A Geometrically Exact Model for Externally Loaded Concentric-Tube Continuum Robots

Area of Science:

• Robotics
• Mechanical Engineering
• Medical Devices

Background:

• Continuum robots, constructed from concentric, precurved elastic tubes, offer surgical needle-scale dexterity.
• Existing models accurately predict robot shape in free space but lack external load considerations.
• Accurate modeling under load is crucial for practical applications involving environmental interaction and force application.

Purpose of the Study:

• To develop a forward kinematic model for continuum robots that accounts for deformation under external loading.
• To extend existing models to predict large deflections caused by general point and/or distributed wrench loads.
• To incorporate independent torsional deformation of individual tubes within the model.

Main Methods:

• Application of geometrically exact rod theory to model continuum robots.
• Development of a forward kinematic model accommodating multiple, arbitrarily preshaped tubes.
• Inclusion of independent torsional deformation for each tube.
• Experimental validation using both point and distributed loads.

Main Results:

• The developed model accurately describes large deflections of continuum robots under external wrench loads.
• Experimental results show an average tip error of 2.91 mm (1.5%-3% of robot length) under load.
• The model's accuracy under load is comparable to existing free-space models.
• The model successfully accounts for arbitrary tube configurations and torsional deformations.

Conclusions:

• Geometrically exact rod theory provides an effective framework for modeling continuum robots under external loads.
• The new model enhances the practical applicability of continuum robots in scenarios requiring controlled force interaction.
• The achieved accuracy under load supports the use of these robots in complex surgical procedures.
• This work advances the field of continuum robotics by providing a robust predictive model for loaded scenarios.