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Planning and Inverse Kinematics of Hyper-Redundant Manipulators with VO-FABRIK

Cristian Morasso, Daniele Meli, Yann Divet, Salvatore Sessa, Alessandro Farinelli

Abstract

Hyper-redundant Robotic Manipulators (HRMs) offer great dexterity and flexibility of operation, but solving Inverse Kinematics (IK) is challenging. In this work, we introduce VO-FABRIK, an algorithm combining Forward and Backward Reaching Inverse Kinematics (FABRIK) for repeatable deterministic IK computation, and an approach inspired from velocity obstacles to perform path planning under collision and joint limits constraints. We show preliminary results on an industrial HRM with 19 actuated joints. Our algorithm achieves good performance where a state-of-the-art IK solver fails.

Planning and Inverse Kinematics of Hyper-Redundant Manipulators with VO-FABRIK

Abstract

Hyper-redundant Robotic Manipulators (HRMs) offer great dexterity and flexibility of operation, but solving Inverse Kinematics (IK) is challenging. In this work, we introduce VO-FABRIK, an algorithm combining Forward and Backward Reaching Inverse Kinematics (FABRIK) for repeatable deterministic IK computation, and an approach inspired from velocity obstacles to perform path planning under collision and joint limits constraints. We show preliminary results on an industrial HRM with 19 actuated joints. Our algorithm achieves good performance where a state-of-the-art IK solver fails.
Paper Structure (12 sections, 8 theorems, 72 equations, 2 figures, 2 tables)

This paper contains 12 sections, 8 theorems, 72 equations, 2 figures, 2 tables.

Table of Contents

  1. Hamiltonian Mechanics
  2. Fixed-Period Problems: The Sublinear Case
  3. Autonomous Systems
  4. The General Case: Nontriviality.
  5. Notes and Comments.
  6. Notes and Comments.
  7. Theoretical Contributions
  8. Fixed-Period Problems: The Sublinear Case
  9. Autonomous Systems
  10. The General Case: Nontriviality.
  11. Notes and Comments.
  12. Notes and Comments.

Key Result

proposition 1

Assume $H'(0)=0$ and $H(0)=0$. Set: If $\gamma < - \lambda < \delta$, the solution $\overline{u}$ is non-zero:

Figures (2)

  • Figure 1: This is the caption of the figure displaying a white eagle and a white horse on a snow field
  • Figure 2: This is the caption of the figure displaying a white eagle and a white horse on a snow field

Theorems & Definitions (16)

  • proposition 1
  • proof
  • corollary 1
  • proof
  • lemma 1
  • proof
  • theorem 1: Ghoussoub-Preiss
  • definition 1
  • proposition 2
  • proof
  • ...and 6 more