This paper presents a novel framework to realize proprioception and closed-loop control for soft manipulators. Deformations with large elongation and large bending can be precisely predicted using geometry-based sensor signals obtained from the inductive springs and the inertial measurement units (IMUs) with the help of machine learning techniques. Multiple geometric signals are fused into robust pose estimations, and a data-efficient training process is achieved after applying the strategy of sim-to-real transfer. As a result, we can achieve proprioception that is robust to the variation of external loading and has an average error of 0.7% across the workspace on a pneumatic-driven soft manipulator. The realized proprioception on soft manipulator is then contributed to building a sensor-space based algorithm for closed-loop control. A gradient descent solver is developed to drive the end-effector to achieve the required poses by iteratively computing a sequence of reference sensor signals. A conventional controller is employed in the inner loop of our algorithm to update actuators (i.e., the pressures in chambers) for approaching a reference signal in the sensor-space. The systematic function of closed-loop control has been demonstrated in tasks like path following and pick-and-place under different external loads.

翻译：本文提出了一种新型框架，用于实现软体机械臂的本体感知与闭环控制。通过结合感应弹簧与惯性测量单元（IMU）获取的基于几何结构的传感器信号，并借助机器学习技术，可精确预测包含大伸长量与大弯曲量的变形。多路几何信号融合为鲁棒的位姿估计，同时采用“仿真-现实迁移”策略实现了数据高效的训练过程。最终，我们在气动驱动软体机械臂上实现了对外部载荷变化具有鲁棒性的本体感知，其工作空间内的平均误差仅为0.7%。进而，将所实现的软体机械臂本体感知用于构建基于传感器空间的闭环控制算法。通过迭代计算参考传感器信号序列，开发了一种梯度下降求解器以驱动末端执行器达到目标位姿。算法内环采用传统控制器更新执行器（即气腔压力），以逼近传感器空间中的参考信号。闭环控制系统的整体功能已通过不同外部载荷下的路径跟踪与抓取放置等任务得到验证。