Soft robots are robotic systems made of deformable materials and exhibit unique flexibility that can be exploited for complex environments and tasks. However, their control problem has been considered a challenging subject because they are of infinite degrees of freedom and highly under-actuated. Existing studies have mainly relied on simplified and approximated finite-dimensional models. In this work, we exploit infinite-dimensional nonlinear control for soft robots. We adopt the Cosserat-rod theory and employ nonlinear partial differential equations (PDEs) to model the kinematics and dynamics of soft manipulators, including their translational motions (for shear and elongation) and rotational motions (for bending and torsion). The objective is to achieve position tracking of the whole manipulator in a planar task space by controlling the moments (generated by actuators). The control design is inspired by the energy decay property of damped wave equations and has an inner-outer loop structure. In the outer loop, we design desired rotational motions that rotate the translational component into a direction that asymptotically dissipates the energy associated with position tracking errors. In the inner loop, we design inputs for the rotational components to track their desired motions, again by dissipating the rotational energy. We prove that the closed-loop system is exponentially stable and evaluate its performance through simulations.
翻译:软体机器人是机器人系统,由变形材料制成,具有独特的灵活性,可用于复杂的环境和任务。然而,它们的控制问题被认为是一个具有挑战性的主题,因为它们的自由度是无限的,触动力非常低。现有的研究主要依靠简化和近似有限维度模型。在这项工作中,我们利用软体机器人的无限维非线性控制。我们采用Cosserat-rod理论,并使用非线性局部偏差方程式(PDEs)来模拟软体操纵者的动力和动态,包括它们的翻译动作(剪裁和延长)和旋转动作(弯曲和弯曲)以及旋转动作。目标是通过控制时空来跟踪整个操纵器在平面任务空间的位置(由动作器生成 ) 。 控制设计设计是来自摇晃波方程式的能量衰减特性, 并且有一个内向外循环结构。 在外环绕中,我们设计了旋转的旋转动作动作, 将翻译组件旋转成一个方向, 以湿式的方式使能量转换和旋转运动运动运动(弯曲的弯曲), 我们通过移动的内循环系统再次显示其方向, 循环运行的动作的动作的动作将能量转换过程进行。