A circular soft robot integrating the control system is constructed, which is actuated by eight shape memory alloy springs. Four flexible sensors are pasted on the soft robot’s inner face to detect the deformation for the closed-loop control. First, according to the Clausius–Clapeyron equation and Taylor’s expansion, a nonlinear deformation model is built to illustrate the relationship between stress, strain, and temperature during deformation. Then, based on this nonlinear deformation model and the analysis on the dynamic deformation process of the robot, the nonlinear relationship between the robot’s deformation and heating time is derived. Further, the displacement curve is also obtained from the dynamic analysis on the rolling deformation process of the soft robot. In the last, several experiments including different drive modes and heating times are performed. The experiment results show that the circular soft robot is able to finish locomotion and the closed-loop control system could improve the stability.

中文翻译：

---

具有闭环控制系统的SMA驱动的圆形软机器人的非线性建模

构建了一个集成了控制系统的圆形软机器人，该机器人由八个形状记忆合金弹簧驱动。四个柔性传感器粘贴在软机器人的内表面上，以检测变形以进行闭环控制。首先，根据Clausius–Clapeyron方程和泰勒展开，建立了一个非线性变形模型来说明变形过程中应力，应变和温度之间的关系。然后，基于该非线性变形模型并分析了机器人的动态变形过程，得出了机器人变形与加热时间之间的非线性关系。此外，还通过对软机器人的滚动变形过程进行动力学分析来获得位移曲线。在最后，进行了包括不同驱动模式和加热时间在内的多个实验。实验结果表明，圆形软机器人可以完成运动，闭环控制系统可以提高稳定性。