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

TL;DR

This paper introduces the Virtual-Variable-Length (VVL) method, a novel approach that enhances the robustness and convergence speed of inverse kinematics solutions for multi-segment continuum robots by adding virtual degrees of freedom.

Contribution

The VVL method is a new technique that improves convergence success rates and reduces iterations in solving inverse kinematics for continuum robots, outperforming traditional Jacobian-based methods.

Findings

VVL achieves up to 20% higher success rate in convergence.

Reduces average iterations by 40-80% compared to benchmarks.

Effectively mitigates deadlocks near boundary configurations.

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.