The motion complexity and use of exotic materials in soft robotics call for accurate and computationally efficient models intended for control. To reduce the gap between material and control-oriented research, we build upon the existing piece-wise constant curvature framework by incorporating hyperelastic and viscoelastic material behavior. In this work, the continuum dynamics of the soft robot are derived through the differential geometry of spatial curves, which are then related to finite-element data to capture the intrinsic geometric and material nonlinearities. To enable fast simulations, a reduced-order integration scheme is introduced to compute the dynamic Lagrangian matrices efficiently, which in turn allows for real-time (multilink) models with sufficient numerical precision. By exploring the passivity and using the parameterization of the hyperelastic model, we propose a passivity-based adaptive controller that enhances robustness toward material uncertainty and unmodeled dynamics—slowly improving their estimates online. As a study-case, a soft robot manipulator is developed through additive manufacturing, which shows good correspondence with the dynamic model under various conditions, for example, natural oscillations, forced inputs, and under tip-loads. The solidity of the approach is demonstrated through extensive simulations, numerical benchmarks, and experimental validations.

中文翻译：

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基于曲线微分几何的超弹性软体机器人的面向控制模型

软体机器人的运动复杂性和特殊材料的使用需要用于控制的精确且计算高效的模型。为了缩小材料研究与面向控制的研究之间的差距，我们通过结合超弹性和粘弹性材料行为，在现有的分段恒定曲率框架的基础上进行构建。在这项工作中，软体机器人的连续动力学是通过空间曲线的微分几何导出的，然后与有限元数据相关联以捕获内在的几何和材料非线性。为了实现快速模拟，引入了降阶积分方案来有效地计算动态拉格朗日矩阵，这反过来又允许实时（多链路）模型具有足够的数值精度。通过探索被动性和使用超弹性模型的参数化，我们提出了一种基于被动性的自适应控制器，该控制器增强了对材料不确定性和未建模动力学的鲁棒性——缓慢地在线改进了它们的估计。作为一个研究案例，通过增材制造开发了一种软体机器人机械手，它在自然振荡、强制输入和尖端负载等各种条件下与动力学模型具有良好的对应关系。通过广泛的模拟、数值基准和实验验证证明了该方法的可靠性。通过增材制造开发了一种软体机器人机械手，在自然振荡、强制输入和尖端负载等各种条件下与动力学模型具有良好的对应关系。通过广泛的模拟、数值基准和实验验证证明了该方法的可靠性。通过增材制造开发了一种软体机器人机械手，在自然振荡、强制输入和尖端负载等各种条件下与动力学模型具有良好的对应关系。通过广泛的模拟、数值基准和实验验证证明了该方法的可靠性。