Finite Element Method-Based Kinematics and Closed-Loop Control of Soft, Continuum Manipulators.

Area of Science:

• Robotics
• Mechanical Engineering
• Continuum Mechanics

Background:

• Soft manipulators, often termed continuum robots, move through deformation rather than traditional articulations.
• Accurate kinematic modeling is crucial for path planning and position control of these robots.
• Existing modeling methods often lack analytical solutions for complex soft robot geometries.

Purpose of the Study:

• To present a novel modeling methodology for obtaining forward kinematic models (FKM) and inverse kinematic models (IKM) for soft manipulators.
• To provide a computationally efficient approach suitable for real-time applications like path planning and position control.
• To experimentally validate the proposed methodology against existing geometric approaches.

Main Methods:

• Utilizes continuum mechanics principles combined with a real-time numerical integration strategy.
• Employs the finite element method (FEM) and numerical optimization with Lagrange multipliers.
• Incorporates a dimension reduction technique by projecting the model onto the constraint space.

Main Results:

• Successfully obtained FKM and IKM for two soft manipulators with complex geometries.
• Experimental validation demonstrated the efficacy of the proposed methodology compared to alternative geometric approaches.
• A closed-loop controller based on a state estimator was proposed and experimentally validated.

Conclusions:

• The presented methodology offers an effective solution for modeling soft robot kinematics, enabling precise control.
• The real-time numerical approach is suitable for offline path planning and online position control tasks.
• The controller's robustness was confirmed using Lyapunov stability methods, ensuring reliable performance.