AquaROM: shape optimization pipeline for soft swimmers using parametric reduced order models

TL;DR

This work tackles the computational bottleneck of optimizing nonlinear soft-robotic structures by introducing AquaROM, a parametric reduced-order model (PROM) built in a data-free, tensorial framework. By expressing internal, thrust, drag, and actuation forces as polynomial tensors and projecting them onto a reduced basis composed of vibration modes, modal derivatives, and shape-variation sensitivities, the method yields analytical gradients that drive gradient-based optimization of shape parameters. The pipeline is demonstrated on soft robotic fishes, achieving optimal shapes that outperform the nominal design by up to 3.6× in swimming distance, with optimization times on the order of minutes and without offline training. This approach enables rapid prototyping and design-space exploration for nonlinear soft-robotic systems and can be extended to other forces and actuation schemes in soft robotics.

Abstract

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.

Figures (15)

• Figure 1: Optimization pipeline applied to the case of soft robotic fishes. Starting from a nominal shape, our pipeline solves a constrained optimization problem in a computationally efficient way by using a PROM. The pipeline results in an optimal shape that outperforms the nominal setting.
• Figure 2: Nominal, shape-varied, and deformed configurations. The final deformed configuration can be expressed through two successive mappings: $\mathcal{F}_1(\bm{x}_0)$ and $\mathcal{F}_2(\bm{x}_\xi,t)$.
• Figure 3: Reference frame used to derive the reactive force. The spine of the fish is observed from the top in this diagram.
• Figure 4: Procedure for populating the matrix $\bm{U}$ used to describe the shape-varied configuration $\bm{u}_{\xi} = \bm{U}\bm{\xi}$. After defining a shape-varied mesh, we subtract the nominal node positions to obtain a vector field. This vector field is stored as a column of $\bm{U}$. By defining multiple vector field in the different columns of $\bm{U}$, we can scale and combine them by multiplying $\bm{U}$ with the parameter vector $\bm{\xi}$ to obtain the different shape-varied configurations $\bm{u}_{\xi}$.
• Figure 5: Optimization pipeline described in \ref{['sec:05_optimization_pipeline']}. The algorithm runs until convergence.