Using Euler Curves to Model Continuum Robots

Rao, Priyanka; Peyron, Quentin; Burgner-Kahrs, Jessica

doi:10.1109/icra48506.2021.9561700

Cited by 12 publications

(10 citation statements)

References 27 publications

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“…As a result, the linear assumption works well for continuum robots in several application scenarios, even for large deformations. It has been used to represent the shape of slender backbones affected by gravity [25], [26], contact forces with the environment [27], and forces due to tools mounted at the tip [28]. In our previous work [28], we provide a 2D static model to model tip forces on a single segment using Euler arc splines (EAS).…”

Section: B Our Contributionmentioning

confidence: 99%

“…It has been used to represent the shape of slender backbones affected by gravity [25], [26], contact forces with the environment [27], and forces due to tools mounted at the tip [28]. In our previous work [28], we provide a 2D static model to model tip forces on a single segment using Euler arc splines (EAS). While Euler curves require the use of Fresnel integrals which can be computationally expensive, the use of EAS to represent the backbone shape reduces the computational complexity [29].…”

Section: B Our Contributionmentioning

confidence: 99%

“…In this work, we extend our previous work and present the use of EAS in the forward kinematics framework for a TDCR experiencing 3D tip forces. First, we prove their efficacy in representing TDCR shapes in experimental data, whereas [28] only compared them in simulation. Next, we extend the previously proposed 2D static model to 3D that maps the input tendon tensions to corresponding backbone curvatures and can account for gravity, friction, and tip forces.…”

Section: B Our Contributionmentioning

confidence: 99%

“…Since the left hand side of the equation is composed of linear curvature components, we need to project the components of moments in the right hand side of the equation to be linear as well. As done in [28], we use closed form solution of least squares linear regression to obtain the vector of linearly varying component of the experienced moment. Assembling the moment vectors for n subsegments in ( 22) into a matrix gives us…”

Section: B Constitutive Equationsmentioning

confidence: 99%

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Shape Representation and Modeling of Tendon-Driven Continuum Robots Using Euler Arc Splines

Rao

Peyron

Burgner-Kahrs

2022

IEEE Robot. Autom. Lett.

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Due to the compliance of tendon-driven continuum robots, carrying a load or experiencing a tip force result in variations in backbone curvature. While the spatial robot configuration theoretically needs an infinite number of parameters for exact description, it can be well approximated using Euler Arc Splines which use only six of them. In this letter, we first show the accuracy of this representation by fitting the Euler Arc splines directly to experimentally measured robot shapes. Additionally, we propose a 3D static model that can account for gravity, friction and tip forces. We demonstrate the utility of using efficient parameterization by analyzing the computation time of the proposed model and then, using it to propose a hybrid model that combines physics-based model with observed data. The average tip error for the Euler arc spline representation is 0.43% and the proposed static model is 3.25% w.r.t. robot length. The average computation time is 0.56 ms for nonplanar deformations for a robot with ten disks. The hybrid model reduces the maximum error predicted by the static model from 8.6% to 5.1% w.r.t. robot length, while using 30 observations for training.

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Section: B Our Contributionmentioning

confidence: 99%

Section: B Our Contributionmentioning

confidence: 99%

Section: B Our Contributionmentioning

confidence: 99%

Section: B Constitutive Equationsmentioning

confidence: 99%

See 2 more Smart Citations

Shape Representation and Modeling of Tendon-Driven Continuum Robots Using Euler Arc Splines

Rao

Peyron

Burgner-Kahrs

2022

IEEE Robot. Autom. Lett.

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“…This step allows us to reduce the parameter space to only those that can not be easily evaluated experimentally. Thus we can re-write the dynamics as: δ(q, q, q) = Y (q, q, τ )π, (18) where δ collects the first three terms in (8) -the dynamic forces -and Y is such that Y π collects all the remaining terms. We call q1 , q2 τ the measurements of curvature and motor torque gathered in the above discussed experiments.…”

Section: B System Identificationmentioning

confidence: 99%

An Experimental Validation of the Polynomial Curvature Model: Identification and Optimal Control of a Soft Underwater Tentacle

Stella

Obayashi

Santina

et al. 2022

IEEE Robot. Autom. Lett.

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The control possibilities for soft robots have long been hindered by the lack of accurate yet computationally treatable dynamic models of soft structures. Polynomial curvature models propose a solution to this quest for continuum slender structures. Nevertheless, the results produced with this class of models have been so far essentially theoretical. With the present work, we aim to provide a much-needed experimental validation to these recent theories. To this end, we focus on soft tentacles immersed in water. First, we propose an extension of the affine curvature model to underwater structures, considering the drag forces arising from the fluid-solid interaction. Then, we extensively test the model's capability to describe the system behavior across several shapes and working conditions. Finally, we validate model-based control policies, proposing and solving an optimal control problem for directional underwater swimming. Using the model we show an average increase of more than 3.5 times the swimming speed of a sinusoidal baseline controller, with some tentacles showing an improvement in excess of 5.5 times the baseline.

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Active compliance and force estimation of a continuum surgical manipulator based on the tip-pose feedback

Wu,

Zhou,

Wang

et al. 2023

Sci. China Technol. Sci.

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Using Euler Curves to Model Continuum Robots

Cited by 12 publications

References 27 publications

Shape Representation and Modeling of Tendon-Driven Continuum Robots Using Euler Arc Splines

Shape Representation and Modeling of Tendon-Driven Continuum Robots Using Euler Arc Splines

An Experimental Validation of the Polynomial Curvature Model: Identification and Optimal Control of a Soft Underwater Tentacle

Active compliance and force estimation of a continuum surgical manipulator based on the tip-pose feedback

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