Static Modeling of Linear Object Deformation Based on Differential Geometry

Wakamatsu, Hidefumi; Hirai, Shinichi

doi:10.1177/0278364904041882

Cited by 106 publications

(54 citation statements)

References 29 publications

(28 reference statements)

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“…Wakamatsu and Hirai [15] model the static deformation of a linear object with four functions: three to describe the change in orientation along the curve and one to describe the extension along the curve. These functions are approximated by a linear combination of a set of basis functions.…”

Section: Related Workmentioning

confidence: 99%

Path planning for deformable linear objects

2006

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Abstract-We present a new approach to path planning for deformable linear (one-dimensional) objects such as flexible wires. We introduce a method for efficiently computing stable configurations of a wire subject to manipulation constraints. These configurations correspond to minimal-energy curves. By restricting the planner to minimal-energy curves, the execution of a path becomes easier. Our curve representation is adaptive in the sense that the number of parameters automatically varies with the complexity of the underlying curve. We introduce a planner that computes paths from one minimal-energy curve to another such that all intermediate curves are also minimal-energy curves. This planner can be used as a powerful local planner in a sampling-based roadmap method. This makes it possible to compute a roadmap of the entire "shape space," which is not possible with previous approaches. Using a simplified model for obstacles, we can find minimal-energy curves of fixed length that pass through specified tangents at given control points. Our work has applications in cable routing, and motion planning for surgical suturing and snake-like robots.

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Section: Related Workmentioning

confidence: 99%

Path planning for deformable linear objects

2006

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“…In [12], we developed an algorithm based on Ritz's method [13] and a nonlinear programming technique to compute linear object deformation. In this paper, we apply such algorithm to the computation of belt object deformation.…”

Section: A Computation Algorithmmentioning

confidence: 99%

“…It can be applied to path planning for flexible wires. We have proposed a modeling method for linear object deformation based on differential geometry and its applications to manipulative operations [12]. In this method, linear object deformation with flexure, torsion, and extension can be described by only four functions.…”

Section: Introductionmentioning

confidence: 99%

“…This method can be applied to a sheet object if the shape of the object is regarded as rectangle, namely, the object has belt-like shape. However, in [12], it is assumed that the shape of cross-section of a linear object is fixed. This assumption is not appropriate to represent 3D shape of a belt object because the shape of its cross-section can change due to deformation.…”

Section: Introductionmentioning

confidence: 99%

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Fishbone Model for Belt Object Deformation

Wakamatsu¹,

Arai²,

Hirai³

2007

Robotics: Science and Systems III

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Abstract-A modeling method for representing belt object deformation is proposed. Deformation of belt objects such as film circuit boards or flexible circuit boards must be estimated for automatic manipulation and assembly. In this paper, we assume that deformation of an inextensible belt object can be described by the shape of its central axis in a longitudinal direction called "the spine line" and lines with zero curvature called "rib lines". This model is referred to as a "fishbone model" in this paper. First, we describe deformation of a rectangular belt object using differential geometry. Next, we propose the fishbone model considering characteristics of a developable surface, i.e., a surface without expansion or contraction. Then, we formulate potential energy of the object and constraints imposed on it. Finally, we explain a procedure to compute the deformed shape of the object and verify the validity of our proposed method by comparing some computational results with experimental results.

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“…Prior work mainly focuses on modeling of DLOs and planning algorithms for their manipulation. In [1] a physical static model for DLOs based on differential geometry is presented The model is extended to a dynamic model for the two-dimensional case in [2]. But the complexity of the model prevents using it for re-planning during manipulation.…”

Section: Introductionmentioning

confidence: 99%

Autonomous manipulation of deformable objects based on teleoperated demonstrations

Rambow

Schauss

Buss

et al. 2012

2012 IEEE/RSJ International Conference on Intelligent Robots and Systems

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Abstract-While humans can manipulate deformable objects smoothly and naturally, this is still a challenge for autonomous robots due to the complex object dynamics. The presence of rigid environment constraints and altering contact phases between the deformable object, the manipulator, and the environment makes this problem even more challenging. This paper presents a framework for deformable object manipulation that makes use of a single human demonstration of the task. The recorded trajectories are automatically segmented into a sequence of haptic control primitives involving contact with the rigid environment and vision-guided grasp primitives. The recorded motion/force trajectories serve as reference for a compliant control scheme in contact situations. In order to cope with positioning uncertainties a variable admittance control is proposed. The proposed approach is validated in an experimental mounting task for a deformable linear object with multiple re-grasping. The task is demonstrated with a multimodal teleoperation system and transfered to a robotic platform with a pair of seven degrees of freedom manipulators.

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Static Modeling of Linear Object Deformation Based on Differential Geometry

Cited by 106 publications

References 29 publications

Path planning for deformable linear objects

Path planning for deformable linear objects

Fishbone Model for Belt Object Deformation

Autonomous manipulation of deformable objects based on teleoperated demonstrations

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