试中，该方法在等效精度阈值（10⁻⁴–10⁻⁸）下，收敛成功率最高提升20%，平均迭代次数减少40%-80%。尽管死锁并非仅出现在工作空间边界，也可能发生在任意姿态，但实证研究发现边界邻近构型是导致收敛失败的常见原因，而VVL方法在统计样本中显著降低了此类情况的发生。
原文摘要 · Abstract (English)
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.
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