<p>Underwater exploration demands innovative soft robotic systems that can navigate in aquatic environments efficiently and with minimal ecological disruption. This study focuses on simultaneously designing the kinematics and geometry of a bioinspired carangiform swimmer. Using a multidisciplinary design optimization (MDO) framework, we explore how robotic swimmers can achieve enhanced energy efficiency and adaptability across a range of swimming conditions. Gradient-based optimization is enabled through automated adjoint derivative computation, ensuring computational efficiency and scalability for handling high-dimensional design variables. We demonstrate this approach using three sets of optimizations: simplified kinematics optimizations, co-design optimizations, and multipoint co-design optimizations. Simplified kinematics optimization reveals that tail-beat frequency scales linearly with swimming speed (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$ v_x $</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>v</mi> <mi>x</mi> </msub> </math></EquationSource> </InlineEquation>), while the undulation amplitude decreases nonlinearly as speed increases. Co-design optimization, which jointly optimizes kinematics and geometry, achieves a 37.7% reduction in the objective (cost of transport) at a speed of 0.3 m/s, 40.3% at 0.6 m/s, and 41.7% at 0.9 m/s, compared to kinematics-only optimization. The multipoint co-design optimization considers all three swimming conditions simultaneously, along with a quasi-steady turning case, balancing the cost of transport across different scenarios. While it results in a slightly higher objective compared to the single-condition co-design optimization, it achieves a <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$ 13.0\% $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>13.0</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> reduction at a speed of 0.3 m/s, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$ 31.3\% $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>31.3</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> at <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$ v_x = 0.6 $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>v</mi> <mi>x</mi> </msub> <mo>=</mo> <mn>0.6</mn> </mrow> </math></EquationSource> </InlineEquation> m/s, and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$ 40.9\% $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>40.9</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> at <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$ v_x = 0.9 $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>v</mi> <mi>x</mi> </msub> <mo>=</mo> <mn>0.9</mn> </mrow> </math></EquationSource> </InlineEquation> m/s compared to kinematics-only optimization. Our results demonstrate that combining kinematic and geometric optimization significantly enhances swimming efficiency. The proposed gradient-based optimization framework offers a scalable and effective approach for designing energy-efficient bioinspired robotic fish.</p>

Simultaneous kinematics and shape optimization of a carangiform swimmer using gradient-based optimization

期刊论文
发表日期：

2026年4月4日

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Jiayao Yan,
Michael T. Tolley,
Qiang Zhu,
John T. Hwang

摘要

Underwater exploration demands innovative soft robotic systems that can navigate in aquatic environments efficiently and with minimal ecological disruption. This study focuses on simultaneously designing the kinematics and geometry of a bioinspired carangiform swimmer. Using a multidisciplinary design optimization (MDO) framework, we explore how robotic swimmers can achieve enhanced energy efficiency and adaptability across a range of swimming conditions. Gradient-based optimization is enabled through automated adjoint derivative computation, ensuring computational efficiency and scalability for handling high-dimensional design variables. We demonstrate this approach using three sets of optimizations: simplified kinematics optimizations, co-design optimizations, and multipoint co-design optimizations. Simplified kinematics optimization reveals that tail-beat frequency scales linearly with swimming speed ( $ v_x $ $v_{x}$ ), while the undulation amplitude decreases nonlinearly as speed increases. Co-design optimization, which jointly optimizes kinematics and geometry, achieves a 37.7% reduction in the objective (cost of transport) at a speed of 0.3 m/s, 40.3% at 0.6 m/s, and 41.7% at 0.9 m/s, compared to kinematics-only optimization. The multipoint co-design optimization considers all three swimming conditions simultaneously, along with a quasi-steady turning case, balancing the cost of transport across different scenarios. While it results in a slightly higher objective compared to the single-condition co-design optimization, it achieves a $ 13.0\% $ $13.0 %$ reduction at a speed of 0.3 m/s, $ 31.3\% $ $31.3 %$ at $ v_x = 0.6 $ $v_{x} = 0.6$ m/s, and $ 40.9\% $ $40.9 %$ at $ v_x = 0.9 $ $v_{x} = 0.9$ m/s compared to kinematics-only optimization. Our results demonstrate that combining kinematic and geometric optimization significantly enhances swimming efficiency. The proposed gradient-based optimization framework offers a scalable and effective approach for designing energy-efficient bioinspired robotic fish.