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Systematic Analysis of Coupling Effects on Closed-Loop and Open-Loop Performance in Aerial Continuum Manipulators

Niloufar Amiri, Shayan Sepahvand, Iraj Mantegh, Farrokh Janabi-Sharifi

TL;DR

This work assesses decoupled versus coupled dynamic models for an aerial continuum manipulator (ACM) under the piecewise-constant-curvature (PCC) framework, analyzing both open-loop and closed-loop performance. Dynamics are derived with the Euler–Lagrange approach and a curvature regularization addresses near-zero curvature singularities, enabling a fair comparison of modeling choices. A novel dynamics-based proportional-derivative sliding mode IBVS controller (DPD-SM-IBVS) is proposed to regulate image-feature errors, and its performance is evaluated with both coupled and decoupled models. Results show substantial open-loop discrepancies in some configurations, while the decoupled model achieves subpixel-level tracking accuracy in closed-loop tasks and offers meaningful computational savings, highlighting when model simplifications are appropriate for perception-guided control in ACMs.

Abstract

This paper investigates two distinct approaches to the dynamic modeling of aerial continuum manipulators (ACMs): the decoupled and the coupled formulations. Both open-loop and closed-loop behaviors of a representative ACM are analyzed. The primary objective is to determine the conditions under which the decoupled model attains accuracy comparable to the coupled model while offering reduced computational cost under identical numerical conditions. The system dynamics are first derived using the Euler--Lagrange method under the piecewise constant curvature (PCC) assumption, with explicit treatment of the near-zero curvature singularity. A decoupled model is then obtained by neglecting the coupling terms in the ACM dynamics, enabling systematic evaluation of open-loop responses under diverse actuation profiles and external wrenches. To extend the analysis to closed-loop performance, a novel dynamics-based proportional-derivative sliding mode image-based visual servoing (DPD-SM-IBVS) controller is developed for regulating image feature errors in the presence of a moving target. The controller is implemented with both coupled and decoupled models, allowing a direct comparison of their effectiveness. The open-loop simulations reveal pronounced discrepancies between the two modeling approaches, particularly under varying torque inputs and continuum arm parameters. Conversely, the closed-loop experiments demonstrate that the decoupled model achieves tracking accuracy on par with the coupled model (within subpixel error) while incurring lower computational cost.

Systematic Analysis of Coupling Effects on Closed-Loop and Open-Loop Performance in Aerial Continuum Manipulators

TL;DR

This work assesses decoupled versus coupled dynamic models for an aerial continuum manipulator (ACM) under the piecewise-constant-curvature (PCC) framework, analyzing both open-loop and closed-loop performance. Dynamics are derived with the Euler–Lagrange approach and a curvature regularization addresses near-zero curvature singularities, enabling a fair comparison of modeling choices. A novel dynamics-based proportional-derivative sliding mode IBVS controller (DPD-SM-IBVS) is proposed to regulate image-feature errors, and its performance is evaluated with both coupled and decoupled models. Results show substantial open-loop discrepancies in some configurations, while the decoupled model achieves subpixel-level tracking accuracy in closed-loop tasks and offers meaningful computational savings, highlighting when model simplifications are appropriate for perception-guided control in ACMs.

Abstract

This paper investigates two distinct approaches to the dynamic modeling of aerial continuum manipulators (ACMs): the decoupled and the coupled formulations. Both open-loop and closed-loop behaviors of a representative ACM are analyzed. The primary objective is to determine the conditions under which the decoupled model attains accuracy comparable to the coupled model while offering reduced computational cost under identical numerical conditions. The system dynamics are first derived using the Euler--Lagrange method under the piecewise constant curvature (PCC) assumption, with explicit treatment of the near-zero curvature singularity. A decoupled model is then obtained by neglecting the coupling terms in the ACM dynamics, enabling systematic evaluation of open-loop responses under diverse actuation profiles and external wrenches. To extend the analysis to closed-loop performance, a novel dynamics-based proportional-derivative sliding mode image-based visual servoing (DPD-SM-IBVS) controller is developed for regulating image feature errors in the presence of a moving target. The controller is implemented with both coupled and decoupled models, allowing a direct comparison of their effectiveness. The open-loop simulations reveal pronounced discrepancies between the two modeling approaches, particularly under varying torque inputs and continuum arm parameters. Conversely, the closed-loop experiments demonstrate that the decoupled model achieves tracking accuracy on par with the coupled model (within subpixel error) while incurring lower computational cost.
Paper Structure (14 sections, 1 theorem, 29 equations, 6 figures, 1 table)

This paper contains 14 sections, 1 theorem, 29 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Works
  3. Problem Formulation
  4. Single-Section CR Differential Kinematics
  5. ACM Differential Kinematics
  6. ACM Dynamics
  7. DPD-SM-IBVS Control Design
  8. Results
  9. Open-Loop Response Analysis
  10. Parameter Sensitivity Analysis
  11. Closed-loop Visual Tracking Analysis
  12. Conclusions
  13. The geometric Jacobian of the CR
  14. The off-diagonal elements of the dynamics matrices

Key Result

Theorem 1

Consider the system dynamics eq:ACMS_Dynamics undergoing the joint-space control command eq:PD_Joint where $\bm{J}_L=\bm L \bm T_a^{-1}\bm J_t$, and the dynamics-based proportional-derivative sliding mode image-based visual servoing (DPD-SM-IBVS) control law eq:img_controller with In case $\bm K_p, \bm K_d, \bm{C}_p, \bm{C}_d, \bm{C}_s\in \mathbb{R}^{6\times6}$ are symmetric positive definite gai

Figures (6)

  • Figure 1: The configuration space variables of the CR under the PCC assumption.
  • Figure 2: The frame attachment of the ACM.
  • Figure 3: Open-loop responses for various system parameters.
  • Figure 4: The xy-plane tip trace of the ACM for coupled and decoupled under the DPD-SM-IBVS law.
  • Figure 5: The joint-space velocity norm for the letter M.
  • ...and 1 more figures

Theorems & Definitions (3)

  • Remark 1
  • Theorem 1
  • proof