Continuum Robot Control Using Cosserat Rod Model
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Solution Overview
Problem
Current models for tendon-actuated continuum robots are limited in predicting large spatial deformations under external loads and cannot accurately describe non-planar deformations, as they simplify tendon loads to point moments rather than distributed wrenches, restricting their application in complex environments.
Innovation Solution
A Cosserat rod-based model that accounts for distributed tendon wrenches along the length of the elastic member, allowing for geometrically exact treatment of tendon loads and enabling prediction of 3D deformations, including bending, torsion, and elongation, with tendon paths that are not restricted to straight configurations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If simplified beam mechanics models are used for tendon-actuated continuum robots, then the kinematic models are analytically simple and easy to implement, but they cannot accurately predict large spatial deformations when subjected to external loads
Solution Approach 1:
The patent transitions from simplified beam mechanics parameters to Cosserat rod theory parameters, incorporating distributed tendon forces and moments along the robot length. This parameter transformation enables accurate prediction of large spatial deformations while maintaining computational tractability through the derived closed-form solution.
Solution Approach 2:
The patent introduces an intermediate mathematical framework that bridges simplified beam mechanics and full Cosserat rod theory. By using the derived closed-form solution as an intermediary, the model captures distributed tendon effects without requiring complex numerical simulations, thus maintaining analytical simplicity while improving prediction accuracy.
2Device complexity
If point moment approximation is used for tendon loads in Cosserat rod theory, then the model is computationally simpler, but it cannot accurately describe non-planar deformations and large spatial deformations under external loads
Solution Approach 1:
The patent changes the load representation from concentrated point moments to distributed tendon forces and moments along the rod length. This parameter transformation is embedded in the closed-form solution, which maintains computational efficiency while accurately capturing three-dimensional deformation behavior under external loads.
Solution Approach 2:
The patent segments the tendon load into distributed contributions along the length of the elastic member rather than concentrating it at single points. This segmentation is mathematically integrated into the closed-form solution, enabling accurate prediction of non-planar deformations without proportionally increasing model complexity.
3Device complexity
If tendon paths are restricted to straight configurations, then the model is simpler and easier to control, but it limits the design space and dexterity of the continuum robot
Solution Approach 1:
The patent makes the tendon path dynamic and flexible rather than fixed and straight. The closed-form solution accommodates arbitrary tendon routing configurations, allowing the tendon paths to adapt to complex three-dimensional geometries and enabling the robot to achieve greater dexterity and versatility in various applications.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach significantly reduces tip error and expands the design space for tendon-actuated robots, enabling accurate prediction of shapes under various external loads and enhancing their dexterity and versatility in applications like surgical procedures and industrial tasks.
Implementation Method 1
an elastic member, a plurality of guide portions disposed along the length of the elastic member, and at least one tendon extending through the plurality of guide portions
Implementation Method 2
applying a tension to the at least one tendon and computing the resulting shape of the elastic member resulting from said tension
Data Source
AI summary
Method for controlling continuum robots and systems therefrom are provided. In the system and method, a new system of equations is provided for controlling a shape of the elastic member and a tension on a tendon applying a force to an elastic member of the robot. The system of equations can be used to estimate a resulting shape of the elastic member from the tension applied to the tendon. The system of equations can also be used to estimate a necessary tension for the tendon to achieve a target shape.