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A Combined Inverse Kinematics Algorithm Using FABRIK with Optimization

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Abstract

Solving the inverse kinematics of redundant and hyper-redundant manipulators is more challenging because their kinematic redundancy leads to a more complicated mapping from end-effector pose to configuration space. A heuristic inverse kinematics solver, called Forward And Backward Reaching Inverse Kinematics (FABRIK), has been demonstrated to solve the inverse kinematics of complex chain systems with fast convergence and simple implementation. However, as the pose precision of the end-effector increases to a higher value, such as \( 10^{-6} \), FABRIK converges slowly in some configurations and thus exhibits unstable convergence behavior. Hence, this paper presents a novel inverse kinematics algorithm that combines FABRIK and the sequential quadratic programming (SQP) algorithm, in which the joint angles deduced by FABRIK will be taken as the initial seed of the SQP algorithm to realize fast convergence. Meanwhile, a universal and non-trivial mapping from joint Cartesian positions to joint angles is included to enable the extension of FABRIK to redundant and hyper-redundant manipulators while retaining its simplicity. With the \( 10^{-6} \) pose error constraint, quantitative tests on serial chain manipulators demonstrate that the combined algorithm outperforms FABRIK in terms of success rate and runtime. Meanwhile, some popular inverse kinematics algorithms are treated as benchmarks to compare with the combined algorithm. Finally, simulations using serial chain manipulators indicate the effectiveness of the combined algorithm on path tracking.

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Funding

This work has been supported by the National Natural Science Foundation of China [Project Number: 92148203], the State Key Laboratory of Robotics and System (HIT) [Project Number: SKLRS202201A01], and the Key Lab. of Science and Technology on Space Flight Dynamics [Project Number: XTB6142210210303].

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Authors and Affiliations

  1. State Key Laboratory of Robotics and Systems, Harbin Institute of Technology, Harbin, 150001, Heilongjiang Province, China

    Zichun Xu, Yuntao Li, Xiaohang Yang, Zhiyuan Zhao, Jingdong Zhao & Hong Liu

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  1. Zichun Xu
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  2. Yuntao Li
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  3. Xiaohang Yang
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  4. Zhiyuan Zhao
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  5. Jingdong Zhao
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Contributions

Zichun Xu: Conceptualization, Implementation, Analysis, and Writing. Yuntao Li, Xiaohang Yang, and Zhiyuan Zhao: Discussion, Writing, Editing, and Reviewing. Jingdong Zhao and Hong Liu: Supervision and Finalizing.

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Correspondence to Jingdong Zhao.

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Appendix A: DH Parameters for 7-, 9-, and 15-DOF Serial Chain Arms

Appendix A: DH Parameters for 7-, 9-, and 15-DOF Serial Chain Arms

Table 1 DH parameters of the KUKA arm
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Table 2 DH parameters of the 9-DOF arm
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Table 3 DH parameters of the 15-DOF arm
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Xu, Z., Li, Y., Yang, X. et al. A Combined Inverse Kinematics Algorithm Using FABRIK with Optimization. J Intell Robot Syst 108, 62 (2023). https://doi.org/10.1007/s10846-023-01895-2

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