Optimizing Modeling of Continuum Robots: Integration of Lie Group Kinematics and Evolutionary Algorithms

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.