Hidefumi Wakamatsu

Static Modeling of Linear Object Deformation Based on Differential Geometry

We describe the modeling of linear object deformation based on differential geometry and its applications to manipulative operations. A particle-based approach, the finite element method, and the Cosserat theory have been applied to the modeling of linear object deformation. In this paper, we establish an alternative modeling approach based on an extension of differential geometry. First, we extend differential geometry to describe linear object deformation including flexure, torsion, and extension. Secondly, we show computational results to demonstrate the feasibility of the proposed modeling technique, and we compare computational and experimental results to demonstrate the accuracy of the model. Next, we apply the proposed approach to the grasping of a deformable linear object. We propose a disturbance force margin to indicate the stability of the grasping and we describe the computation of the margin using the proposed approach. Finally, we apply the proposed approach to the deformation path planning of a linear object. We formulate the minimization of potential energy during a deformation path. We compute the optimal deformation path and a feasible deformation path, which are compared with an experimental result.

Knotting/Unknotting Manipulation of Deformable Linear Objects

Here, we propose a planning method for knotting/unknotting of deformable linear objects. First, we propose a topological description of the state of a linear object. Second, transitions between these states are defined by introducing four basic operations. Then, possible sequences of crossing state transitions, i.e. possible manipulation processes, can be generated once the initial and the objective states are given. Third, a method for determining grasping points and their directions of movement is proposed to realize derived manipulation processes. Our proposed method indicated that it is theoretically possible for any knotting manipulation of a linear object placed on a table to be realized by a one-handed robot with three translational DOF and one rotational DOF. Furthermore, criteria for evaluation of generated plans are introduced to reduce the candidates of manipulation plans. Fourth, a planning method for tying knots tightly is established because they fulfill their fixing function by tightening them. Finally, we report knotting/unknotting manipulation performed by a vision-guided system to demonstrate the usefulness of our approach.

Static analysis of deformable object grasping based on bounded force closure

A static analysis of deformable object grasping based on bounded force closure is presented. There are many manipulative operations that deal with deformable objects in manufacturing processes. Manipulative operations for these objects are often performed by utilizing their deformation actively while the operations may result in failure because of unexpected deformation of the objects during the manipulation process. In order to perform the manipulative operations for deformable objects successfully, it is necessary to evaluate their deformation by building object models and to derive task strategies by analyzing manipulation processes using the object models. In this paper, we will analyze stable grasping of deformable objects based on the concept of bounded force closure. Firstly, we will introduce the concept of bounded force closure, which is an extension of force closure condition. Secondly, we will investigate the necessary condition for bounded force closure in order to derive the properties of bounded force closure grasping. Thirdly, we will formulate the deformation of linear objects as an example of deformable objects and we will propose a procedure to evaluate stability of deformable object grasping. Finally, some numerical examples will be shown in order to demonstrate the effectiveness of our proposed method.

Modeling of linear objects considering bend, twist, and extensional deformations

Various deformable objects are manipulated in many manufacturing processes. Deformation of these objects is often utilized in order to manipulate them successfully while the manipulation sometimes fails because of unexpected deformation of the objects. Modeling of deformable objects is thus required so that the shape of the objects can be evaluated on a computer in advance. In this paper, we develop an analytical method to model the shape of a deformable linear object such as cords and tubes. First, a geometric representation to describe the shape of a linear object with bending and torsional deformation is introduced. The potential energy of the object and the geometric constraints imposed on it are then formulated. The shape of the object in the stable state can be derived by minimizing the potential energy under the geometric constraints. Next, procedure to compute the deformed shape is developed by applying a nonlinear programming technique. Finally, some numerical examples are shown in order to demonstrate how deformed shapes of linear objects are computed using the proposed approach.

Modeling of deformable thin parts for their manipulation

Various deformable parts such as cords, leather products, and sheet metals are manipulated and are handled in many manufacturing processes. Deformation of these parts is often utilized in order to manipulate them successfully while the manipulation sometimes fails because of unexpected deformation of the parts. Modeling of deformable objects is thus required so that the shape of the soft parts can be analyzed and evaluated on a computer. In this paper, we develop an analytical method to model the shape of a deformable object. Especially, we deal with deformation of a bendable thin object. The process of manipulating a deformable object is analyzed with regard to how the object interacts with other objects around it. The model of a bendable thin object is formulated according to the principle that the potential energy of the object reaches the minimum at its stable shape. An algorithm to compute the deformed shape of the object is developed by applying a nonlinear programming technique. Finally, a simple experiment is done to demonstrate the validity of the modeling method proposed in this paper.<<ETX>>

Dynamic Modeling of Linear Object Deformation based on Differential Geometry Coordinates

This paper describes the dynamic modeling of linear object deformation based on differential geometry coordinates. Deformable linear objects such as cables and strings are widely used in our daily life, electric industries, medical operations. Modeling, control, and manipulation of deformable linear objects are keys to many applications. We have proposed the differential geometry coordinates to describe the 2D/3D deformation of a linear object with the minimum number of parameters. Based on this description, we have formulated the static deformation of a linear object using the differential geometry coordinates but the dynamic deformation has not been investigated yet. In this paper, we apply differential geometry coordinates to the dynamic modeling of linear objects. First, we formulate the dynamic 2D deformation of an inextensible linear object based on a differential geometry coordinate system. Second, we show simulation results using the proposed modeling technique. Next, we apply the proposed dynamic modeling to the control of a flexible link.

Dynamic analysis of rodlike object deformation towards their dynamic manipulation

In manufacturing processes, there are many manipulative operations which deal with deformable objects. In this paper we analyse the dynamic motion analysis of deformable rodlike objects. First, a geometric representation to describe the shape of a rodlike object with dynamic deformation is introduced. The potential and kinetic energy of the object and the geometric constraints imposed on it are then formulated. The shape of the dynamically deforming object can be derived by minimizing the difference between the kinetic energy and potential energy under the geometric constraints. Next, a procedure to compute the deformed shape is developed by use of Eulers approach. Finally, some numerical examples are shown in order to demonstrate how the proposed approach computes the shapes of deformed rodlike objects.

Manipulation Planning for Knotting/Unknotting and Tightly Tying of Deformable Linear Objects

A planning method for knotting/unknotting and tightening manipulation of deformable linear objects is proposed. It is important for linear object manipulation in industrial/medical field to analyze knotting. Modeling of knotting/unknotting process is useful for design of knotting/unknotting system with different mechanism from human arms/hands and manipulation planning suitable for such system. Firstly, knotting/unknotting processes of a linear object is represented as a sequence of finite crossing state transitions. Secondly, grasping points and their moving direction to perform each state transition are defined. Then, possible qualitative manipulation plans can be generated on a computer system once the initial state and the objective state of a linear object are given. Thirdly, a planning method for tightly tying is proposed. Pulling parts for tightening knots can be determined by using this method. Finally, an experiment for tying an overhand knot by our developed system is shown.

Planning of one-handed knotting/raveling manipulation of linear objects

A planning method for linear object manipulation including knotting/unknotting by one hand is proposed. Firstly, topological states of a linear object are represented as finite permutations of crossing points. Secondly, transitions among topological states are defined. Then, we can generate possible sequences of state transitions, that is, possible manipulation processes from the initial state to a given objective state. Thirdly, a method for determination of grasping points and their moving direction is proposed in order to realize derived manipulation processes. Furthermore, a planning method for one-handed manipulation is proposed. Knotting by one hand is possible as any manipulation processes can be realized by iteration of one-handed operations. Finally, it is demonstrated that our developed system based on the above method can generate manipulation plans for raveling out of an overhand knot.

Manipulation planning for unraveling linear objects

A planning method for unraveling manipulation of deformable linear objects is proposed. In manipulation of a linear object, its raveling must be avoided. It takes much time to unravel it once it is raveled. Therefore, it is important to generate unraveling plans efficiently. First, a manipulation process of a linear object including its unraveling is represented as a sequence of its crossing state transitions. Then, possible manipulation processes can be generated once the initial and the objective crossing states are given. Second, qualitative actions to realize manipulation processes are determined. Third, a method for unraveling a linear object as far as possible when its crossing state can not be identified completely is proposed. Finally, an example of unraveling process generation is demonstrated