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Modular fabrication and design of thick rigid-foldable origami metamaterials
Authors:
Sunao Tomita,
Hiroki Kobayashi,
Shoko Arita,
Masato Tanaka,
Atsushi Kawamoto,
Tsuyoshi Nomura,
Tomohiro Tachi
Abstract:
Origami metamaterials offer significant potential for stiff deployable structures However, fabricating load-bearing cellular structures from thick panels introduces geometric interference at non-manifold junctions. Conventional thick-panel fabrication often disrupt ideal kinematics, thereby compromising smooth motion and scalability. This study proposes a modular fabrication framework that preserv…
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Origami metamaterials offer significant potential for stiff deployable structures However, fabricating load-bearing cellular structures from thick panels introduces geometric interference at non-manifold junctions. Conventional thick-panel fabrication often disrupt ideal kinematics, thereby compromising smooth motion and scalability. This study proposes a modular fabrication framework that preserves one-degree-of-freedom rigid-folding kinematics in thick and non-manifold origami metamaterials. By decomposing non-manifold junctions into a hierarchy of stacked, modular hinged panels, our approach successfully accommodates synchronized hinge motions using scissor-like linkages. Exploiting this representation, we implement a graph-based topology optimization framework that tailors macroscopic stiffness while preserving folding connectivity. We demonstrate this approach by fabricating optimized prototypes that deploy seamlessly with a one-degree-of-freedom motion. Furthermore, we demonstrate engineering scalability through the large-scale construction of extensive deployable systems assembled from modular panels, which exhibit high load-bearing capacity. These results pave the way for the practical fabrication of structural, large-scale deployable metamaterials.
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Submitted 20 August, 2026;
originally announced August 2026.
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Automated design of soft-rigid hybrid robots for dynamic locomotion
Authors:
Hiroki Kobayashi,
Yuki Takaha,
Changyoung Yuhn,
Yuki Sato,
Sunao Tomita,
Atsushi Kawamoto,
Tsuyoshi Nomura
Abstract:
Rigid-bodied robots often lack compliance needed to adapt to unstructured environments, while fully soft robots, though highly adaptable, struggle with scalability and load capacity. In nature, musculoskeletal systems balance strength and flexibility by integrating hard and soft tissues. Inspired by this principle, we present an automated design method for soft-rigid hybrids that optimizes a freef…
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Rigid-bodied robots often lack compliance needed to adapt to unstructured environments, while fully soft robots, though highly adaptable, struggle with scalability and load capacity. In nature, musculoskeletal systems balance strength and flexibility by integrating hard and soft tissues. Inspired by this principle, we present an automated design method for soft-rigid hybrids that optimizes a freeform soft-body shape, a stiff truss layout, and multi-channel actuation. Our differentiable simulator couples the material point method (MPM) for deformable bodies with extended position-based dynamics (XPBD) for truss elements, enabling gradient-based search. The optimization generates truss skeletons that transmit actuation forces to the soft body. We fabricate the optimized design and evaluate it on a walking task. Experiments reproduce the walking mode predicted by the optimization, which does not emerge without the skeleton. Modal analysis further suggests that the skeleton enables deformation modes near the actuation frequency that promote effective stride generation.
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Submitted 28 May, 2026;
originally announced May 2026.
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Computational co-design of structure and feedback controller for locomoting soft robots
Authors:
Yuki Sato,
Changyoung Yuhn,
Hiroki Kobayashi,
Atsushi Kawamoto,
Tsuyoshi Nomura
Abstract:
Soft robots have gained significant attention due to their flexibility and safety, particularly in human-centric applications. The co-design of structure and controller in soft robotics has presented a longstanding challenge owing to the complexity of the dynamics involved. Despite some pioneering work dealing with the co-design of soft robot structures and actuation, design freedom has been limit…
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Soft robots have gained significant attention due to their flexibility and safety, particularly in human-centric applications. The co-design of structure and controller in soft robotics has presented a longstanding challenge owing to the complexity of the dynamics involved. Despite some pioneering work dealing with the co-design of soft robot structures and actuation, design freedom has been limited by stochastic design search approaches. This study proposes the simultaneous optimization of structure and controller for soft robots in locomotion tasks, integrating topology optimization-based structural design with neural network-based feedback controller design. Here, the feedback controller receives information about the surrounding terrain and outputs actuation signals that induce the expansion and contraction of the material. We formulate the simultaneous optimization problem under uncertainty in terrains and construct an optimization algorithm that utilizes automatic differentiation within topology optimization and neural networks. We present numerical experiments to demonstrate the validity and effectiveness of our proposed method.
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Submitted 12 July, 2024;
originally announced July 2024.
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Shell topology optimization based on level set method
Authors:
Hiroki Kobayashi,
Katsuya Nomura,
Yuqing Zhou,
Masato Tanaka,
Atsushi Kawamoto,
Tsuyoshi Nomura
Abstract:
This paper proposes a level set-based method for optimizing shell structures with large design changes in shape and topology. Conventional shell optimization methods, whether parametric or nonparametric, often only allow limited design changes in shape. In the proposed method, the shell structure is defined as the isosurface of a level set function. The level set function is iteratively updated ba…
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This paper proposes a level set-based method for optimizing shell structures with large design changes in shape and topology. Conventional shell optimization methods, whether parametric or nonparametric, often only allow limited design changes in shape. In the proposed method, the shell structure is defined as the isosurface of a level set function. The level set function is iteratively updated based on the shape sensitivity on the surface mesh. Therefore, the proposed method can represent an arbitrary manifold surface while dealing with topological changes, for example, from a spherical surface to a toroidal surface. We applied the proposed method to the mean compliance minimization problems of 3D shell structural designs for dome, bending plate and cantilever beam examples to demonstrate its efficacy of the proposed method.
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Submitted 27 August, 2024; v1 submitted 24 January, 2024;
originally announced January 2024.
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Computational synthesis of locomotive soft robots by topology optimization
Authors:
Hiroki Kobayashi,
Farzad Gholami,
S. Macrae Montgomery,
Masato Tanaka,
Liang Yue,
Changyoung Yuhn,
Yuki Sato,
Atsushi Kawamoto,
H. Jerry Qi,
Tsuyoshi Nomura
Abstract:
Locomotive soft robots (SoRos) have gained prominence due to their adaptability. Traditional locomotive SoRo design is based on limb structures inspired by biological organisms and requires human intervention. Evolutionary robotics, designed using evolutionary algorithms (EAs), have shown potential for automatic design. However, EA-based methods face the challenge of high computational cost when c…
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Locomotive soft robots (SoRos) have gained prominence due to their adaptability. Traditional locomotive SoRo design is based on limb structures inspired by biological organisms and requires human intervention. Evolutionary robotics, designed using evolutionary algorithms (EAs), have shown potential for automatic design. However, EA-based methods face the challenge of high computational cost when considering multiphysics in locomotion, including materials, actuations, and interactions with environments. Here, we present a design approach for pneumatic SoRos that integrates gradient-based topology optimization with multiphysics material point method (MPM) simulations. This approach starts with a simple initial shape (a cube with a central cavity). The topology optimization with MPM then automatically and iteratively designs the SoRo shape. We design two SoRos, one for walking and one for climbing. These SoRos are 3D printed and exhibit the same locomotion features as in the simulations. This study presents an efficient strategy for designing SoRos, demonstrating that a purely mathematical process can produce limb-like structures seen in biological organisms.
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Submitted 24 July, 2024; v1 submitted 17 October, 2023;
originally announced October 2023.
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4D topology optimization: Integrated optimization of the structure and self-actuation of soft bodies for dynamic motions
Authors:
Changyoung Yuhn,
Yuki Sato,
Hiroki Kobayashi,
Atsushi Kawamoto,
Tsuyoshi Nomura
Abstract:
Topology optimization is a powerful tool utilized in various fields for structural design. However, its application has primarily been restricted to static or passively moving objects, mainly focusing on hard materials with limited deformations and contact capabilities. Designing soft and actively moving objects, such as soft robots equipped with actuators, poses challenges due to simulating dynam…
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Topology optimization is a powerful tool utilized in various fields for structural design. However, its application has primarily been restricted to static or passively moving objects, mainly focusing on hard materials with limited deformations and contact capabilities. Designing soft and actively moving objects, such as soft robots equipped with actuators, poses challenges due to simulating dynamics problems involving large deformations and intricate contact interactions. Moreover, the optimal structure depends on the object's motion, necessitating a simultaneous design approach. To address these challenges, we propose "4D topology optimization," an extension of density-based topology optimization that incorporates the time dimension. This enables the simultaneous optimization of both the structure and self-actuation of soft bodies for specific dynamic tasks. Our method utilizes multi-indexed and hierarchized density variables distributed over the spatiotemporal design domain, representing the material layout, actuator layout, and time-varying actuation. These variables are efficiently optimized using gradient-based methods. Forward and backward simulations of soft bodies are done using the material point method, a Lagrangian-Eulerian hybrid approach, implemented on a recent automatic differentiation framework. We present several numerical examples of self-actuating soft body designs aimed at achieving locomotion, posture control, and rotation tasks. The results demonstrate the effectiveness of our method in successfully designing soft bodies with complex structures and biomimetic movements, benefiting from its high degree of design freedom.
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Submitted 29 June, 2023; v1 submitted 2 February, 2023;
originally announced February 2023.
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Free material optimization of thermal conductivity tensors with asymmetric components
Authors:
Yuki Sato,
Teppei Deguchi,
Tsuyoshi Nomura,
Atsushi Kawamoto
Abstract:
Free Material Optimization (FMO), a branch of topology optimization, in which the design variables are the full constitutive tensors, can provide the most general form of the design problems. Considering the microstructure composed of isotropic materials, the constitutive tensors are yet positive definite and symmetric. On the other hand, it has been reported that the symmetry of this constitutive…
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Free Material Optimization (FMO), a branch of topology optimization, in which the design variables are the full constitutive tensors, can provide the most general form of the design problems. Considering the microstructure composed of isotropic materials, the constitutive tensors are yet positive definite and symmetric. On the other hand, it has been reported that the symmetry of this constitutive tensor can be broken in appearance by considering other physical phenomena. In the present study, we focus on the thermal Hall effect, which is explained as the phenomena that induces the temperature gradient orthogonal to a given temperature gradient across a solid when a magnetic field is applied to the solid. This effect makes the thermal conductivity tensor asymmetric and justifies extending the space of the constitutive tensors to be an asymmetric domain. We propose the FMO for asymmetric constitutive tensors, parameterizing the design space so that the physically available property could be naturally satisfied. Several numerical experiments are provided to show the validity and the utility of the proposed method.
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Submitted 5 September, 2022;
originally announced September 2022.
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Substring Complexities on Run-length Compressed Strings
Authors:
Akiyoshi Kawamoto,
Tomohiro I
Abstract:
Let $S_{T}(k)$ denote the set of distinct substrings of length $k$ in a string $T$, then the $k$-th substring complexity is defined by its cardinality $|S_{T}(k)|$. Recently, $δ= \max \{ |S_{T}(k)| / k : k \ge 1 \}$ is shown to be a good compressibility measure of highly-repetitive strings. In this paper, given $T$ of length $n$ in the run-length compressed form of size $r$, we show that $δ$ can b…
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Let $S_{T}(k)$ denote the set of distinct substrings of length $k$ in a string $T$, then the $k$-th substring complexity is defined by its cardinality $|S_{T}(k)|$. Recently, $δ= \max \{ |S_{T}(k)| / k : k \ge 1 \}$ is shown to be a good compressibility measure of highly-repetitive strings. In this paper, given $T$ of length $n$ in the run-length compressed form of size $r$, we show that $δ$ can be computed in $\mathit{C}_{\mathsf{sort}}(r, n)$ time and $O(r)$ space, where $\mathit{C}_{\mathsf{sort}}(r, n) = O(\min (r \lg\lg r, r \lg_{r} n))$ is the time complexity for sorting $r$ $O(\lg n)$-bit integers in $O(r)$ space in the Word-RAM model with word size $Ω(\lg n)$.
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Submitted 24 May, 2022;
originally announced May 2022.
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Cellular Topology Optimization on Differentiable Voronoi Diagrams
Authors:
Fan Feng,
Shiying Xiong,
Ziyue Liu,
Zangyueyang Xian,
Yuqing Zhou,
Hiroki Kobayashi,
Atsushi Kawamoto,
Tsuyoshi Nomura,
Bo Zhu
Abstract:
Cellular structures manifest their outstanding mechanical properties in many biological systems. One key challenge for designing and optimizing these geometrically complicated structures lies in devising an effective geometric representation to characterize the system's spatially varying cellular evolution driven by objective sensitivities. A conventional discrete cellular structure, e.g., a Voron…
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Cellular structures manifest their outstanding mechanical properties in many biological systems. One key challenge for designing and optimizing these geometrically complicated structures lies in devising an effective geometric representation to characterize the system's spatially varying cellular evolution driven by objective sensitivities. A conventional discrete cellular structure, e.g., a Voronoi diagram, whose representation relies on discrete Voronoi cells and faces, lacks its differentiability to facilitate large-scale, gradient-based topology optimizations. We propose a topology optimization algorithm based on a differentiable and generalized Voronoi representation that can evolve the cellular structure as a continuous field. The central piece of our method is a hybrid particle-grid representation to encode the previously discrete Voronoi diagram into a continuous density field defined in a Euclidean space. Based on this differentiable representation, we further extend it to tackle anisotropic cells, free boundaries, and functionally-graded cellular structures. Our differentiable Voronoi diagram enables the integration of an effective cellular representation into the state-of-the-art topology optimization pipelines, which defines a novel design space for cellular structures to explore design options effectively that were impractical for previous approaches. We showcase the efficacy of our approach by optimizing cellular structures with up to thousands of anisotropic cells, including femur bone and Odonata wing.
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Submitted 27 September, 2022; v1 submitted 21 April, 2022;
originally announced April 2022.
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Topology optimization of locomoting soft bodies using material point method
Authors:
Yuki Sato,
Hiroki Kobayashi,
Changyoung Yuhn,
Atsushi Kawamoto,
Tsuyoshi Nomura,
Noboru Kikuchi
Abstract:
Topology optimization methods have widely been used in various industries, owing to their potential for providing promising design candidates for mechanical devices. However, their applications are usually limited to the objects which do not move significantly due to the difficulty in computationally efficient handling of the contact and interactions among multiple structures or with boundaries by…
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Topology optimization methods have widely been used in various industries, owing to their potential for providing promising design candidates for mechanical devices. However, their applications are usually limited to the objects which do not move significantly due to the difficulty in computationally efficient handling of the contact and interactions among multiple structures or with boundaries by conventionally used simulation techniques. In the present study, we propose a topology optimization method for moving objects incorporating the material point method, which is often used to simulate the motion of objects in the field of computer graphics. Several numerical experiments demonstrate the effectiveness and the utility of the proposed method.
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Submitted 28 February, 2023; v1 submitted 31 March, 2022;
originally announced March 2022.