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 space cable-driven continuous manipulator (SCCM) has a slender structure, ultra-high degrees of freedom, and a low mass, which make it suitable for equipment inspection and maintenance operations in an unstructured and limited space environment. In this paper, the SCCM including the cable network and plenty of joint links was deeply modeled. Firstly, the mapping relationship between the cable-driving space, joint space, and task space of the SCCM was studied, and the complete kinematic relationship of the SCCM was established. Secondly, the stiffness components of the SCCM are discussed, and the stiffness modeling method of each part is given. Finally, the Cartesian space equivalent stiffness model of the end was established. Then, a dynamic co-modeling method of Matlab + Adams is proposed, which greatly improved the modeling efficiency while ensuring the modeling accuracy. Finally, based on the stiffness model, the end stiffness characteristics of a specific configuration were analyzed, and the influence of the cable tension on the stiffness and frequency of the manipulator was analyzed. Based on the dynamic co-modeling, the task trajectory dynamics’ simulation analysis and space slit crossing experiment were carried out, which verified that the designed SCCM can meet the needs of slit crossing.