This paper describes the dynamic modeling of linear object deformation considering geometrical constraints and contact with obstacles. Deformable linear objects such as cables and strings are widely used in our daily life, some industries, and medical operations. Modeling, control, and manipulation of deformable linear objects are keys to many applications. We have formulated the static deformation of a linear object using the differential geometry coordinates. In this paper, we apply differential geometry coordinates to the dynamic modeling of linear objects. First, we formulate dynamic 2D deformation of an inextensible linear object based on a differential geometry coordinate system. Second, we consider dynamic deformation of the linear object when forces/moments and geometrical constraints are imposed on the object. Third, we model contact of a linear object with a circular obstacle. It can be applied to self-contact of the linear object. Finally, we show simulation results using the proposed modeling technique

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

A planning method for unraveling deformable linear objects based on 2D information about their crossing states 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, an unraveling process of a linear object is represented a sequence of crossing state transitions. It can be generated on a computer if 3D information about the current crossing state is given. Second, the crossing sequence of a linear object, which corresponds to its 2D information, is categorized into two types: unravelable and not-unravelable. Third, a procedure to generate efficient unraveling processes based on unravelability of the crossing sequence is explained. Finally, examples of unraveling process generation with our developed system are demonstrated

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.

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.

A planning method for linear object manipulation including knotting/raveling in the three-dimensional space is proposed. Firstly, topological states of a linear object are represented as finite permutations of crossing points including the crossing type of each crossing point. Secondly, transitions among the topological states are defined. They correspond to operations that change the number of crossing points or crossing point permutation. Then, we can generate possible sequences of crossing state transitions, that is, possible manipulation processes from an 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, criteria for evaluation of manipulation processes are introduced in order to reduce the candidates of manipulation plans. Finally, it is demonstrated that our developed system based on the above method can generate manipulation plans for raveling from an overhand knot.