Neural network-based quasi-static modeling using Cosserat theory and proportional-integral control of ferromagnetic continuum robot

Ferromagnetic continuum robots, characterized by their remarkable flexibility, offer significant potential for advanced medical applications. However, the nonlinear behavior of these robots requires complex modeling, which incurs high computational costs, and presents significant challenges in developing precise, real-time controllers. Ensuring accuracy and computational efficiency in critical procedures, such as minimally invasive surgery, is challenging, as precise control of the robot is essential. Overcoming these challenges requires innovative modeling and control strategies that leverage the unique properties of these robots while maintaining stability and responsiveness in medical environments. To address these challenges and considering the nature of the system, including its low inertia and slow system behavior, the system is treated as quasi-static. Additionally, an artificial neural network approach is employed for modeling the ferromagnetic continuum robot. The data required for training the neural network are collected using the Cosserat theory. Additionally, considering the quasi-static nature of the system, a proportional-integral controller will be used to control the tip position of the robot. To evaluate the performance of the Cosserat theory for calculating the deformation of the robot and the proposed controller, the results obtained from the simulations of trajectory tracking for various paths are compared with experimental data, showing an acceptable agreement with the experimental results.