Cosserat Rod Modeling and Validation for a Soft Continuum Robot with Self-Controllable Variable Curvature (2402.12315v2)

Abstract: This paper introduces a Cosserat rod based mathematical model for modeling a self-controllable variable curvature soft continuum robot. This soft continuum robot has a hollow inner channel and was developed with the ability to perform variable curvature utilizing a growing spine. The growing spine is able to grow and retract while modifies its stiffness through milli-size particle (glass bubble) granular jamming. This soft continuum robot can then perform continuous curvature variation, unlike previous approaches whose curvature variation is discrete and depends on the number of locking mechanisms or manual configurations. The robot poses an emergent modeling problem due to the variable stiffness growing spine which is addressed in this paper. We investigate the property of growing spine stiffness and incorporate it into the Cosserat rod model by implementing a combined stiffness approach. We conduct experiments with the soft continuum robot in various configurations and compared the results with our developed mathematical model. The results show that the mathematical model based on the adapted Cosserat rod matches the experimental results with only a 3.3\% error with respect to the length of the soft continuum robot.

• The paper presents a novel integration of the Cosserat rod model with a combined stiffness approach for precise variable curvature control.
• The paper validates its model through experiments, achieving a low error rate of 3.3% over configurations with spine lengths up to 30 cm and pressures up to 250 kPa.
• The paper’s findings support practical applications in fields like minimally invasive surgery, search and rescue, and industrial automation.

Overview of Cosserat Rod Modeling for Soft Continuum Robots with Self-Controllable Curvature

The paper under review introduces a novel approach to model and validate a self-controllable variable curvature soft continuum robot utilizing a refined Cosserat rod model. This research addresses the advanced requirements for appropriately capturing the behavior of a unique soft continuum robot, which includes a hollow inner channel that allows dynamic length adjustment through a self-growing spine. This design leverages granular jamming techniques with glass bubbles to achieve customizable stiffness, enabling continuous curvature variation.

Key Insights and Methodological Approaches

The core contribution of this paper is the integration of a Cosserat rod-based model, augmented with a combined stiffness approach to incorporate the properties of a variable stiffness growing spine. This model departs from traditional static models which are incapable of adequately describing such advancements in continuum robotics.

• Variable Curvature Mechanism: The proposed robot diverges from previous designs that rely on discrete curvature adjustments. It adopts a continuous adjustment capability by altering the local stiffness via a self-growing spine mechanism. The growing spine's stiffness is modulated using milli-size particle granular jamming, and the model adapts this characteristic into its formulation.
• Cosserat Rod Model Utilization: This model is leveraged due to its ability to accommodate external loads, a known advantage over traditional constant curvature or piecewise constant curvature approaches. The paper modifies this framework to suit the high adaptability of the proposed continuum robot.
• Synthesis of Combined Stiffness: The modeling challenge posed by variable stiffness from the self-growing spine is tackled by predicting the Young's modulus of jammed configurations at multiple lengths. This allows for an effective incorporation of a combined stiffness model within the Cosserat rod equations.

Experimental Validation and Results

The experimental protocol was detailed and thorough, involving various configurations of the continuum robot to validate the model's accuracy:

• The model was compared against physical experiments for configurations with different spine lengths (0 to 30 cm) and pressures up to 250 kPa.
• Error rates were remarkably low, with a 3.3% error in modeled predictions compared to the physical length measurements, demonstrating high fidelity.

The experimental set-up using a load cell and motion-tracking technology effectively quantified the mechanical properties of the robot, corroborating the theoretical model results.

Implications and Future Directions

The implications of this paper are substantial for the development of adaptive soft robots capable of operating in constrained and dynamic environments. Practically, such robots could have widespread applications, including minimally invasive surgery, search and rescue operations, and complex industrial automation tasks.

On a theoretical level, this research advances the field by providing a detailed analysis and an effective modeling approach to soft robots with variable curvature, addressing complexities that traditional models have not yet overcome.

For future research, the paper suggests extending the model to incorporate dynamic elements that could include time-variant boundary conditions and varying external forces over operational time. Such advancements could dramatically enhance the precision and applicability of soft continuum robots in real-world scenarios. Control strategies for managing the variable curvature dynamically could also be a viable research prospect, potentially leading to more autonomous and robust soft robotic systems.