Flexible continuum manipulators are valued for minimally invasive surgery, offering access to confined spaces through nonlinear paths. However, cable-driven manipulators face control difficulties due to hysteresis from cabling effects such as friction, elongation, and coupling. These effects are difficult to model due to nonlinearity and the difficulties become even more evident when dealing with long and multi-segmented manipulator. This paper proposes a data-driven approach based on recurrent neural networks to capture these nonlinear and previous states-dependent characteristics of cable actuation. We design customized fiducial markers to collect physical joint configurations as a dataset. Result on a study comparing the learning performance of four Deep Neural Network (DNN) models show that the Temporal Convolution Network (TCN) demonstrates the highest predictive capability. Leveraging trained TCNs, we build a control algorithm to compensate for hysteresis. Tracking tests in task space using unseen trajectories show that the best controller reduces the mean position and orientation error by 61.39% (from 13.7 mm to 5.29 mm) and 64.04% (from 31.17{\deg} to 11.21{\deg}), respectively.

翻译：柔性连续体操作臂因其能够通过非线性路径进入受限空间，在微创手术中具有重要价值。然而，线缆驱动操作臂因摩擦、伸长和耦合等线缆效应导致的迟滞现象，给控制带来困难。由于非线性特性，这些效应难以建模，尤其是在处理长节段和多节段操作臂时更为突出。本文提出一种基于循环神经网络的数据驱动方法，用于捕捉线缆驱动中这些非线性且依赖先前状态的特征。我们设计定制化基准标记，收集物理关节构型作为数据集。通过对比四种深度神经网络（DNN）模型的学习性能，结果表明时间卷积网络（TCN）具有最高的预测能力。利用训练好的TCN，我们构建了补偿迟滞的控制算法。基于未观测轨迹的任务空间跟踪测试显示，最佳控制器将平均位置误差和姿态误差分别降低了61.39%（从13.7毫米降至5.29毫米）和64.04%（从31.17°降至11.21°）。