The efficient optimization of actuated soft structures, particularly under complex nonlinear forces, remains a critical challenge in advancing robotics. Simulations of nonlinear structures, such as soft-bodied robots modeled using the finite element method (FEM), often demand substantial computational resources, especially during optimization. To address this challenge, we propose a novel optimization algorithm based on a tensorial parametric reduced order model (PROM). Our algorithm leverages dimensionality reduction and solution approximation techniques to facilitate efficient solving of nonlinear constrained optimization problems. The well-structured tensorial approach enables the use of analytical gradients within a specifically chosen reduced order basis (ROB), significantly enhancing computational efficiency. To showcase the performance of our method, we apply it to optimizing soft robotic swimmer shapes. These actuated soft robots experience hydrodynamic forces, subjecting them to both internal and external nonlinear forces, which are incorporated into our optimization process using a data-free ROB for fast and accurate computations. This approach not only reduces computational complexity but also unlocks new opportunities to optimize complex nonlinear systems in soft robotics, paving the way for more efficient design and control.

翻译：高效优化驱动软体结构，尤其是在复杂非线性力作用下的优化，仍然是推动机器人技术发展的关键挑战。非线性结构（如使用有限元法建模的软体机器人）的仿真通常需要大量计算资源，在优化过程中尤为突出。为应对这一挑战，我们提出了一种基于张量参数化降阶模型的新型优化算法。该算法利用降维与解近似技术，有效求解非线性约束优化问题。其结构清晰的张量化方法支持在特定选择的降阶基中使用解析梯度，显著提升了计算效率。为展示本方法的性能，我们将其应用于软体游动机器人的形状优化。这些受驱动的软体机器人承受流体动力，同时受到内部与外部非线性力的作用；我们通过无数据降阶基将这些力纳入优化过程，以实现快速精确的计算。该方法不仅降低了计算复杂度，还为优化软体机器人中的复杂非线性系统开辟了新途径，为更高效的设计与控制奠定了基础。