Continuum robots, known for their high flexibility and adaptability, offer immense potential for applications such as medical surgery, confined-space inspections, and wearable devices. However, their non-linear elastic properties and complex kinematics present significant challenges in digital modeling and effective control. This research proposes a novel computational framework that integrates Lie group kinematics with an evolutionary algorithm (EA) to identify optimal control coefficients for specific robot models. Our method starts by generating datasets from physics-based simulations and fractional order control, defining both ideal configurations and models to be optimized. By using EA, we iteratively minimize deviations through two fitness objectives \textemdash deviation mean squared error (\(\text{MSE}_1\)) and TCP vector error (\(\text{MSE}_2\)) \textemdash to align the robot's backbone with the desired configuration. Built on the Computer-Aided Design (CAD) platform Grasshopper, this framework provides real-time visualization, enabling dynamic control of robot configurations. Results show that the proposed method achieves precise alignment of the robot's backbone with minimal computation. This approach not only simplifies the coefficient identification process but also demonstrates the advantages of EA in multi-objective optimization, contributing to efficient modeling and control of continuum robots.

翻译：连续体机器人以其高灵活性和适应性著称，在医疗手术、受限空间检测和可穿戴设备等领域展现出巨大潜力。然而，其非线性弹性特性与复杂运动学特性为数字化建模与有效控制带来了显著挑战。本研究提出一种新颖的计算框架，将李群运动学与进化算法（EA）相结合，以识别特定机器人模型的最优控制系数。我们的方法首先通过基于物理的仿真和分数阶控制生成数据集，定义理想构型及待优化模型。通过使用进化算法，我们迭代地最小化两个适应度目标——偏差均方误差（\(\text{MSE}_1\)）与TCP向量误差（\(\text{MSE}_2\)）——以使机器人主骨架与目标构型对齐。该框架构建于计算机辅助设计（CAD）平台Grasshopper之上，提供实时可视化功能，实现对机器人构型的动态控制。结果表明，所提方法能以最小计算量实现机器人主骨架的精确对齐。该方法不仅简化了系数识别过程，还展示了进化算法在多目标优化中的优势，有助于实现连续体机器人的高效建模与控制。