A virtual-variable-length method for robust inverse kinematics of multi-segment continuum robots
Authors: Weiting Feng, Federico Renda, Yunjie Yang, Francesco Giorgio-Serchi
Organizations: the School of Engineering, University of Edinburgh, Edinburgh, U.K. · Department of Mechanical Engineering, Khalifa University, Abu Dhabi, UAE.
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 1.8×106 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.
Figures & tables
Fig. 1 : Schematic of Constant Curvature segment, as in [ 17 ] .
Fig. 2 : Illustration of convergence progression to desired configuration (a) identified with a green color, from two distinct initial guesses (b) and (c) when using a traditional Jacobian method. In (b) a solution is obtained after 81 iterations, as demonstrated by the final configuration overlapping with the reference state. In (c) a solution is not reached due to a deadlock configuration, shown in red in (d). In (e), solution via the proposed VVL method is reached within 30 iterations; notice the initial variable segments’ length which aid in the convergence process.
Fig. 3 : Workspace of the continuum manipulator (blue) and failed IK solutions (red) obtained with Jacobian method (a)-(f) and DLS method (g)-(l). Subfigures (a) and (g) correspond to the two-segment manipulator, (b) and (h) to a three-segment manipulator, (c) and (i) to a four-segment manipulator, (d) and (j) to a five-segment manipulator, (e) and (k) to a six-segment manipulator, and (f) and (l) to a seven-segment manipulator. Subfigures (a)–(f) are obtained using the benchmark Jacobian method described in Sec. II-B , while (g)–(l) are obtained using the DLS method described in Sec. II-C .
Fig. 4 : Workspace of the continuum manipulator, in blue, and failed IK solutions in red obtained with the VVL method (sec. II-D ), respectively for the case of a manipulator made of (a) two segments, (b) three segments, (c) four segments, (d) five segments, (e) six segments and (f) seven segments.
Fig. 5 : Convergence success rate with tolerances of 10 -4 , 10 -6 , 10 -8 for manipulators with 2, in (a), 3, in (b), and 5, in (c), segments respectively for the Jacobian method (indicated with the o symbol in the legend), the VVL method (indicated by the v symbol), and the DLS method (indicated by the d symbol).
Fig. 6 : Convergence success rate for the benchmark Jacobian method (orange bar), the VVL method (yellow bar) and the DLS (brown bar) method with a tolerance of 10 -4 within (a) 30 iterations and (b) up to 500 iterations.
Oct 3, 2026·Duc Cuong Vu, Van Tung Nguyen, Duc Hai Nguyen +3Inverse Kinematics
VinRobotics, Hanoi 100000, Vietnam · School of Electrical and Electronic Engineering, Nanyang Technological University 639798, Singapore · VinRobotics JSC, Hanoi 100000, Vietnam +1