Real-Time Conformal-Seeded Hybrid Inverse Kinematics for Offset Redundant Manipulators

Duc Cuong Vu; Van Tung Nguyen; Duc Hai Nguyen; Manh Cuong Nguyen; Vu Trung Tran; Minh Nhat Vu

cs.ROOct 3, 2026

Real-Time Conformal-Seeded Hybrid Inverse Kinematics for Offset Redundant Manipulators

Authors: Duc Cuong Vu, Van Tung Nguyen, Duc Hai Nguyen, Manh Cuong Nguyen, Vu Trung Tran, Minh Nhat Vu

Organizations: VinRobotics, Hanoi 100000, Vietnam · School of Electrical and Electronic Engineering, Nanyang Technological University 639798, Singapore · VinRobotics JSC, Hanoi 100000, Vietnam · Center for AI Research (CAIR), VinUniversity, Hanoi 100000, Vietnam

Abstract

This paper presents a conformal-seeded hybrid strategy for solving inverse kinematics of offset, redundant 7-DoF robot arms of the humanoid class. Analytical inverse kinematics (AIK) provides closed-form solutions with very low computational cost. However, for offset kinematic structures, the exact closed-form solution is generally unavailable, and practical AIK must rely on an approximate or simplified kinematic model. In contrast, numerical inverse kinematics (NIK) can achieve high-precision solutions on the full kinematic model. However, its convergence is highly sensitive to initialization. To overcome these limitations, we propose a two-stage hybrid inverse kinematics framework with conformal-calibrated seed selection. First, an approximate analytical model efficiently enumerates a finite set of candidate joint solutions. Second, we rank these candidates using a lightweight learned predictor of post-refinement difficulty, wrapped by split-conformal prediction into a calibrated upper bound that serves as the selection score. The best-ranked seed is then refined using a Levenberg-Marquardt solver on the full kinematic model. The proposed method combines fast candidate generation, learned seed ranking with a calibrated difficulty bound, and accurate numerical refinement, achieving real-time performance of less than 40us and a success rate of 100% in our evaluation on reachable targets. We validate the approach through large-scale stochastic simulation across the workspace and experimental demonstrations with motion planning on a humanoid robot arm. Demonstration videos are available at https://youtu.be/aeiBmw1XRbw.

Figures & tables

Panel of Figure 1 — Fig. 1: Overview of the proposed novel Conformal-Seeded Hybrid Inverse Kinematics (CS-HIK) framework. The method combines approximate analytical inverse kinematics with numerical refinement : each candidate receives a conformal upper bound $U^{(k)}$ on its predicted refinement difficulty and the candidates are refined in increasing order of $U^{(k)}$ up to the fail-safe budget $M$ ; no candidate is removed by a threshold , thereby ensuring robust convergence and real-time performance across the entire workspace.

Fig. 2: Ideal kinematic configuration of the humanoid robot arm (right), and the simplified kinematics chain (left)

Link	$\alpha_{i}$ (rad)	$\theta_{i}$ (rad)	$d_{i}$ (m)
1	${5\pi}/{9}$	$q_{1}-{\pi}/{2}$	-0.20624
2	${\pi}/{2}$	$q_{2}+{5\pi}/{9}$	-0.009
3	$-{\pi}/{2}$	$q_{3}+{\pi}/{2}$	-0.2247
4	${\pi}/{2}$	$q_{4}+{\pi}/{2}$	0
5	${\pi}/{2}$	$q_{5}+{\pi}/{2}$	-0.2196
6	${\pi}/{2}$	$q_{6}+{\pi}/{2}$	0

TABLE I: Ideal MDH parameters of the manipulator

Methods	Success rate (%)	Exec. time ( $\mu\mathrm{s}$ )	Pos. error ( $\mu\mathrm{m}$ )	Rot. error ( $\mu\mathrm{rad}$ )
AIK ( 3 )	100	0.227	9640	2520
NIK ( 6 )	65.37	283.8	285	489
KDL-LMA [ 14 ]	12.00 a	154.1	2.8	1649
KDL-NR-JL [ 14 ]	21.67	780.35	0.03	0.4
TracIK [ 13 ]	99.38	728.70	2.9	4.2
PyRoki [ 12 ]	80.45	448.0	6586	16.3

TABLE II: Performance comparison of inverse kinematics methods

Ranking score	$\Delta\varphi$	Success rate (%) @ $M=1$	Success rate (%) @ $M=3$
Raw $\hat{y}$	$\pi/6$	99.93	99.95
Floored $\max(0,\hat{y})$	$\pi/6$	99.38	99.94
CS-HIK, $\max(0,\hat{y}+\hat{q}_{\alpha})$	$\pi/6$	99.93	99.95
Raw $\hat{y}$	$\color[rgb]{0,0,0}\pi/9$	99.97	100
Floored $\max(0,\hat{y})$	$\pi/9$	99.26	99.99
CS-HIK, $\max(0,\hat{y}+\hat{q}_{\alpha})$	$\pi/9$	99.97	100

TABLE III: Ablation of the ranking score. All rows use the identical predictor

\hat{y}

(same training samples and features) and differ only in the score sorted in Line 9 of Algorithm 1 .

Fig. 3: Success rate comparison under different swivel-angle sampling intervals

\Delta\varphi

, varying numbers of candidate seeds, and varying used methods.

Fig. 4: Joint-state evolution over time in three experiment scenarios.

Fig. 5: Experimental validation of the proposed (CS-HIK) on a humanoid robot arm. (a) Redundant illustration showing that multiple joint configurations can achieve the same desired end-effector pose. (b) Joint-space interpolation between an initial configuration and the IK solution. (c) TCP-space interpolation generating a Cartesian straight-line trajectory. (d) Motion capture (MoCap)-based reference for end-effector tracking evaluation. The experiments are shown at https://youtu.be/aeiBmw1XRbw.

Inverse Kinematics

Inverse kinematics maps desired robot or articulated-body motions to joint configurations while handling constraints, redundancy, and multiple solutions.

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Australian Robotic Inspection and Asset Management (ARIAM) Hub, the Australian Centre for Robotics (ACFR), and the School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Australia

Inverse Kinematics Robot Kinematics Latent Space Optimization

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We introduce Learned Optimal Inverse Kinematics (LOInK), a method to generate approximately optimal solutions to an inverse kinematics problem. When trained on data consisting of sampled configurations and associated task variables and a given cost function, LOInK learns a bi-Lipschitz invertible mapping from configuration space to a decoupled task/latent space, and moreover, the latent space is structured so as to place cost-minimizing solutions at the origin. This enables efficient sampling of cost-minimizing solutions via a network-inversion algorithm based on operator splitting. We demonstrate the proposed approach on three problems: an illustrative three degree-of-freedom manipulator problem; a quadrupedal climbing robot for which LOInK can generate near-optimal solutions on average 31 times faster and up to 100 times faster than a constrained optimization approach; and a simulated soft actuator as a purely data-driven example, in which LOInK can explicitly generate high-quality solutions, unlike existing generative approaches that require diverse sampling and evaluation of candidate solutions.

Abstract

Inverse Kinematics

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