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Piecewise constant strain kinematic model of externally loaded concentric tube robots
Mechatronics ( IF 3.3 ) Pub Date : 2021-02-03 , DOI: 10.1016/j.mechatronics.2021.102502
Mahdi Pourafzal , Heidar Ali Talebi , Kanty Rabenorosoa

This paper presents a piecewise constant strain kinematic model for concentric tube robots (CTR) in externally loaded conditions. It discretizes the pre-curved tubes comprising the robot into a finite number of pieces and involves external effects as a set of wrench vectors exerted along the robot backbone. Constant strain lets us describe the pieces with helices in which shear deformation and elongation are neglected. The resulting piecewise helix is the simplest curve that can catch the torsion of tubes that play a crucial role in kinematic behavior. This approximation transforms the conventional boundary value problem (BVP) of CTRs models into a set of nonlinear equations that drastically decreases the model resolution time. The present method uses a Lyapunov function and torsional Jacobian to ensure the distal torsion constraint consistently and, as a result, the solution’s convergence. The paper’s primary purpose is to present a fast, numerically stable, and relatively accurate kinematic model not reliant on measurement data. Experimental results on a two-tube prototype and provided for different tip loading conditions reveal maintaining a balance between adequate accuracy and reasonable running time, about 7 ms for five pieces per section, for real-time applications in the presence of external load.



中文翻译:

外载同心管机器人的分段恒应变运动学模型

本文提出了在外部负载条件下用于同心管机器人(CTR)的分段恒定应变运动学模型。它将组成机器人的预弯曲管离散化为有限数量的零件,并产生了沿机器人主干施加的一组扳手矢量的外部影响。恒定应变让我们用忽略剪切变形和伸长率的螺旋形零件来描述。产生的分段螺旋是最简单的曲线,可以捕捉在运动行为中起关键作用的管的扭转。这种近似将CTR模型的常规边值问题(BVP)转换为一组非线性方程,从而极大地减少了模型的解析时间。本方法使用李雅普诺夫函数和扭转雅可比矩阵来确保远端扭转约束始终如一,从而确保解的收敛性。本文的主要目的是提出一种不依赖于测量数据的快速,数值稳定和相对准确的运动学模型。在具有不同尖端负载条件的两管原型上的实验结果表明,在存在外部负载的情况下进行实时应用时,在适当的精度和合理的运行时间之间保持平衡,每节五片约7 ms。

更新日期:2021-02-03
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