A model for the embedded tendon control of a slender three-dimensional flexible robot link

Davis, Jon H.; Hirschorn, R.M.

doi:10.1007/bf01985941

Cited by 10 publications

(5 citation statements)

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“…An early theoretical work toward elastica dynamics with embedded tendons is that of Davis and Hirschorn [32] where the dynamic model for a single flexible link has been derived based on Frenet formulation. The derived equations are in form of partial differential equations.…”

Section: Related Work On Spatial Catheter Modelingmentioning

confidence: 99%

Modeling, force estimation and control of steerable catheters for robot-assisted intra-cardiac navigation

Hasanzadeh¹

2021

Preprint

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Intra-cardiac catheterization is an effective procedure for diagnosis and treatment of many cardiac disorders such as arrhythmia. The objective of the catheter manipulation is to accurately position the catheter tip at the target tissue on the endocardium and provide a stable contact force for a specific duration to the region of interest. However, this is a challenging task due to the high flexibility of the catheter, ineffective visualization and dynamic environment of the heart. Additionally, the catheter-tissue interaction force, that the procedure outcome highly depends on, is not known to the interventionalist during the catheterization. This thesis deals with improving the safety and effectiveness of the catheterization by making contributions to two main areas; catheter contact force estimation and automatic force/position control of a robotic catheter system. First, a quasi-static model of the planar catheter that predicts the catheter pose for the given actuation variables and external forces in the plane of catheter motion, is proposed. In the next step, the computational efficiency of the proposed model is utilized to develop an online approach for the estimation of the external force at the tip of a catheter based on the pose measurement. The proposed force estimation approach is also extended to 3D by developing an efficient model of the catheter that is derived by coupling the classical Cosserat rod model with a new model of the pull-wire actuation. Experiments performed using electromagnetic sensors verify the feasibility of the proposed schemes in medical applications. In the control area, a position control scheme for a robotic assisted manipulation system is proposed, using the experimentally obtained inverse kinematics that compensates for the non-smooth dynamics of the distal shaft bending mechanism. Compensation of the backlash behavior of the catheter due to its interaction with the surrounding veins is also incorporated in the control scheme. The proposed position controller is then adopted as the internal loop of a hybrid position/force controller that positions the catheter tip to the target tissue and simultaneously, regulates the contact force to a desired value. The viability of the proposed controllers is then verified through simulations and experiments.

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Section: Related Work On Spatial Catheter Modelingmentioning

confidence: 99%

Modeling, force estimation and control of steerable catheters for robot-assisted intra-cardiac navigation

Hasanzadeh¹

2021

Preprint

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“…On sufficiently long time scales, and when longitudinal waves are not important, the effective action is often taken to be metrically constrained, with a low-dimensional body stress tensor enforcing local distances between moving pieces of material. This approach, either at the level of the action or equations of motion, has been used to describe systems at many scales, from the overdamped motions of flagella [1,2], filaments [3,4], or macromolecules [5], to the inertial dynamics of elastic rods [6][7][8][9][10], soft robot links [11], yarn [12], flags [13], or sonar and telegraph cables in the ocean [14][15][16].…”

mentioning

confidence: 99%

“…This can also be reformulated in terms of an elliptic integral in r 2 [38], but we need not do that here. Solving for r, one then obtains σ directly from (11), and the other two coordinates by quadratures using (14) and (15) or (16). Nondimensionalizing (17), using some chosen length scale along with µ and ω, will lead to a family of equations with our three constants P z , J z , and C s as parameters.…”

mentioning

confidence: 99%

“…The constants C η and C s coincide when T = 0. Note the resemblance of (11) and (23) to Bernoulli's equation, applied to ideal fluid flowing along a fixed or rotating streamline. In fluid or solid, Coriolis terms arising from simultaneous flow and rotation do not contribute to the conserved quantities.…”

mentioning

confidence: 99%

“…Note that we can form an orthonormal triad of ẑ, θ ≡ ẑ×X ẑ×X , and r ≡ −ẑ × θ, and that with the origin of X on the ẑ axis, X ≡ rr + zẑ and, thus, ẑ × X = r θ and ∂ s X • r = ∂ s r. For a string rigidly rotating with angular frequency ω about ẑ, ∂ t X = ωr θ, so σ may be written as a function of a single variable r = ẑ × X . Now use the three constants (11), (14), and (15) to write:…”

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confidence: 99%

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A conserved quantity in thin body dynamics

Hanna

Pendar

2016

Physics Letters A

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Thin, solid bodies with metric symmetries admit a restricted form of reparameterization invariance. Their dynamical equilibria include motions with both rigid and flowing aspects. On such configurations, a quantity is conserved along the intrinsic coordinate corresponding to the symmetry. As an example of its utility, this conserved quantity is combined with linear and angular momentum currents to construct solutions for the equilibria of a rotating, flowing string, for which it is akin to Bernoulli's constant.The mechanics of thin bodies are amenable to a description in which energies are effectively expressed with an integral over a surface or curve. On sufficiently long time scales, and when longitudinal waves are not important, the effective action is often taken to be metrically constrained, with a low-dimensional body stress tensor enforcing local distances between moving pieces of material. This approach, either at the level of the action or equations of motion, has been used to describe systems at many scales, from the overdamped motions of flagella [1,2] Thin bodies such as rods and solid membranes moving in a higher-dimensional space share characteristics with both rigid bodies and fluids. The metric constraints of inextensible solids preclude the broad reparameterization invariance inherent to fluids and fluid membranes, leaving only highly restricted reparameterization invariance associated with any metric symmetries the body may possess. Effectively one has global, rather than local, symmetries on the body. However, these intrinsic symmetries are not trivially identifiable with rigid transformations of embedding coordinates, because a lower-dimensional body can adopt extrinsic curvature in the surrounding space. Thus, unlike space-filling rigid continua, the body may display additional material flows in equilibrium in addition to, and distinct from, rigid motions. Simple examples include a string being unspooled [12], a cable being laid down on the ocean floor [14], or the flowing skirt of a rotating dancer [17]. Figure 1 is a schematic of such a combined rigid-flowing configuration.We will describe such a system using several types of coordinates. Aside from a time coordinate, there are three important sets of spatial coordinates to consider. First, there are time-independent coordinates attached to pieces of material. For an inextensible body, these can also be associated with geometric parameters, such as arc length. Second, there are coordinates for which material motions tangent to the body have been removed. These are effectively Eulerian from the intrinsic viewpoint of the body, but they are attached to a body moving through an embedding space, so have some Lagrangian character as well. This viewpoint is called the "orthogonal gauge" in [18]

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Mechanics of Continuum Robots with External Loading and General Tendon Routing

Rucker

Webster

2014

Experimental Robotics

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A model for the embedded tendon control of a slender three-dimensional flexible robot link

Cited by 10 publications

References 15 publications

Modeling, force estimation and control of steerable catheters for robot-assisted intra-cardiac navigation

Modeling, force estimation and control of steerable catheters for robot-assisted intra-cardiac navigation

A conserved quantity in thin body dynamics

Mechanics of Continuum Robots with External Loading and General Tendon Routing

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