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.

翻译：本文提出了一种基于Cosserat杆的数学模型，用于对一种具有自控可变曲率的软体连续体机器人进行建模。该软体连续体机器人具有中空的内通道，其开发时利用生长脊柱实现了可变曲率能力。该生长脊柱能够通过毫米级颗粒（玻璃微珠）的颗粒阻塞机制，在生长与收缩的同时调节自身刚度。因此，该软体连续体机器人可实现连续的曲率变化，而以往方法的曲率变化是离散的，且依赖于锁定机构的数量或手动配置。由于采用了可变刚度的生长脊柱，该机器人提出了一个新的建模问题，本文对此进行了探讨。我们研究了生长脊柱的刚度特性，并通过实施组合刚度方法将其纳入Cosserat杆模型。我们在多种构型下对该软体连续体机器人进行了实验，并将结果与我们开发的数学模型进行了比较。结果表明，基于改进Cosserat杆的数学模型与实验结果吻合良好，相对于软体连续体机器人的长度误差仅为3.3%。