Visualization and Optimization of Continuum Robots: Integration of Lie Group Kinematics and Evolutionary Algorithm

TL;DR

This paper presents a computational framework combining Lie group kinematics and evolutionary algorithms to efficiently model and visualize continuum robots, reducing reliance on physical experiments and enabling real-time simulation.

Contribution

It introduces a novel integration of Lie group kinematics with evolutionary algorithms for accurate coefficient identification and visualization of continuum robots.

Findings

Achieves precise alignment of robot configurations.

Reduces modeling complexity and experimental requirements.

Enables real-time visualization on CAD platforms.

Abstract

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 nature and complex kinematics present significant challenges in digital modeling and visualization. Identifying the modal shape coefficients of specific robot configuration often requires plenty of physical experiments, which is time-consuming and robot-specific. To address this issue, this research proposes a computational framework that utilizes evolutionary algorithm (EA) to simplify the coefficient identification process. Our method starts by generating datasets using Lie group kinematics and physics-based simulations, defining both ideal configurations and models to be optimized. With the deployment of EA solver, the deviations were iteratively minimized through two fitness objectives \textemdash mean square error of shape deviation (\(\text{MSE}_1\)) and tool center point (TCP) vector deviation (\(\text{MSE}_2\)) \textemdash to align the robot's backbone curve with the desired configuration. Built on the Computer-Aided Design (CAD) platform Grasshopper, this framework provides real-time visualization suitable for development of continuum robots. Results show that this integrated method achieves precise alignment and effective identification. Overall, the objective of this research aims to reduce the modeling complexity of continuum robots, enabling precise, efficient virtual simulation before robot programming and implementation.