Modeling and Control of an Eel-Inspired Soft Robot for Design Optimization

In this paper, we introduce the Soft Lamprey-Inspired Dual Environment Robot (SLIDER) and a proper modeling and optimization procedure employed to design the robot. We represent the primary fluid environment actions - inertial effects, vortex forces, and viscous dissipation - using Lighthill's theory for large-amplitude elongated bodies. For structural design parameters such as internal pressure, tail size, and body stiffness, a fast, geometrically and materially nonlinear model is developed and validated. The fluid-structure interaction equations are solved implicitly with an efficient second-order box method. A pneumatic manifold robotic system is employed to actuate SLIDER in a quiescent water tank environment, allowing cross-comparison of computational and experimental results. We find that low-frequency swimming is dominated by resistant environmental forces, whereas higher-frequency swimming is primarily affected by inertial fluid forces. Using our efficient model alongside a genetic algorithm, we co-optimize a swimming control pattern and caudal fin design (subject to SLIDER's climbing morphology) to achieve a tethered swimming speed of 21.7 +/- 0.4 cm/s (0.59 Bl/s). Furthermore, we investigate the optimization procedure for a multimodal robot performing both swimming and climbing tasks.

Soft robots leverage compliant materials to generate motion through controlled elastic deformation, making them ideal for delicate tasks such as underwater exploration and biomimetic marine systems. Although hydraulic/pneumatic actuation remains pivotal for such systems, the lack of systematic design frameworks has hindered the development of robots capable of complex 3D motion, such as fish-like swimming. This work introduces a topology optimization method to automate the design of a hydraulic soft fish tail, explicitly addressing the design-dependent coupling between fluidic actuation and structural deformation. We use a Darcy law-based model augmented with a drainage term to simulate spatially varying hydraulic pressure loads, translating these into consistent nodal forces via finite element analysis. The employed robust multi-criteria optimization formulation balances deformation efficiency, fluid-structure interaction, geometric manufacturability, and required stiffness for optimizing a bioinspired soft fish tail for 3D swimming kinematics. The optimized tail topology is incorporated into a pneumatic network actuator and computationally validated under various hydraulic loads, achieving tunable undulatory amplitudes and multiaxis bending for depth adjustment. The optimized 2D tail outperforms its rectangular counterpart. By cascading optimized tail segments, we demonstrate programmable swimming patterns in soft robotic fish tails at different hydraulic loads. This work advances the systematic codesign of hydraulic actuators and soft structures, offering a pathway to automate underwater robots with optimized design and vertebrate-like agility in confined aquatic environments. Our implementations and simulations are publicly available at 'https://github.com/PrabhatIn/TO-SoFiT'.

In the automated co-design of soft robots, precisely adapting the material stiffness field to task environments is crucial for unlocking their full physical potential. However, mainstream platforms (e.g., EvoGym) strictly discretize the material dimension, artificially restricting the design space and performance of soft robots. To address this, we propose EvoGymCM (EvoGym with Continuous Materials), a benchmark suite formally establishing continuous material stiffness as a first-class design variable alongside morphology and control. Aligning with real-world material mechanisms, EvoGymCM introduces two settings: (i) EvoGymCM-R (Reactive), motivated by programmable materials with dynamically tunable stiffness; and (ii) EvoGymCM-I (Invariant), motivated by traditional materials with invariant stiffness fields. To tackle the resulting high-dimensional coupling, we formulate two Morphology-Material-Control co-design paradigms: (i) Reactive-Material Co-Design, which learns real-time stiffness tuning policies to guide programmable materials; and (ii) Invariant-Material Co-Design, which jointly optimizes morphology and fixed material fields to guide traditional material fabrication. Systematic experiments across diverse tasks demonstrate that continuous material optimization boosts performance and unlocks synergy across morphology, material, and control.