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.

Soft manipulators attract increasing interests in robotic applications involving unstructured environment and human-robot interaction. The majority of the soft manipulator with fluidic actuators consists of joints that are constructed by parallel actuators, achieving rotation and extension. The inability to output twisting and lateral translations concurrently in the joints hinders the applications of such soft manipulators that require dexterous manipulation. In this work, the Tilted Actuator Soft Robotic (TASR) joint with 6-DOF mobility, i.e., 3 rotations and 3 translations, is studied by kinematic modelling, simulations and experiments. The 6-DOF joint has a light weight (74.8g) due to the implementation of soft origami actuators (SOA) and soft-rigid structure. The investigation on the characteristics of the 4-joint assembly recorded maximum in-plane translations over a 70mm range (70% of its diameter), axial translation over 50mm (27% of its length), and rotations over 120° in all three directions. Kinematic modelling and FEM simulations have been carried out on the mechanical behaviors of the joint. A soft manipulator has been produced to verify the practicality of the joint in constructing soft robotic systems, with the repetitive accuracy and movements demonstrated in an application scenario. The 6-DOF TASR joint showed the potential to be implemented in constructing dexterous and light weight soft robotic systems, with mass-production readiness.