Strain-Parameterized Coupled Dynamics and Dual-Camera Visual Servoing for Aerial Continuum Manipulators

Niloufar Amiri; Farrokh Janabi-Sharifi

cs.ROMar 24, 2026

Strain-Parameterized Coupled Dynamics and Dual-Camera Visual Servoing for Aerial Continuum Manipulators

Authors: Niloufar Amiri, Farrokh Janabi-Sharifi

Organizations: Department of Mechanical, Industrial, and Mechatronics Engineering, Toronto Metropolitan University, ON, Canada.

Abstract

Tendon-driven aerial continuum manipulators (TD-ACMs) combine the maneuverability of uncrewed aerial vehicles (UAVs) with the compliance of lightweight continuum robots (CRs). Existing coupled dynamic modeling approaches for TD-ACMs incur high computational costs and do not explicitly account for aerial platform underactuation. To address these limitations, this paper presents a generalized dynamic formulation of a coupled TD-ACM with an underactuated base. The proposed approach integrates a strain-parameterized Cosserat rod model with a rigid-body model of the UAV into a unified Lagrangian ordinary differential equation (ODE) framework on $\mathrm{SE}(3)$ , thereby eliminating computationally intensive symbolic derivations. Building upon the developed model, a robust dual-camera image-based visual servoing (IBVS) scheme is introduced. The proposed controller mitigates the field-of-view (FoV) limitations of conventional IBVS, compensates for attitude-induced image motion caused by UAV lateral dynamics, and incorporates a low-level adaptive controller to address modeling uncertainties with formal stability guarantees. Extensive simulations and experimental validation on a compact custom-built prototype demonstrate the effectiveness and robustness of the proposed framework in real-world scenarios.

Figures & tables

Fig. 1 : Schematic of the TD-ACM and key coordinate frames.

Nitinol backbone
Parameter	Value	Unit
Length ( $L_{1}$ )	$1$	m
Diameter ( $d_{1}$ )	$2\times 10^{-3}$	m
Density ( $\rho_{1}$ )	$6.45\times 10^{3}$	kg/m 3
Young’s modulus ( $E$ )	$5\times 10^{10}$	Pa
Poisson’s ratio ( $\nu$ )	$0.33$	–

TABLE I : Physical and geometric properties of the TD-ACM in the strain-based simulated model.

Parameter	$C_{L}$	$C_{G}$	Unit
Image resolution ( $W\times H$ )	$1024\times 1024$	$500\times 500$	px
Vertical field of view ( $\mathrm{FoV}_{v}$ )	$60$	$71$	deg
Horizontal field of view ( $\mathrm{FoV}_{h}$ )	$60$	$71$	deg
Focal length ( $f_{x}=f_{y}$ )	$886.8$	$350.5$	px
Principal point ( $c_{x},c_{y}$ )	$(512,512)$	$(250,250)$	px
Near / far clipping planes	$0.5/10$	$0.01/20$	m

TABLE II : Intrinsic parameters of the local (

C_{L}

) and global (

C_{G}

) cameras in the PyBullet simulator.

Fig. 2 : State error evolution with target in local camera FoV.

Fig. 3 : TD-ACM input actuation evolution with target visible to local camera.

Fig. 4 : Feature trajectories and normalized error norm evolutions with target in local camera FoV.

Fig. 5 : TD-ACM state error evolution; target initially outside local camera FoV.

Fig. 6 : TD-ACM input actuation evolution; target initially outside local camera FoV.

Fig. 7 : Feature trajectories and normalized error norm evolution; target initially outside camera FoV.

Fig. 8 : TD-ACM CAD model designed in SolidWorks.

Fig. 9 : The customized TD-ACM experimental setup and its components.

Panel of Figure 12 — Fig. 10 : Test A: (a) Time evolution of the advanced feature error; (b) evolution of the local camera twist; (c) time derivative of the CR generalized coordinates; and (d) four snapshots of the markers during operation.

Panel of Figure 13 — Fig. 11 : Test B: (a) Time evolution of the advanced feature error; (b) time evolution of the local camera twist; (c) time derivative of the CR generalized coordinates; and (d) four snapshots of the markers during operation.

Panel of Figure 14 — Fig. 12 : Test C: (a) Time evolution of the advanced feature error; (b) time evolution of the local camera twist; and (c) time derivative of the CR generalized coordinates.

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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

Department of Mechanical, Industrial, and Mechatronics Engineering, Toronto Metropolitan University, Toronto, ON M5B 2K3, Canada · Aerospace Research Center, National Research Council of Canada (NRC), Montreal, QC H3T 2B2, Canada

Continuum Robot Control Aerial Manipulation Dynamical Systems

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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.

Abstract

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