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

TL;DR

The paper addresses the challenge of modeling a soft continuum robot that can vary curvature continuously via a self-growing spine whose stiffness is tunable by granular jamming. It adopts an adapted Cosserat rod framework with a combined stiffness formulation to handle spatially varying stiffness along the robot. The authors calibrate the growing spine stiffness experimentally and validate the model across multiple spine lengths and actuation pressures, achieving about 3.3% end-to-length position error. The work enables accurate prediction and control of continuous curvature soft robots with internal stiffness modulation, reducing modeling complexity while expanding soft robot capabilities.

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.

Figures (5)

• Figure 1: Examples of variable curvature of the soft continuum robot under study, which is based on a variable stiffness self-growing spine. (A) Curvataure of the robot with 0 cm growing spine length when pressurized at 250 kPa. (B) Curvature of the robot with 30 cm growing spine length when pressurized at 250 kPa.
• Figure 2: Detailed system design. (A) Soft continuum robot system with motion tracking markers on the end-effector. (B) Cross-section area to show the inner structure of the robot. Inside the steel box, airtight fabric divides the volume into two. The bottom volume contains glass bubbles and a length control mechanism. The filter paper on top of the pegboard prevents glass bubbles from going into the vacuum chamber when jamming. (C) The state transitions to allow the robot to reconfigure. The growing spine is filled with granules. It changes length inside the continuum robot and stiffness when jammed using negative pressure.
• Figure 3: (A) Experiment setup for testing the stiffness of the growing robot using UR5 robotic arm and ROBOTiq ft300-s. (B) Experiment setup for testing the stiffness of the soft continuum robot
• Figure 4: (A) Experiment setup for testing the extending of the soft continuum robot with different growing robot configuration inside. The end-effector position is captured through the motion tracking system. (B) An elongated soft continuum robot. (C) The relationship between the elongation of the robot and applied pressure for different growing spine configurations inside the continuum robot
• Figure 5: Comparison between the mathematical model and experimental results covers the range of soft continuum robot configurations from 0 to 30 cm, and pressurized from 50 to 250 kPa with increments of 50 kPa.