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Accelerated Quasi-Static FEM for Real-Time Modeling of Continuum Robots with Multiple Contacts and Large Deformation

Hao Chen, Jian Chen, Xinran Liu, Zihui Zhang, Yuanrui Huang, Zhongkai Zhang, Hongbin Liu

TL;DR

This work addresses the real-time simulation challenge of continuum robots undergoing large deformations with multiple environmental contacts. It introduces Acc-FEM, an accelerated quasi-static finite element approach that formulates contact-rich deformation as a mixed linear complementarity problem, linearizes via the tangent stiffness from the previous step, and solves a resulting convex quadratic program with OSQP. A GPU-accelerated pipeline handles tangent-stiffness updates and collision detection, while a postprocessing step stabilizes step sizes to prevent penetration. The method is validated against a SOFA-based baseline and in real-robot experiments, demonstrating significant speed advantages and accurate deformation/force estimation in multi-contact scenarios. The approach has potential to enable real-time planning and control for flexible surgical robots in narrow cavities and other complex environments.

Abstract

Continuum robots offer high flexibility and multiple degrees of freedom, making them ideal for navigating narrow lumens. However, accurately modeling their behavior under large deformations and frequent environmental contacts remains challenging. Current methods for solving the deformation of these robots, such as the Model Order Reduction and Gauss-Seidel (GS) methods, suffer from significant drawbacks. They experience reduced computational speed as the number of contact points increases and struggle to balance speed with model accuracy. To overcome these limitations, we introduce a novel finite element method (FEM) named Acc-FEM. Acc-FEM employs a large deformation quasi-static finite element model and integrates an accelerated solver scheme to handle multi-contact simulations efficiently. Additionally, it utilizes parallel computing with Graphics Processing Units (GPU) for real-time updates of the finite element models and collision detection. Extensive numerical experiments demonstrate that Acc-FEM significantly improves computational efficiency in modeling continuum robots with multiple contacts while achieving satisfactory accuracy, addressing the deficiencies of existing methods.

Accelerated Quasi-Static FEM for Real-Time Modeling of Continuum Robots with Multiple Contacts and Large Deformation

TL;DR

This work addresses the real-time simulation challenge of continuum robots undergoing large deformations with multiple environmental contacts. It introduces Acc-FEM, an accelerated quasi-static finite element approach that formulates contact-rich deformation as a mixed linear complementarity problem, linearizes via the tangent stiffness from the previous step, and solves a resulting convex quadratic program with OSQP. A GPU-accelerated pipeline handles tangent-stiffness updates and collision detection, while a postprocessing step stabilizes step sizes to prevent penetration. The method is validated against a SOFA-based baseline and in real-robot experiments, demonstrating significant speed advantages and accurate deformation/force estimation in multi-contact scenarios. The approach has potential to enable real-time planning and control for flexible surgical robots in narrow cavities and other complex environments.

Abstract

Continuum robots offer high flexibility and multiple degrees of freedom, making them ideal for navigating narrow lumens. However, accurately modeling their behavior under large deformations and frequent environmental contacts remains challenging. Current methods for solving the deformation of these robots, such as the Model Order Reduction and Gauss-Seidel (GS) methods, suffer from significant drawbacks. They experience reduced computational speed as the number of contact points increases and struggle to balance speed with model accuracy. To overcome these limitations, we introduce a novel finite element method (FEM) named Acc-FEM. Acc-FEM employs a large deformation quasi-static finite element model and integrates an accelerated solver scheme to handle multi-contact simulations efficiently. Additionally, it utilizes parallel computing with Graphics Processing Units (GPU) for real-time updates of the finite element models and collision detection. Extensive numerical experiments demonstrate that Acc-FEM significantly improves computational efficiency in modeling continuum robots with multiple contacts while achieving satisfactory accuracy, addressing the deficiencies of existing methods.

Paper Structure

This paper contains 16 sections, 26 equations, 3 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. MODEL FORMULATION
  3. The Continuum Robot
  4. FEM Model of Continuum Robot
  5. Formulation of Contact Force
  6. Fixed Nodes Constraints
  7. Actuation Constraints
  8. PROPOSED METHOD
  9. Mixed Linear Complementarity Problem
  10. Solve the Problem
  11. Parallelization on GPU
  12. Postprocessing for Contact Forces
  13. Experiments and Results
  14. Comparison Experiment with SOFA
  15. Accuracy Verification In Real Robot
  16. ...and 1 more sections

Figures (3)

  • Figure 1: Continuum robot for bronchial surgery. (a) The continuum robot, mounted on a robotic arm, has two position sensors at its end. (b) At the end of the robot, three cables are connected to drive the robot's steering. (c) The tension $\boldsymbol{F}_{i}$ of the cables can be translated to the center of the section into a force $\boldsymbol{F}_{a}$ and a moment $\boldsymbol{M}_{a}$.
  • Figure 2: Comparison of Acc-FEM and SOFA. (a) Simulation setup for Acc-FEM. (b) Simulation setup for SOFA. (c) Simulation results with 100 nodes. (d) Simulation results with 200 nodes. (e) Simulation results with 300 nodes. (f) Simulation results with 400 nodes.
  • Figure 3: Experimental results of accuracy verification: (a) Tube with ‘T’-shaped model. (b) Tube with ‘T’-shaped model. (c) Robot with ‘T’-shaped model. (d) Robot with a bronchial model.