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

Abstract

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 are of great importance, in particular to enable robotic manipulation of DLOs. The main motivation of this work is to enable efficient pre- diction 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.

Deformable Linear Objects Manipulation With Online Model Parameters Estimation

“…Many different physical models of DLOs have been proposed in the past [8], ranging from simpler mass-spring [9] and energy-based models to more accurate but computationally demanding elastic-rod, dynamic splines, and finite element models [8]. Other than the selection of a specific model, the choice of the integration method is crucial to achieve a good trade-off between simulation accuracy and efficiency, and different integration approaches like Runge-Kutta and symplectic have been proposed [23]. As opposed to the mentioned forcebased methods, a differentiable position-based simulation of DLOs is proposed in [11] where the integration steps are avoided leading to a more efficient and stable simulation.…”