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The forward kinematics of a parallel robot’s 6-6 Universal-Prismatic-Spherical (UPS) structure are characterized by high nonlinearity, coupling, and a one-to-many mapping nature. Finding a closed-form solution to the Forward Kinematic Problem (FKP) is challenging, making real-time kinematic control extremely difficult. This paper introduces a time-efficient and robust solution for FKP, utilizing the trajectory modifier algorithm in conjunction with the Newton–Raphson (NR) method. The achieved accuracy is of the order of 1 μm in translation and 0.001° in orientation, with an average pose computation time of 2.3 ms @ i3-3rd Gen. 3.30 GHz 4 GB and 1.1 ms @ i9-10th Gen. 2.80 GHz 64 GB. The novel algorithm is explained, and detailed performance parameters are presented in a table. The paper includes trajectory-following experiments, demonstrating the robustness and real-time capability of the Forward Kinematic (FK) solution.

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Robust Forward Kinematic Algorithm for Control of 6-DoF Parallel Robot

  • 会议论文

  • 发表日期：

    2026年

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  • Ravinder Kumar,
  • T. A. Dwarakanath,
  • Gaurav Bhutani,
  • S. K. Sinha

摘要

The forward kinematics of a parallel robot’s 6-6 Universal-Prismatic-Spherical (UPS) structure are characterized by high nonlinearity, coupling, and a one-to-many mapping nature. Finding a closed-form solution to the Forward Kinematic Problem (FKP) is challenging, making real-time kinematic control extremely difficult. This paper introduces a time-efficient and robust solution for FKP, utilizing the trajectory modifier algorithm in conjunction with the Newton–Raphson (NR) method. The achieved accuracy is of the order of 1 μm in translation and 0.001° in orientation, with an average pose computation time of 2.3 ms @ i3-3rd Gen. 3.30 GHz 4 GB and 1.1 ms @ i9-10th Gen. 2.80 GHz 64 GB. The novel algorithm is explained, and detailed performance parameters are presented in a table. The paper includes trajectory-following experiments, demonstrating the robustness and real-time capability of the Forward Kinematic (FK) solution.