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P-FABRIK: A General Intuitive and Robust Inverse Kinematics Method for Parallel Mechanisms Using FABRIK Approach

Daqian Cao, Quan Yuan, Weibang Bai

TL;DR

The paper tackles inverse kinematics for parallel mechanisms, including redundant configurations, where traditional geometric methods struggle with constraint complexity and workspace limits. It introduces P-FABRIK, a FABRIK-based framework that uses a topological decomposition strategy (TDS) to split a parallel device into serial sub-chains and an adaptive target projection (ATP) to handle targets outside the workspace, ensuring a feasible solution. The method is validated on three representative systems—the planar 5-bar, the 6-UPS Stewart platform, and a redundant NRPM—demonstrating generality, computational efficiency comparable to geometric IK, and robustness to out-of-workspace targets. These results indicate that P-FABRIK can extend FABRIK’s applicability to a broad class of parallel mechanisms, with potential extensions to forward kinematics in future work.

Abstract

Traditional geometric inverse kinematics methods for parallel mechanisms rely on specific spatial geometry constraints. However, their application to redundant parallel mechanisms is challenged due to the increased constraint complexity. Moreover, it will output no solutions and cause unpredictable control problems when the target pose lies outside its workspace. To tackle these challenging issues, this work proposes P-FABRIK, a general, intuitive, and robust inverse kinematics method to find one feasible solution for diverse parallel mechanisms based on the FABRIK algorithm. By decomposing the general parallel mechanism into multiple serial sub-chains using a new topological decomposition strategy, the end targets of each sub-chain can be subsequently revised to calculate the inverse kinematics solutions iteratively. Multiple case studies involving planar, standard, and redundant parallel mechanisms demonstrated the proposed method's generality across diverse parallel mechanisms. Furthermore, numerical simulation studies verified its efficacy and computational efficiency, as well as its robustness ability to handle out-of-workspace targets.

P-FABRIK: A General Intuitive and Robust Inverse Kinematics Method for Parallel Mechanisms Using FABRIK Approach

TL;DR

The paper tackles inverse kinematics for parallel mechanisms, including redundant configurations, where traditional geometric methods struggle with constraint complexity and workspace limits. It introduces P-FABRIK, a FABRIK-based framework that uses a topological decomposition strategy (TDS) to split a parallel device into serial sub-chains and an adaptive target projection (ATP) to handle targets outside the workspace, ensuring a feasible solution. The method is validated on three representative systems—the planar 5-bar, the 6-UPS Stewart platform, and a redundant NRPM—demonstrating generality, computational efficiency comparable to geometric IK, and robustness to out-of-workspace targets. These results indicate that P-FABRIK can extend FABRIK’s applicability to a broad class of parallel mechanisms, with potential extensions to forward kinematics in future work.

Abstract

Traditional geometric inverse kinematics methods for parallel mechanisms rely on specific spatial geometry constraints. However, their application to redundant parallel mechanisms is challenged due to the increased constraint complexity. Moreover, it will output no solutions and cause unpredictable control problems when the target pose lies outside its workspace. To tackle these challenging issues, this work proposes P-FABRIK, a general, intuitive, and robust inverse kinematics method to find one feasible solution for diverse parallel mechanisms based on the FABRIK algorithm. By decomposing the general parallel mechanism into multiple serial sub-chains using a new topological decomposition strategy, the end targets of each sub-chain can be subsequently revised to calculate the inverse kinematics solutions iteratively. Multiple case studies involving planar, standard, and redundant parallel mechanisms demonstrated the proposed method's generality across diverse parallel mechanisms. Furthermore, numerical simulation studies verified its efficacy and computational efficiency, as well as its robustness ability to handle out-of-workspace targets.
Paper Structure (10 sections, 18 equations, 8 figures, 2 tables)

This paper contains 10 sections, 18 equations, 8 figures, 2 tables.

Table of Contents

  1. Introduction
  2. P-FABRIK: FABRIK FOR PARALLEL MECHANISMS
  3. Background of FABRIK
  4. P-FABRIK: FABRIK for Parallel Mechanisms
  5. Case Studies
  6. Planar 5-bar Mechanism
  7. 6-UPS Stewart Mechanism
  8. Redundant Parallel mechanism
  9. Simulation Verifications
  10. Conclusion

Figures (8)

  • Figure 1: An example of a full iteration of FABRIK for a planar serial mechanism with 4 revolute joints.
  • Figure 2: Flowchart of the P-FABRIK algorithm.
  • Figure 3: Diagram of a classic planar 5-bar mechanism
  • Figure 4: An example of a full iteration of P-FABRIK for a planar 5-bar mechanism. (a) The initial configuration of the 5-bar planar mechanism and the target $\boldsymbol{t}$. The mechanism is decomposed into 2 serial sub-chains. Sub-chain 1's base and end effector are $\boldsymbol{p}_{1}$ and $\boldsymbol{p}_{3_{1}}$ and sub-chain 2's are $\boldsymbol{p}_{5}$ and $\boldsymbol{p}_{3_{2}}$. (b) Apply forward-reaching on sub-chain 1. (c) Apply backward-reaching on sub-chain 1. (d) Apply forward-reaching on sub-chain 2. (e) Apply backward-reaching on sub-chain 2. (e) Reconfigured closed-chain posture after full iteration.
  • Figure 5: (a) Diagram of a 6-UPS Stewart platform. (b) The target $\boldsymbol{t}$ and sub-targets $\boldsymbol{t}_i$ set for the 6-UPS mechanism.
  • ...and 3 more figures