# Energy-Based Modeling of Deformable Linear Objects

• S. Hirai
Chapter

## Abstract

An energy-based approach to the modeling of deformable linear objects is presented. Many manipulative operations in manufacture deal with deformable linear objects such as wires, cords, and threads with bend, twist, and extension in 3D space. Simulation of their behavior is required in product design and in evaluation of manipulative operations. It is, however, difficult to build a model of deformable linear objects and to simulate their behavior. I will develop an energy-based modeling of deformable linear objects and will show the computation results of their deformation.

First, I will introduce a differential geometry coordinate system, which is appropriate to describing the deformation of linear objects. Second, internal energy of a deformable linear object and geometric constraints imposed on it are formulated. Deformation of a linear object can be computed by minimizing its internal energy under the geometric constraints. This conditional variation problem is solved by parametrization and nonlinear programming. Finally, computational results and experimental results demonstrate the effectiveness of the energy-based approach.

## Keywords

Internal Energy Geometric Constraint Twist Angle Flexural Rigidity Gravitational Energy
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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