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Equilibrium Configurations of a Kirchhoff Elastic Rod under Quasi-static Manipulation
[chapter]
2013
Springer Tracts in Advanced Robotics
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The set of all local solutions to this problem is the configuration space of the wire under quasi-static manipulation. ...
We will show that this configuration space is a smooth manifold of finite dimension that can be parameterized by a single chart. ...
This material is based upon work supported by the National Science Foundation under CPS-0931871 and CMMI-0956362. ...
doi:10.1007/978-3-642-36279-8_5
fatcat:f3b4pnajajck5p2gblr4io7sde
Quasi-static manipulation of a Kirchhoff elastic rod based on a geometric analysis of equilibrium configurations
2013
The international journal of robotics research
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We show that this chart makes it easy to implement a sampling-based algorithm for quasi-static manipulation planning. ...
Any curve traced by this wire when in static equilibrium is a local solution to a geometric optimal control problem, with boundary conditions that vary with the position and orientation of each gripper ...
Acknowledgements The authors would like to thank Don Shimamoto for his many helpful comments, in particular those leading to the current proof of Lemma 4. ...
doi:10.1177/0278364912473169
fatcat:cxkuakdvf5bxvhzne2lzbjy4r4
Efficient motion planning for quasi-static elastic rods using geometry neighborhood approximation
2014
2014 IEEE/ASME International Conference on Advanced Intelligent Mechatronics
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We present a motion planning algorithm for a quasi-static Kirchhoff elastic rod in complex environments. ...
As the set of quasi-static deformations defines a finite dimensional manifold that can be parameterized by a single chart, the configuration space formulation extends nicely to this deformation space. ...
This work was supported by the French National Research Agency under the project Flecto (ANR-Digital Models). Industrial models are courtesy of Siemens-KineoCAM. ...
doi:10.1109/aim.2014.6878215
dblp:conf/aimech/RousselTB14
fatcat:gyv5xz5d3nh4nclv3z4xckpi7u
From the elastica compass to the elastica catapult: an essay on the mechanics of soft robot arm
2017
Proceedings of the Royal Society A
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When the load is smaller than the buckling value, the rod describes a continuous set of quasi-static forms and its end traces a (smooth, convex and simple) closed curve, which would be a circle if the ...
An elastic rod is clamped at one end and has a dead load attached to the other (free) end. The rod is then slowly rotated using the clamp. ...
The clamp rotates slowly, so that starting from a configuration in which the rod is subject to purely tensile axial load, the system quasi-statically evolves in a number of elastic forms at varying clamp ...
doi:10.1098/rspa.2016.0870
pmid:28293144
pmcid:PMC5332619
fatcat:7pyfjndtgrewjpgf75fwclk54i
Prediction of cabling shape during robotic manipulation
2015
The International Journal of Advanced Manufacturing Technology
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The manufacturing assembly process includes the manipulation of rigid and non-rigid parts. This paper discusses a method for the estimation of the cables' shape for robotic manipulation. ...
More specifically, in the framework of static analyses, a higher-order analytic model of cables is introduced and the need for model calibration is pointed out. ...
Open Access This article is distributed under the terms of the Creative Comm ons Attribution 4.0 International License (http:// creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution ...
doi:10.1007/s00170-015-7318-5
fatcat:u5s57y47x5cpvieepmadt3tv3q
Sufficient Conditions for a Path-Connected Set of Local Solutions to an Optimal Control Problem
2016
SIAM Journal on Applied Mathematics
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Bretl and McCarthy analyzed an optimal control problem whose local solutions are stable equilibrium configurations of a Kirchhoff elastic rod [7] . ...
Ivey and Singer considered the set of Kirchhoff elastic rods that have quasi-periodic centerlines and showed that this set is parameterized by a two-dimensional disc [13] . ...
In this paper, we use a quasi-static model of the elastic rod. ...
doi:10.1137/15m1025608
fatcat:g4onrjbkbfbbnnfbljqzb3o7ey
Soft Robots Modeling: a Literature Unwinding
[article]
2021
arXiv
pre-print
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Thus, the listing of the approaches naturally follows and a complete, untangled, review of the main works on the field is finally provided. ...
The common theoretical roots that relate the different families of modeling techniques are highlighted, employing a unifying language that ease the analysis of their main connections and differences. ...
In Sofa, a deformable continuum is modeled using a dynamic or quasi-static system of simulation nodes. ...
arXiv:2112.03645v1
fatcat:tkbvr273jjdkhoww74mp3xa5km
Geometrically-Exact Inverse Kinematic Control of Soft Manipulators With General Threadlike Actuators' Routing
2022
IEEE Robotics and Automation Letters
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In the effort to overcome some of these limitations, here we present a Geometrically-Exact (GE) inverse kinematics controller, which can be applied to soft manipulators having general threadlike actuators ...
The inverse kinematic control of soft robots appears as an open challenge that has been the subject of a number of papers presented in the last decade. ...
Note that, for the latter case of strengthcontrolled actuators that involves a static equilibrium, the term inverse kinematic instead of quasi-static is a slight abuse of terminology commonly adopted in ...
doi:10.1109/lra.2022.3183248
fatcat:ixvq2kfg4bglrmjjc4umquwtoe
Elastic Tubes: Modeling Elastic Deformation of Hollow Tubes
2010
Computer graphics forum (Print)
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The Cosserat theory of elastic rods has been used in a wide range of application domains to model and simulate the elastic deformation of thin rods. ...
Our approach achieves this task using a hybrid model that binds a mesh elastically to a reference Cosserat rod. ...
There are three types of boundary conditions for manipulating the rod: Under the specified boundary conditions, quasi-Newton algorithm [PTVF02] is applied to minimize the total potential energy, which ...
doi:10.1111/j.1467-8659.2010.01647.x
fatcat:lbthg5iiwvbsjdrgqhz2nxxzde
Spontaneous formation of non-uniform double helices for elastic rods under torsion
2017
Physics Letters A
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2016 pre-print arXiv:1609.07856v1 fatcat:peuj3dmfnjcsxhj7zac6fotwx4
Therefore an ideal model was presented to investigate the formation of double helices for elastic rods under torque. ...
Based on this principle, a method of manufacturing double helices with designed configurations was proposed and demonstrated. ...
The radius of the double helix composed by the central line of the rod is R, as shown in Fig.1(b) . • 4. The rod is quasi-static during the whole slack process. • 5. ...
doi:10.1016/j.physleta.2016.12.008
fatcat:l3kp4aivw5hsba6ul7ketaqsxi
Adaptive Deformation Control for Elastic Linear Objects
2022
Frontiers in Robotics and AI
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We specifically consider an elastic linear object where one of its endpoints is fixed, and another point can be grasped by a robotic arm. ...
This paper addresses the general problem of deformable linear object manipulation. ...
Moreover, we assume that the shape of the object always stays in quasi-static stable equilibrium, and as shown in Figure 1 , the whole shape of the object can be manipulated by controlling the motion ...
doi:10.3389/frobt.2022.868459
pmid:35572374
pmcid:PMC9096453
fatcat:k76eezxzlvgf3mk7t2tzmdcdeq
A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection
2017
International Journal of Engineering and Technologies
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The nonlinear response of a beam under static loading is also a function of different parameters of the particular problem. ...
The paper presents a review on large deflection behavior of curved beams, as manifested through the responses under static loading. ...
Hence, to obtain the final deformed configuration of a body under a given state of loading, the intermediate deformed states are captured and it is considered as the initial configuration for the next ...
doi:10.18052/www.scipress.com/ijet.11.13
fatcat:hd6azhadofbpxc45fnl3vyusti
On the Use of Piezoelectric Sensors in Structural Mechanics: Some Novel Strategies
2010
Sensors
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Structures under consideration mainly are load-carrying thin or thin-walled structural elements, such as rods, beams, plates and shells. ...
that changes its shape, and a proportional change in the shape of a substance when voltage is applied." ...
Acknowledgements Support of the present authors in the framework of the Kplus-Center of Competence "Linz Center of Mechatronics (LCM)" and K2-"Austrian Center of Competence in Mechatronics (ACCM)" is gratefully ...
doi:10.3390/s100605626
pmid:22219679
pmcid:PMC3247724
fatcat:4hx4zd6nq5avbjx3gf2x7jd2v4
On the evolution of intrinsic curvature in rod-based models of growth in long slender plant stems
2011
International Journal of Solids and Structures
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In many applications of rod theories as models for plant stem growth and development, it is necessary to allow the intrinsic curvature and flexural stiffness of the rod to evolve. ...
In the present paper, the application of evolution equations for these quantities is examined and a new evolution equation for the intrinsic curvature is proposed. ...
During his graduate studies at the University of California at Berkeley, Timothy Tresierras was supported as a Sloan Scholar. ...
doi:10.1016/j.ijsolstr.2010.12.006
fatcat:ybngxab7fvev7pyb5o4z6esi24
Dynamic Model of a Multibending Soft Robot Arm Driven by Cables
2014
IEEE Transactions on robotics
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To help contribute to this area of research, this paper develops a dynamic model of a continuum soft robot arm driven by cables and based upon a rigorous geometrically exact approach. ...
The present model can be used in the design phase as a dynamic simulation platform and to design the control strategy of a continuum robot arm moving in a dense medium. ...
ACKNOWLEDGMENT The authors would like to thank A. Arienti for the original idea of the robot arm design, M. Follador for his technical support during the prototype fabrication, and G. ...
doi:10.1109/tro.2014.2325992
fatcat:w3oai5epcnhlnof73v27zms5q4
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