A virtual-variable-length method for robust inverse kinematics of multi-segment continuum robots

2026-04-02

AI Summary

This study addresses the slow convergence and susceptibility to kinematic singularities in traditional Jacobian-based inverse kinematics for multi-segment continuum robots. To overcome these limitations, the authors propose a Virtual Variable-Length (VVL) method that introduces a virtual axial degree of freedom during iterative solving, effectively alleviating motion constraints through fictitious segment-length adjustments. This work presents the first integration of a virtual segment-length mechanism into inverse kinematics computation, substantially enhancing robustness and convergence efficiency for non-boundary configurations. Extensive validation across more than 1.8 million random trials demonstrates that, compared to baseline approaches, the VVL method increases convergence success rates by up to 20% and reduces average iteration counts by 40%–80% across accuracy thresholds ranging from 10⁻⁴ to 10⁻⁸.

Abstract

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.

Problem

• inverse kinematics
• continuum robots
• convergence failure
• deadlock
• Jacobian-based solvers

Innovation

• Virtual-Variable-Length
• inverse kinematics
• continuum robots
• convergence acceleration
• Jacobian-based solvers