Symplectic Integration for Multivariate Dynamic Spline-Based Model of Deformable Linear Objects

Deformable linear objects (DLOs) such as ropes, cables, and surgical sutures have a wide variety of uses in automotive engineering, surgery, and electromechanical industries. Therefore, modeling of DLOs as well as a computationally efficient way to predict the DLO behavior is of great importance, in particular to enable robotic manipulation of DLOs. The main motivation of this work is to enable efficient prediction of the DLO behavior during robotic manipulation. In this paper, the DLO is modeled by a multivariate dynamic spline, while a symplectic integration method is used to solve the model iteratively by interpolating the DLO shape during the manipulation process. Comparisons between the symplectic, Runge-Kutta, and Zhai integrators are reported. The presented results show the capabilities of the symplectic integrator to overcome other integration methods in predicting the DLO behavior. Moreover, the results obtained with different sets of model parameters integrated by means of the symplectic method are reported to show how they influence the DLO behavior estimation.