Pith. sign in

REVIEW 5 major objections 6 minor 60 references

Computational Design and Fabrication of Modular Robots with Untethered Control

T0 review · 5 major / 6 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A universal building block—a 3D-printed bone paired with infrared-heated liquid crystal elastomer muscles—lets modular robots be designed computationally and driven wirelessly to both change shape and move.

desk verdict Real modular hardware with untethered laser-driven LCE muscles and a credible shape-morphing design tool—but the locomotion-control co-optimization is never actually run on the fabricated robots. read the letter →

arxiv 2508.05410 v2 pith:HWPHYMMX submitted 2025-08-07 cs.RO

Manas Bhargava , Takefumi Hiraki , Malina Strugaru , Yuhan Zhang , Michal Piovarci , Chiara Daraio , Daisuke Iwai , Bernd Bickel This is my paper · ORCID
classification cs.RO
keywords modularrobotsliquidcrystalelastomersuntetheredactuationinfraredlasercontrolcomputationaldesignshapemorphinglocomotionoptimizationskeletalgraphs
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper aims to show that a single modular building block—a 3D-printed flexible bone fitted with two liquid-crystal-elastomer (LCE) rods that contract when heated—can serve as the muscle unit for robots that change shape and move without any wires. The authors make the LCE rods heatable by an infrared laser by doping them with an infrared-absorbing dye, so each muscle can be activated remotely and selectively, and the whole skeleton can be controlled by laser scan patterns. On top of that hardware, they contribute two computational design tools: one that optimizes a skeletal graph so a flat-printed robot morphs into several user-specified 3D shapes, and one that co-optimizes skeleton and gait for locomotion on a chosen terrain. They validate the claims with five physical robots: face-bot, grid-bot, morph-bot, Xbot, and frog-bots. A sympathetic reader would care because the combination—modular structure, wireless distributed actuation, and computational design—addresses three bottlenecks that usually prevent soft robots from being both versatile and untethered.

What carries the argument

The central object is the universal building block: one flexible 3D-printed bone with two LCE muscle rods, each doped with IR820 to absorb infrared light, contract up to 33% when heated to about 120 °C, and produce preferential bending of up to ±90 degrees when only one rod is heated. The carrying abstraction is the skeletal graph, whose nodes are joints and whose edges are building blocks; every actuated behavior is an instruction set of which muscle to heat, for how long, and how often. Shape morphing is carried by the bijection between flat-fabricated and target edges plus the shrinkage/curvature map, optimized as a compatible triangulation shared by all target shapes. Locomotion is carri

What would settle it

Fabricate the same morph-bot skeletal graph twice from the same LCE batch, run the identical laser profile on both, and track each edge's contraction and the final 3D shape; if robot-to-robot variation is large enough that one robot misses the target shape without per-robot recalibration, the claim that the design tools output transferable actuation profiles is falsified. A more direct check is to image IR absorption across an LCE rod's cross-section and correlate local dye concentration with local contraction under a scanned laser.

Watch

Extended reading notes

Core claim

The central claim is that active, untethered control can be pushed down to individual muscles in a modular robotic skeleton, and that the wider design space this opens can be searched computationally instead of hand-built. The enabling object is the universal building block: a flexible 3D-printed bone (TPU or PLA) with two liquid crystal elastomer (LCE) rods glued along it. The rods are doped with IR820 dye so they absorb 808 nm laser light; heating one rod bends the bone in a prescribed direction, heating both shrinks it by up to 33%, and the block reaches curvatures of ±90 degrees. Because a two-axis laser scanner can selectively heat each muscle from a distance, the robot is untethered ye

Load-bearing premise

The framework assumes that every fabricated LCE muscle, once glued to its bone and heated by the laser, contracts with the same reliability and predictability that the design and simulation tools assume; the paper itself notes that non-uniform IR820 dye causes uneven heating and that each assembled robot requires manual calibration offsets.

Editorial extensions

If this is right

  • A designer can specify target shapes or terrains and receive a print-ready skeletal graph plus a laser actuation profile, without hand-designing the robot.
  • The same fabricated robot can be remorphed into multiple target configurations, since each target shares the same flat graph connectivity and the control algorithm re-heats the same muscles differently.
  • Robots remain wireless while retaining active per-muscle control, with roughly 30 muscles driveable concurrently under the measured cooling budget.
  • Locomotion gaits and skeletons can be co-optimized per terrain, and the optimized designs outperform the shared baseline skeleton in simulation and in physical tests.
  • Stiffness and task tradeoffs are selectable at fabrication time through bone material (TPU vs PLA) and cross-section radius, giving designers two cheap tuning knobs.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If IR820 dispersion and LCE repeatability improve, the same architecture should scale to hundreds of actuators, because the binding constraint is the laser's heating/cooling schedule rather than wiring or onboard power.
  • Because actuation is addressed by position instead of wires, the framework invites a planning-level interface: any task reducible to per-edge target lengths or periodic gait parameters becomes reprogrammable in software without changing the hardware.
  • The partially reached saddle shape suggests the verification simulator underestimates gravity on compliant TPU; an extension would move gravity compensation into the shape-morphing optimizer rather than applying it only after the design is fixed.
  • The building block does not require LCE chemistry specifically; any heat-contractile rod with a strong IR absorption peak could be swapped in, so the design tools should transfer to faster or stronger actuator materials as they appear.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 6 minor

Summary. The paper presents a modular robotic building block: a 3D-printed flexible bone with two IR820-doped liquid crystal elastomer (LCE) rod muscles, actuated remotely by an infrared laser through a galvo-scanner system. The authors claim a framework for computational design of modular robots with active, untethered control, and introduce two computational tools: one that optimizes a skeletal graph to approximate user-specified 3D shapes via edge contraction, and a second that co-optimizes skeleton geometry and periodic control gaits for locomotion. Physical demonstrations include a face-bot for facial animations, a 3x5 grid-bot and a morph-bot for shape morphing (dome and saddle), an Xbot for simple locomotion, and three frog-bots for walking, climbing, and swimming. The material characterization reports 33% LCE contraction, an absorption peak near 800 nm, and bone force–contraction curves. The paper also acknowledges several limitations, including a sim-to-real gap, manual calibration offsets for every robot, and non-uniform IR820 dye distribution.

Significance. If substantiated, the work would be a meaningful step toward untethered soft robotics that combine modular fabrication with computational design. The physical system—particularly the laser-actuated LCE muscles and the modular bone-muscle assembly—is credible and well grounded in material characterization. The authors provide open-source code and are transparent about current limitations. However, the strongest claim, namely that the framework provides computational design of control for locomotion, is not supported by the reported hardware experiments: the frog-bot gaits were hand-tuned in the real world. The shape-morphing design tool is demonstrated only partially (the saddle morph is incomplete), and the numerical verification uses a simulator whose parameters were adjusted on the same base block used for validation. These gaps are load-bearing for the paper's central claims, but they are addressable with additional experiments or by carefully scoping the claims.

major comments (5)
  1. [Materials and Methods: Exploring the Design and Control of Terrain Navigating Robots; Fig. 6 caption] The fabricated frog-bots do not validate the co-optimized control gaits. The caption states 'their gaits were hand-tuned for the real-world performance' and the Methods state 'We use the skeletal design produced by our tool and manually tune the actuation profiles for the frog-bots to maximize their performance in the real world.' Therefore, the hardware demonstrations support only skeleton optimization, not control optimization. The abstract and Fig. 2 claim computational design of control for locomotion. Please either run the hardware using the optimizer's raw control parameters (amplitudes, phases, frequencies) or explicitly scope the control-optimization claim to simulation only.
  2. [Materials and Methods: Exploring the Design and Control of Terrain Navigating Robots] The claim that 'the design tool successfully optimizes the skeletal graph of frog-bots for their specific tasks, outperforming the non-optimized skeleton frog-bot' lacks quantitative support. Fig. 6 shows only start and end snapshots, with no measured distances, speeds, times, or comparison to the non-optimized baseline. Please report quantitative metrics (e.g., displacement per time, height gained, speed in water) and, ideally, error bars across repeated trials.
  3. [Materials and Methods: Numerical simulation to Verify Shape Morphing Robots] The simulation verification is potentially circular. The authors write that material parameters were 'adjusted... to ensure that the motion of the base building block matches its behavior in the real world,' and then use the same simulator to verify the morph-bot design. This tuning on the calibration structure does not guarantee predictive accuracy for a different, more complex structure. Moreover, the morph-bot achieves only a partial saddle shape in hardware, which the authors attribute to gravity and the sim-to-real gap; this directly undermines the statement that simulation can 'ensure the correct behavior of the robot after fabrication.' Please provide an independent validation (e.g., prediction for a structure not used in calibration) or temper the verification claim.
  4. [Supplementary Information: Limitations in using LCEs as Muscles; Calibrating the Robot] The paper explicitly states that non-uniform IR820 dye distribution leads to 'clumped and uneven heating' and that manual calibration offsets are needed for every assembled robot. Because the computational design tools assume reliable, predictable per-edge contraction, this material variability is load-bearing for the framework's validity. Please quantify the variability across muscles and batches (e.g., contraction ratio distributions, heating response variation) and explain how the closed-loop control compensates for it. Without such data, the reproducibility of the design tools' outputs remains unclear.
  5. [Results: Morph-bot and Fig. 5] The shape-morphing design tool is evaluated qualitatively. The text reports 'good visual accuracy' for the dome and a 'partial configuration' for the saddle, but provides no quantitative error metric comparing the achieved shape to the target mesh. Please add a quantitative evaluation, such as per-vertex distance, edge-length error, or curvature error, for both targets. This is necessary to assess the design tool's performance.
minor comments (6)
  1. [Algorithm 1, Eq. (2)] The fabrication constraints in Eq. (2) are difficult to parse because of formatting: the union of constraints and the inequality '<= 300' appear interleaved with set-builder notation. Please reformat for clarity.
  2. [Materials and Methods: Exploring the Design and Control of Terrain Navigating Robots] 'Mujoco' should be 'MuJoCo'.
  3. [Throughout] There are repeated typographical issues, e.g., 'Sec. : Materials and Methods' with an extra space before the colon, and 'Ef ab' with a missing subscript. Please proofread.
  4. [Fig. 3] The definition of the rod radius 'r' in panels (A) and (B) is not explicitly given in the caption; please clarify. Also, the color legend for 'r' values should be clearly separated from the line plots.
  5. [Table 1] The column 'Cross Sec. radius' should be spelled out or abbreviated consistently with the text.
  6. [Supplementary Information] The videos S1–S6 are referred to but not included in the text; please provide a link or explicit supplementary video file information.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the derivation chain is supported by physical fabrication, calibrated-but-not-fitted simulation, and external prior work.

full rationale

No load-bearing step reduces to its own inputs. The shape-morphing simulator is calibrated on the base building block—"We adjusted the material parameters of the simulation model to ensure that the motion of the base building block matches its behavior in the real world"—and is then used to pre-verify the morph-bot, but the target dome/saddle shapes were not used to fit those parameters. The subsequent physical morph-bot fabrication provides independent validation of the simulation and design tool. The frog-bot co-optimization is performed in MuJoCo with evolutionary search, and the paper explicitly states that the real-world frog-bots use manually tuned actuation profiles—"We use the skeletal design produced by our tool and manually tune the actuation profiles for the frog-bots to maximize their performance in the real world." Thus the unvalidated transfer of optimized control gaits to hardware is a sim-to-real validation gap, not a circular derivation. Citations to prior work such as [38] (laser heating), [43] (LCE synthesis), [51] (surface maps), and [52,53] (rod simulation/calibration) are published, independently checkable results; some have overlapping authors, but none is invoked as a uniqueness theorem or as the sole justification for a central claim. The design tool's fabrication constraints (33% shrinkage, 300 mm actuation budget) are inputs to the optimizer, not outputs relabeled as predictions. The paper is self-contained against physical demos, and no prediction is forced by construction.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

Everything the central claim rests on that a reader did not pay for upstream: hand-tuned optimization weights and simulation parameters that materially shape the optimized outputs; domain assumptions about LCE behavior, conformal edge-shrinkage morphing, and MuJoCo fidelity; and no invented physical entities beyond the fabricated materials themselves. The main external anchors are the physical robots and their videos.

free parameters (2)
  • Shape-morphing optimization weights and epsilons = wmap=1.0, wbij=1e-5, wboundary=1.0, wtri=1.0, wapprox=1.0, wfabmap=1.0, wshrink=200.0 (fab stage); ϵapprox=0.035/0.030;
    The skeletal graph output of the design tool depends on these hand-tuned weights and softening parameters; no sensitivity analysis is reported.
  • Discrete elastic rod simulation material parameters = not specified
    Tuned so that the simulated building block matches the real one (Materials and Methods: Numerical simulation to Verify Shape Morphing Robots), making the simulation-based verification non-independent.
assumptions (4)
  • domain assumption LCE rods contract up to 33% and bend up to ±90 degrees when heated to 120°C
    Relies on LCE material behavior per Warner & Terentjev (ref 42) and the specific synthesis from Saed et al. (ref 43); the paper's own characterization in Fig. 3D supports this for single rods, but assembled robots show variability.
  • domain assumption Target shapes can be approximated by a common triangulation such that morphing reduces to edge contraction
    The design tool assumes a conformal map between targets and the flat graph exists, as encoded in the energy Emap (SI, based on refs 44 and 51); the saddle result suggests this is not always achieved in practice.
  • domain assumption MuJoCo rigid-body simulation is an adequate model for optimizing frog-bot skeletons and gaits
    The methods state that rigid-linkage modeling 'introduces a significant sim-to-real gap' (Materials and Methods: Exploring the Design and Control of Terrain Navigating Robots), yet gaits are optimized in this model and hand-tuned afterward.
  • domain assumption The closed-loop ArUco tracking and the laser actuation budget (300 mm total contraction) are sufficient to realize target configurations
    The design constraint in Eq. 2 is built on the 300 mm budget estimated from a single characterization experiment (SI: Constraints on the Number of Actuators in a Robot).

how reviews work

0 comments
Cite this review

Pith. "Pith review of Computational Design and Fabrication of Modular Robots with Untethered Control." pith.science (2026). https://pith.science/paper/HWPHYMMX

@misc{pith2026250805410,
  author       = {Pith},
  title        = {Pith review of: Computational Design and Fabrication of Modular Robots with Untethered Control},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HWPHYMMX}},
  note         = {Machine review of arXiv:2508.05410}
}
read the original abstract

Natural organisms utilize distributed actuation through their musculoskeletal systems to adapt their gait for traversing diverse terrains or to morph their bodies for varied tasks. A longstanding challenge in robotics is to emulate this capability of natural organisms, which has motivated the development of numerous soft robotic systems. However, such systems are generally optimized for a single functionality, lack the ability to change form or function on demand, or remain tethered to bulky control systems. To address these limitations, we present a framework for designing and controlling robots that utilize distributed actuation. We propose a novel building block that integrates 3D-printed bones with liquid crystal elastomer (LCE) muscles as lightweight actuators, enabling the modular assembly of musculoskeletal robots. We developed LCE rods that contract in response to infrared radiation, thereby providing localized, untethered control over the distributed skeletal network and producing global deformations of the robot. To fully capitalize on the extensive design space, we introduce two computational tools: one for optimizing the robot's skeletal graph to achieve multiple target deformations, and another for co-optimizing skeletal designs and control gaits to realize desired locomotion. We validate our framework by constructing several robots that demonstrate complex shape morphing, diverse control schemes, and environmental adaptability. Our system integrates advances in modular material building, untethered and distributed control, and computational design to introduce a new generation of robots that brings us closer to the capabilities of living organisms.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

60 extracted references · 52 canonical work pages

  1. [1]

    K. Liu, F. Hacker, C. Daraio, Robotic surfaces with reversible, spatiotemporal control for shape morphing and object manipulation. Science Robotics 6 (53), eabf5116 (2021)

    work page 2021

  2. [2]

    J. Sun, E. Lerner, B. Tighe, C. Middlemist, J. Zhao, Embedded shape morphing for morphologically adaptive robots. Nature Communications 14 (1), 6023 (2023)

    work page 2023

  3. [3]

    Kotikian, et al., Untethered soft robotic matter with passive control of shape morph- ing and propulsion

    A. Kotikian, et al., Untethered soft robotic matter with passive control of shape morph- ing and propulsion. Science Robotics 4 (33), eaax7044 (2019), doi:10.1126/scirobotics. aax7044, https://www.science.org/doi/abs/10.1126/scirobotics.aax7044

    doi:10.1126/scirobotics 2019

  4. [4]

    N. T. Jafferis, E. F. Helbling, M. Karpelson, R. J. Wood, Untethered flight of an insect- sized flapping-wing microscale aerial vehicle. Nature 570 (7762), 491–495 (2019). 21

    work page 2019

  5. [5]

    C. H. Belke, J. Paik, Mori: a modular origami robot. IEEE/ASME Transactions on Mechatronics 22 (5), 2153–2164 (2017)

    work page 2017

  6. [6]

    Panetta, et al

    J. Panetta, et al. , Computational inverse design of surface-based inflatables. ACM Trans. Graph.40 (4) (2021), doi:10.1145/3450626.3459789, https://doi.org/10.1145/ 3450626.3459789

    arXiv 2021

  7. [7]

    Zhao, et al., Robogrammar: graph grammar for terrain-optimized robot design

    A. Zhao, et al., Robogrammar: graph grammar for terrain-optimized robot design. ACM Transactions on Graphics (TOG) 39 (6), 1–16 (2020)

    work page 2020

  8. [8]

    Konakovi´ c-Lukovi´ c, J

    M. Konakovi´ c-Lukovi´ c, J. Panetta, K. Crane, M. Pauly, Rapid deployment of curved surfaces via programmable auxetics. ACM Trans. Graph. 37 (4) (2018), doi:10.1145/ 3197517.3201373, https://doi.org/10.1145/3197517.3201373

    arXiv 2018

Show all 60 references
  1. [9]

    T. Chen, J. Panetta, M. Schnaubelt, M. Pauly, Bistable auxetic surface structures. ACM Trans. Graph.40 (4) (2021), doi:10.1145/3450626.3459940, https://doi.org/10.1145/ 3450626.3459940

    2021

  2. [10]

    Panetta, M

    J. Panetta, M. Konakovi´ c-Lukovi´ c, F. Isvoranu, E. Bouleau, M. Pauly, X-Shells: a new class of deployable beam structures. ACM Trans. Graph. 38 (4) (2019), doi:10.1145/ 3306346.3323040, https://doi.org/10.1145/3306346.3323040

    2019

  3. [11]

    Ren, et al

    Y. Ren, et al. , Umbrella meshes: elastic mechanisms for freeform shape deployment. ACM Trans. Graph. 41 (4) (2022), doi:10.1145/3528223.3530089, https://doi.org/ 10.1145/3528223.3530089

    2022

  4. [12]

    Wang, et al

    G. Wang, et al. , 4DMesh: 4D printing morphing non-developable mesh surfaces. UIST ’18 pp. 623–635 (2018)

    2018

  5. [13]

    Guseinov, C

    R. Guseinov, C. McMahan, J. P´ erez, C. Daraio, B. Bickel, Programming temporal mor- phing of self-actuated shells. Nature communications 11 (1), 237 (2020)

    2020

  6. [14]

    Narumi, et al

    K. Narumi, et al. , Inkjet 4D Print: Self-folding Tessellated Origami Objects by Inkjet UV Printing. ACM Trans. Graph. 42 (4) (2023), doi:10.1145/3592409, https://doi. org/10.1145/3592409. 22

    2023 doi

  7. [15]

    Bai, et al., A dynamically reprogrammable surface with self-evolving shape morphing

    Y. Bai, et al., A dynamically reprogrammable surface with self-evolving shape morphing. Nature 609 (7928), 701–708 (2022)

    2022

  8. [16]

    D. K. Patel, et al., Highly dynamic bistable soft actuator for reconfigurable multimodal soft robots. Advanced Materials Technologies 8 (2), 2201259 (2023)

    2023

  9. [17]

    Sihite, A

    E. Sihite, A. Kalantari, R. Nemovi, A. Ramezani, M. Gharib, Multi-Modal Mobility Morphobot (M4) with appendage repurposing for locomotion plasticity enhancement. Nature communications 14 (1), 3323 (2023)

    2023

  10. [18]

    Chen, et al., Bio-mimic, fast-moving, and flippable soft piezoelectric robots

    E. Chen, et al., Bio-mimic, fast-moving, and flippable soft piezoelectric robots. Advanced Science 10 (20), 2300673 (2023)

    2023

  11. [19]

    Wang, et al

    G. Wang, et al. , PneuFab: designing low-cost 3D-printed inflatable structures for blow molding artifacts. CHI ’23 pp. 1–17 (2023)

    2023

  12. [20]

    Guseinov, E

    R. Guseinov, E. Miguel, B. Bickel, CurveUps: shaping objects from flat plates with tension-actuated curvature. ACM Trans. Graph. 36 (4), 64–1 (2017)

    2017

  13. [21]

    Aharoni, Y

    H. Aharoni, Y. Xia, X. Zhang, R. D. Kamien, S. Yang, Universal inverse design of surfaces with thin nematic elastomer sheets. Proceedings of the National Academy of Sciences 115 (28), 7206–7211 (2018)

    2018

  14. [22]

    Jourdan, P.-A

    D. Jourdan, P.-A. Hugron, C. Schreck, J. Martinez, S. Lefebvre, Shrink & Morph: 3D- printed self-shaping shells actuated by a shape memory effect. ACM Transactions on Graphics (TOG) 42 (6), 1–13 (2023)

    2023

  15. [23]

    A. P. Sabelhaus, et al. , System design and locomotion of SUPERball, an untethered tensegrity robot. ICRA pp. 2867–2873 (2015), doi:10.1109/ICRA.2015.7139590

    2015

  16. [24]

    Y. Kim, H. Yuk, R. Zhao, S. A. Chester, X. Zhao, Printing ferromagnetic domains for untethered fast-transforming soft materials. Nature 558 (7709), 274–279 (2018)

    2018

  17. [25]

    S. I. Rich, R. J. Wood, C. Majidi, Untethered soft robotics. Nature Electronics 1 (2), 102–112 (2018). 23

    2018

  18. [26]

    Zhai, et al

    F. Zhai, et al. , 4D-printed untethered self-propelling soft robot with tactile perception: Rolling, racing, and exploring. Matter 4 (10), 3313–3326 (2021)

    2021

  19. [27]

    Wu, et al

    Y. Wu, et al. , Locally controllable magnetic soft actuators with reprogrammable contraction-derived motions. Science Advances 8 (25), eabo6021 (2022)

    2022

  20. [28]

    Lee, et al., Magnetically actuated fiber-based soft robots

    Y. Lee, et al., Magnetically actuated fiber-based soft robots. Advanced Materials 35 (38), 2301916 (2023)

    2023

  21. [29]

    Chen, et al

    Y. Chen, et al. , Light-driven dandelion-inspired microfliers. Nature Communications 14 (1), 3036 (2023)

    2023

  22. [30]

    Y. Jung, K. Kwon, J. Lee, S. H. Ko, Untethered soft actuators for soft standalone robotics. Nature Communications 15 (1), 3510 (2024)

    2024

  23. [31]

    Skouras, B

    M. Skouras, B. Thomaszewski, S. Coros, B. Bickel, M. Gross, Computational design of actuated deformable characters. ACM Trans. Graph.32 (4) (2013), doi:10.1145/2461912. 2461979, https://doi.org/10.1145/2461912.2461979

    2013

  24. [32]

    S. Min, J. Won, S. Lee, J. Park, J. Lee, Softcon: Simulation and control of soft-bodied animals with biomimetic actuators. ACM Transactions on Graphics (TOG) 38 (6), 1–12 (2019)

    2019

  25. [33]

    J. H. Park, K. H. Lee, Computational design of modular robots based on genetic algo- rithm and reinforcement learning. Symmetry 13 (3), 471 (2021)

    2021

  26. [34]

    Ma, et al., Diffaqua: A differentiable computational design pipeline for soft underwater swimmers with shape interpolation

    P. Ma, et al., Diffaqua: A differentiable computational design pipeline for soft underwater swimmers with shape interpolation. ACM Transactions on Graphics (TOG) 40 (4), 1–14 (2021)

    2021

  27. [35]

    Xu, et al

    J. Xu, et al. , An end-to-end differentiable framework for contact-aware robot design. arXiv preprint arXiv:2107.07501 (2021)

    2021 arXiv

  28. [36]

    Gjoka, E

    A. Gjoka, E. Knoop, M. B¨ acher, D. Zorin, D. Panozzo, Soft Pneumatic Actuator Design using Differentiable Simulation. ACM Transactions on Graphics pp. 1–11 (2024). 24

    2024

  29. [37]

    Schulz, et al

    A. Schulz, et al. , Interactive robogami: An end-to-end system for design of robots with ground locomotion. The International Journal of Robotics Research 36 (10), 1131–1147 (2017)

    2017

  30. [38]

    Hiraki, et al., Laser Pouch Motors: Selective and Wireless Activation of Soft Actuators by Laser-Powered Liquid-to-Gas Phase Change

    T. Hiraki, et al., Laser Pouch Motors: Selective and Wireless Activation of Soft Actuators by Laser-Powered Liquid-to-Gas Phase Change. IEEE Robotics and Automation Letters 5 (3), 4180–4187 (2020), doi:10.1109/LRA.2020.2982864

    2020

  31. [39]

    E. M. Terentjev, Liquid Crystal Elastomers: 30 Years After. Macromolecules 58 (6), 2792–2806 (2025)

    2025

  32. [40]

    Yuan, et al

    C. Yuan, et al. , 3D printed reversible shape changing soft actuators assisted by liquid crystal elastomers. Soft Matter 13 (33), 5558–5568 (2017)

    2017

  33. [41]

    Zhu, et al., Light-Driven Liquid Crystal Elastomer Actuators Based on Surface Plas- mon Resonance for Soft Robots

    C. Zhu, et al., Light-Driven Liquid Crystal Elastomer Actuators Based on Surface Plas- mon Resonance for Soft Robots. ACS Applied Materials & Interfaces 16 (50), 69858– 69869 (2024)

    2024

  34. [42]

    Warner, E

    M. Warner, E. M. Terentjev, Liquid crystal elastomers, vol. 120 (Oxford university press) (2007)

    2007

  35. [43]

    M. O. Saed, A. H. Torbati, D. P. Nair, C. M. Yakacki, Synthesis of programmable main- chain liquid-crystalline elastomers using a two-stage thiol-acrylate reaction. Journal of Visualized Experiments (107) (2016), doi:10.3791/53546

    2016 doi

  36. [44]

    Chern, F

    A. Chern, F. Kn¨ oppel, U. Pinkall, P. Schr¨ oder, Shape from metric.ACM Trans. Graph. 37 (4), 63 (2018)

    2018

  37. [45]

    Xu, et al., Locomotion of an untethered, worm-inspired soft robot driven by a shape- memory alloy skeleton

    L. Xu, et al., Locomotion of an untethered, worm-inspired soft robot driven by a shape- memory alloy skeleton. Scientific reports 12 (1), 12392 (2022)

    2022

  38. [46]

    T. J. Buchner, et al., Vision-controlled jetting for composite systems and robots. Nature 623 (7987), 522–530 (2023)

    2023

  39. [47]

    Zang, et al

    T. Zang, et al. , 4D printing of shape-morphing liquid crystal elastomers. Chem & Bio Engineering 1 (6), 488–515 (2024). 25

    2024

  40. [48]

    Clery, Has a new dawn arrived for space-based solar power

    D. Clery, Has a new dawn arrived for space-based solar power. Science 378 (6617), 238–239 (2022)

    2022

  41. [49]

    Sun, et al

    X. Sun, et al. , Machine learning-enabled forward prediction and inverse design of 4D- printed active plates. Nature Communications 15 (1), 5509 (2024)

    2024

  42. [50]

    Authors, Genesis: A Universal and Generative Physics Engine for Robotics and Be- yond (2024), https://github.com/Genesis-Embodied-AI/Genesis

    G. Authors, Genesis: A Universal and Generative Physics Engine for Robotics and Be- yond (2024), https://github.com/Genesis-Embodied-AI/Genesis

    2024

  43. [51]

    Schmidt, D

    P. Schmidt, D. Pieper, L. Kobbelt, Surface Maps via Adaptive Trian- gulations. Computer Graphics Forum 42 (2), 103–117 (2023), eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1111/cgf.14747, doi:10.1111/cgf.14747, https://onlinelibrary.wiley.com/doi/abs/10.1111/cgf.14747

    2023 doi

  44. [52]

    Bergou, M

    M. Bergou, M. Wardetzky, S. Robinson, B. Audoly, E. Grinspun, Discrete elastic rods. ACM Trans. Graph. pp. 1–12 (2008)

    2008

  45. [53]

    P´ erez,et al

    J. P´ erez,et al. , Design and fabrication of flexible rod meshes. ACM Transactions on Graphics (TOG) 34 (4), 1–12 (2015)

    2015

  46. [54]

    Todorov, T

    E. Todorov, T. Erez, Y. Tassa, Mujoco: A physics engine for model-based control. RSJ pp. 5026–5033 (2012)

    2012

  47. [55]

    Onshape, Onshape, https://www.onshape.com/ (n.d.), accessed: 2025-06-29

    2025

  48. [56]

    Wolfram, Wolfram Mathematica The world’s definitive system for modern technical com- puting, https://www.wolfram.com/mathematica/ (n.d.), accessed: 2025-06-29

    2025

  49. [57]

    Sawhney, K

    R. Sawhney, K. Crane, Boundary first flattening. ACM Transactions on Graphics (ToG) 37 (1), 1–14 (2017)

    2017

  50. [58]

    Dunyach, D

    M. Dunyach, D. Vanderhaeghe, L. Barthe, M. Botsch, Adaptive remeshing for real-time mesh deformation, in 34th Annual Conference of the European Association for Computer Graphics (Eurographics 2013) (The Eurographics Association) (2013)

    2013

  51. [59]

    Storn, K

    R. Storn, K. Price, Differential evolution–a simple and efficient heuristic for global opti- mization over continuous spaces. Journal of global optimization 11 (4), 341–359 (1997). 26 Acknowledgments The authors express gratitude to Magali Lorion for assisting in the initial f...

    1997

  52. [60]

    This gives us surface approximation energy formulation as: Eapprox(Ωi 0, Ωi) = X v∈Ωi 0 area(v) ϵ2 approx ||(v − ¯v)||

    The vertices v ∈ Ωi 0 with normalized voronoi area area(v) are projected on Ω i from embedding space using barycentric coordinates to obtain ¯ v. This gives us surface approximation energy formulation as: Eapprox(Ωi 0, Ωi) = X v∈Ωi 0 area(v) ϵ2 approx ||(v − ¯v)||. Fabrication...

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.