Soft actuators offer compliant and safe interaction with an unstructured environment compared to their rigid counterparts. However, control of these systems is often challenging because they are inherently under-actuated, have infinite degrees of freedom (DoF), and their mechanical properties can change by unknown external loads. Existing works mainly relied on discretization and reduction, suffering from either low accuracy or high computational cost for real-time control purposes. Recently, we presented an infinite-dimensional feedback controller for soft manipulators modeled by partial differential equations (PDEs) based on the Cosserat rod theory. In this study, we examine how to implement this controller in real-time using only a limited number of actuators. To do so, we formulate a convex quadratic programming problem that tunes the feedback gains of the controller in real time such that it becomes realizable by the actuators. We evaluated the controller's performance through experiments on a physical soft robot capable of planar motions and show that the actual controller implemented by the finite-dimensional actuators still preserves the stabilizing property of the desired infinite-dimensional controller. This research fills the gap between the infinite-dimensional control design and finite-dimensional actuation in practice and suggests a promising direction for exploring PDE-based control design for soft robots.

翻译：软体致动器相较于刚性致动器，在与非结构化环境的交互中具有柔顺性和安全性。然而，这些系统的控制往往具有挑战性，因为它们天生欠驱动、具有无限自由度，且其机械特性可能因未知外部载荷而改变。现有研究主要依赖离散化与降阶方法，但要么精度较低，要么为满足实时控制需求而计算成本过高。近期，我们基于科瑟拉杆理论提出了一种用于偏微分方程建模的软体机械臂的无限维反馈控制器。本研究探讨了如何仅用有限数量的致动器实现该控制器的实时部署。为此，我们构建了一个凸二次规划问题，通过实时调节控制器反馈增益，使其能够被致动器实际执行。我们通过平面运动物理软体机器人实验评估了控制器性能，结果表明由有限维致动器实现的实际控制器仍保留了期望无限维控制器的稳定特性。这项研究填补了无限维控制器设计与实际有限维致动之间的空白，为探索基于偏微分方程的软体机器人控制设计提供了有前景的方向。