A bionic robotic trunk with tensegrity-enabled elephant-comparable stiffness variability for assisted daily living

Domain: chemistry
Published: 2026-03-06
Editorial outcome: major_revision

Abstract
Elephant trunks can rapidly vary their stiffness over a broad range, seamlessly switching between soft states for dexterous operation and rigid states for load-bearing tasks. Despite extensive efforts to mimic this stiffness variability using various approaches, such as jamming structures and phase-change materials, existing bionic robots are limited to narrow tunable stiffness ranges and/or slow switching frequencies. In this work, we present a bionic robotic trunk with a cable-driven tensegrity skeleton, leveraging synergistic and antagonistic muscle-mimicking mechanisms to achieve dynamic stiffness regulation. Through coordinated contraction of motor-actuated cables (i.e., antagonistic action), the robotic trunk achieves a stiffness range of 23.94 to 542.47 N/m and a switching frequency of 1.06 Hz, matching the adaptability of elephant trunks. This rapid and large-scale stiffness variation enables dexterous navigation in unstructured environments and powerful manipulation of heavy objects. Incorporated into an electric wheelchair with the human-machine interface, the robotic trunk assists a post-stroke individual with daily activities, such as opening cabinet doors, retrieving milk from refrigerators, and watering flowers. This work advances bio-inspired robotics and highlights the potential of stiffness-tunable robotic trunks in assistive applications.

Introduction
Elephant trunks, with their nearly infinite number of degrees of freedom (DoFs), exemplify an extraordinary balance of dexterity and strength1. Their soft and compliant nature enables delicate tasks such as peeling a banana, while still allowing them to lift loads up to 270 kg2,3. Despite their complex muscular structure, elephant trunks perform rapid, precise movements across diverse tasks, largely thanks to their ability to rapidly modulate stiffness through synergistic and antagonistic muscle actions3,4.

Inspired by this biological marvel, decades of research have focused on developing soft robots mimicking elephant trunks5-9. Currently, three primary approaches are commonly used to realize unique stiffness variability: mechanical locking structures10-12, pneumatic jamming systems13-15, and phase-change materials16-18. Mechanical locking structures utilize body friction or geometric constraint to lock specific configurations, adjusting stiffness for diverse tasks19,20. Pneumatic jamming systems modulate the stiffness by varying the pressure to alter friction between particles, fibers, or layers within fluidic channels21-23. Phase-change materials, such as shape memory alloys (SMAs) and low melting point alloys (LMPAs), exploit temperature-induced phase transition to reversibly change material stiffness24,25. However, each approach has notable limitations26. For example, mechanical locking structures provide only discrete stiffness states, lacking continuous modulation observed in elephant trunks27. Pneumatic jamming systems usually involve bulky external pumps or vacuum sources to adjust the pressure28,29. Phase-change materials, while capable of continuous stiffness changes, suffer from their prolonged actuation cycles, e.g., the notoriously slow cooling process of SMAs30,31.

An alternative strategy, directly inspired by the elephant’s biology, leverages synergistic and antagonistic mechanisms to modulate stiffness32-36. Synergistic mechanisms involve the coordinated contraction/extension of multiple actuators working together to reduce overall stiffness, allowing for soft and compliant motion37. Conversely, antagonistic mechanisms rely on opposing actuator actions that generate counterbalancing forces, rapidly increasing stiffness for loading-bearing tasks27. Although this approach provides a simple and effective means of stiffness modulation without additional complex structures or materials, existing implementations-particularly in cable-driven systems-fail to match the stiffness modulation performance of biological trunks. The primary limitation of existing designs is that their antagonistic actions depend solely on the elastic deformation of actuators-such as cables-while the main structure remains nearly undeformed, resulting in only slight variations in elastic energy and thus a limited stiffness range. For instance, soft continuum robots proposed by Kim et al. exhibited tunable stiffness through synergistic and antagonistic actions of the cables, enhancing adaptive capability for robotic single-port surgery38. However, buckling in the main structure introduces structural instability during antagonistic actions. This instability restricts the large-scale increase in elastic energy, thereby resulting in stiffness that can only be tuned within a narrow range39,40.

In this study, we present a bionic robotic trunk (BRT) that leverages synergistic and antagonistic mechanisms to implement rapid and wide-range stiffness modulation (Fig. 1A). Inspired by the biomechanics of elephant trunks, which modulate internal stiffness through active tensioning of antagonistic muscles to redistribute elastic energy 3, our BRT adopts a cable-driven tensegrity skeleton—a lightweight and compliant architecture that can redistribute elastic energy via cable-induced deformation of struts and springs41,42. Within this skeleton, synergistic actuator contractions enable soft and compliant movements, while antagonistic actions increase stiffness significantly, as showcased in Fig. 1B. Enabled by reconfigurable tensegrity, stored elastic energy is increased by 10 times at antagonistic configuration, yielding stiffness ranging from 23.94 to 542.47 N/m at switching frequency of 1.06 Hz, comparable to that of the elephant trunk (Fig. 1C, Table S1)20,28,37,39,43-53. Subsequently, positional finite element analysis further elucidates the underlying stiffness modulation mechanism. The BRT’s rapid response and broad stiffness range enable it to dynamically adapt to diverse demands and external stimuli. To demonstrate its practical utility, we integrate the BRT into an electric wheelchair with a human-machine interface, showcasing its effectiveness in assisting individuals with daily activities, such as opening cabinet doors, retrieving items from refrigerators, and watering flowers (Fig. 1D). By combing flexibility, strength, and efficiency, the BRT establishes a new benchmark for robotic trunk design, providing a versatile solution for navigating complex environments and assistive robotics.

Results
2.1 Tensegrity-based Design of BRT

We proposed a tensegrity-based BRT (length: 920 mm and weight: 1.05 kg) that achieves both dexterous morphing and powerful load-bearing capabilities through controlled cable interactions. As shown in Fig. 2A

Methods

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript presents a cable-driven tensegrity bionic robotic trunk (BRT) that achieves variable stiffness modulation inspired by the muscular architecture of elephant trunks. The system is integrated into an assistive electric wheelchair platform and demonstrates practical utility through real-world user trials.\nWhile the manuscript is clearly written and the engineering effort is commendable, I have concerns regarding the novelty, scientific depth, and generalizability of the work—particularly in the context of Nature Communications. Detailed comments are outlined below.\nMajor Comments:\n1. Limited Novelty in Design and Mechanism\nThe proposed system combines a cable-driven tensegrity structure, antagonistic actuation, and nonlinear spring-based stiffness modulation. However, all of these elements are based on established techniques in robotics and tensegrity mechanisms, and the manuscript does not present a clearly distinguishable advancement in structural design or mechanism compared to prior work.\nRelevant prior work includes (and is recommended for citation):\n• [1] Shah DS et al. Tensegrity robotics. Soft Robotics, 2022: A comprehensive review of tensegrity structures for robotic actuation and stiffness control.\nThese two works present similar designs and mechanisms that utilize tensegrity structures and springs for stiffness modulation:\n• [2] Ikemoto S et al. Development of a modular tensegrity robot arm. Frontiers in Robotics and AI, 2021: Demonstrated modular tensegrity arms capable of continuum bending using cable actuation.\n• [3] Chen D et al. Bionic tensegrity robotic fish. Biomimetics, 2024: Showcased variable compliance using spring-tethered tensegrity modules for underwater applications.\nGiven the above, the system lacks a clear advancement in structural principle or mechanism beyond the existing literature.\nAdditional limitations of the proposed mechanical design include:\n• 1.1 Coupling between stiffness and manipulator length: The system modulates stiffness through antagonistic cable pulling, which shortens the entire structure (ΔL). This inherently couples stiffness with posture, limiting independent control of impedance and workspace.\n• 1.2 Orientation-dependent gravity compensation: The use of reinforcing springs to maintain alignment appears tuned for a specific mounting configuration. It is unclear how the system performs when mounted vertically or in mobile, orientation-varying applications, raising concerns about generalizability.\n• 1.3 Limited adaptability to payload variation: The stiffness adjustment is not dynamically decoupled from geometry or actuation mode, which may reduce robustness in tasks involving variable object dynamics or interactions.\n2. Lack of Modeling and Control Contribution\nDespite claims of dynamic adaptability and task versatility, the modeling and control aspects of this work remain underdeveloped and do not meet the standards expected for publication in Nature Communications.\n2.1 No Control-Theoretic Innovation\n• The system operates entirely under open-loop kinematic control using joystick inputs.\n• There is no discussion or implementation of dynamic modeling, trajectory planning, impedance/admittance control, or adaptive learning strategies, techniques that are well-established in robotic manipulation.\n• The “control model” referenced in Fig. S11 is not formulated mathematically nor validated experimentally.\n2.2 No Generalizable Modeling Framework\n• The stiffness estimation is based on an empirical analysis of nonlinear spring elongation and elastic energy accumulation. While visually intuitive, this method lacks analytical formulation and does not generalize to other designs or conditions.\n• There is no attempt to derive reduced-order models, continuum approximations, or tensegrity statics that would support broader reuse or theoretical insight.\n2.3 No Sensor Integration or Feedback\n• The robot lacks onboard sensing (e.g., cable tension, force, proprioception, or vision), precluding feedback control or autonomous adaptability.\n• This directly contradicts the claims of adaptability and safe interaction (e.g., in the egg-drop test or during human-robot assistance).\n• Without sensing and feedback, the system behavior is limited to predefined actuation patterns, with no capacity for reactive decision-making or robustness to uncertainty.\nTaken together, these limitations in modeling and control significantly weaken the scientific contribution of the work.\n3. Concerns on Application Relevance and Justification\nThe integration of the BRT into a wheelchair platform with a human–machine interface is well executed and visually compelling. However, the system appears to be developed primarily for demonstration purposes, rather than to address a clearly defined assistive need or user-driven challenge. The work lacks a comparison with alternative solutions, such as existing lightweight robotic arms, which could also be mounted on a wheelchair with similar or better functional outcomes. As such, the superiority or necessity of the proposed system is not convincingly justified.\nMinor Comments\n• It is also unclear whether long-term reliability concerns, such as cable creep, spring fatigue, or material degradation, have been assessed or mitigated.\n• The human evaluation is limited to a single post-stroke participant. Broader user studies or a more systematic assessment would be needed to substantiate the assistive potential of the system.\nConclusion:\nWhile the authors present a well-integrated and experimentally validated robotic platform, the contribution lies primarily in engineering implementation. However, the work exhibits clear limitations in terms of novelty in structural design, the absence of generalizable modeling frameworks, and minimal development in control strategy. These shortcomings render the manuscript, in its current form, unsuitable for publication in Nature Communications.", "reviewer_2": "Nature Comms review\nThe manuscript under consideration presents a novel cable-driven robotic trunk which leverages tensegrity structures and passive springs to provide continuously-variable stiffness over a large range. Importantly, the tensegrity structure and passive spring configuration is such that although the springs are close to linear, the macroscopic deformation behavior is highly nonlinear, and the variable stiffness is obtained by exploiting this nonlinearity.\nThe authors describe their trunk design, study its behavior through modeling and a series of experiments, and demonstrate a real-world use case where the trunk is mounted on an electric wheelchair.\nThe trunk design is novel and highly interesting, thoroughly evaluated with the presented experiments, and the paper is well written.\nI have some smaller comments:\n* I am missing a description of the overall size/weight of the trunk in the main text. This is important to interpret results such as length change, which is given in cm.\n* I am missing a description of how the cable attaches to the frames. Presumably the cables driving the distal portion are anchored at the most distal frame, pass through eyelets in 7 frames, before entering the cable sheath at the 9th frame?\n* How does cable friction come into play? Would be pertinent to discuss what effect unmodelled friction would be expected to have on the trunk behavior.\n* What is the natural frequency of the trunk for different stiffness configuration? And how does it change with end effector load? One problem frequently arising with soft systems is that they are susceptible to vibrations - is this an issue here? If so, how can it be circumvented? (e.g. you only have springs within the trunk, but no dampers).\n* Fig 2: \"Reinforcing Spring\" label points to sheathed cable; should be pointing to purple spring.\n* What is the reason for a 2 x 9 frame configuration? Presumably one could vary both the number of frames per portion and the number of different portions (using 3 cables per portion)?\n* It would be useful, though not required, if the authors could provide some intuition regarding the particular design of the tensegrity structure used in the trunk. Which properties are important (e.g. the resultant nonlinear macroscopic behavior)?\n* Fig 3 E+F: Is the stiffness a true exponential curve? Or is it just that it is well approximated by an exponential curve? If it is an approximation then I would suggest to make the language more precise. I would find it counterintuitive if linear springs + geometric nonlinearities were to produce an exponential relationship?\n* In images/video, I would recommend to make consecutive frames alternating colors, for improved legibility."}, "author_response": "Responses to Comments on Manuscript No. NCOMMS-25-50877-T\nWe sincerely thank two reviewers for thoroughly reading our manuscript. The constructive comments and suggestions are fully addressed point-by-point in this letter. For the convenience of the reviewers, we marked the corresponding modifications in our revised manuscript in blue. We believe that the concerns raised by two reviewers have highlighted areas in need of further attention and our modifications have made the manuscript more suitable for publication in Nature Communications.\nReviewer #1\nThis manuscript presents a cable-driven tensegrity bionic robotic trunk (BRT) that achieves variable stiffness modulation inspired by the muscular architecture of elephant trunks. The system is integrated into an assistive electric wheelchair platform and demonstrates practical utility through real-world user trials. While the manuscript is clearly written and the engineering effort is commendable, I have concerns regarding the novelty, scientific depth, and generalizability of the work—particularly in the context of Nature Communications.\nDetailed comments are outlined below.\nOur Response:\nWe sincerely thank the reviewer for your thoughtful evaluation of our manuscript and for acknowledging the clarity of our writing and the engineering effort involved. We appreciate the reviewer’s concerns regarding the novelty, scientific depth, and generalizability of the work, and we respectfully address each in our point-by-point responses below.\nComment #1\n1. Limited Novelty in Design and Mechanism\nThe proposed system combines a cable-driven tensegrity structure, antagonistic actuation, and nonlinear spring-based stiffness modulation. However, all of these elements are based on established techniques in robotics and tensegrity mechanisms, and the manuscript does not present a clearly distinguishable advancement in structural design or mechanism compared to prior work.\nRelevant prior work includes (and is recommended for citation):\n[1] Shah DS et al. Tensegrity robotics. Soft Robotics, 2022: A comprehensive review of tensegrity structures for robotic actuation and stiffness control.\nThese two works present similar designs and mechanisms that utilize tensegrity structures and springs for stiffness modulation:\n[2] Ikemoto S et al. Development of a modular tensegrity robot arm. Frontiers in Robotics and AI, 2021: Demonstrated modular tensegrity arms capable of continuum bending using cable actuation.\n[3] Chen D et al. Bionic tensegrity robotic fish. Biomimetics, 2024: Showcased variable compliance using spring-tethered tensegrity modules for underwater applications.\nGiven the above, the system lacks a clear advancement in structural principle or mechanism beyond the existing literature.\nResponse #1\n1. Synergistic-Antagonistic Stiffness Modulation Mechanism:\nWhile prior tensegrity robots (e.g., Ikemoto et al. [2], Chen et al. [3]) used spring-cable actuation for shape change or compliance our system is, to our knowledge, the first to leverage both synergistic and antagonistic cable patterns within a tensegrity skeleton to achieve large-scale and high-frequency stiffness modulation (23.94-542.47 N/m at up to 1.06 Hz). This dual-mode modulation enables both soft deformation and load-bearing rigidity transitions, a performance not demonstrated in the cited works.\n2. System-Level Integration and Real-World Validation:\nEnabled by rapid and wide-range stiffness modulation via synergistic and antagonistic actuation, our BRT can be readily integrated into a human-assistive mobile robotic platform with real-time joystick control and task execution by a post-stroke user (see Fig. 5 and Fig. 6). These real-world validations, especially in healthcare contexts, mark a significant departure from existing tensegrity-based robots designed mainly for locomotion or underwater propulsion [2, 3].\nModification #1\nIn response to the reviewer’s helpful comment, we have added the suggested citations to the revised manuscript. Specifically: Ikemoto et al. (2021), Chen et al. (2024), and Shah DS et al (2022) have been added as references [35], [36] and [41], respectively. The revised Fig. 1C now explicitly positions our BRT in comparison with prior tensegrity robots including [36]. Two new rows have been added to Supplementary Table S1 to summarize key distinctions between [35, 36] and our BRT.\nFig. 1C. Comparison of the stiffness variability and switching frequency between BRT and existing robotic trunks20, 28, 36, 37, 39, 43-53.\nTable S1. Programmable stiffness range and switching frequency\nLength Low High\nFrequency\nApproach (mm) stiffness stiffness Ratio Reference\n(Hz)\n(N/m) (N/m)\nMLS 500 78.64 604.40 7.68 1 [20]\n2\n800 13.33 140 10.50 0.33 [S4]\n30 290 410 1.41 0.02 [43]\n480 35.05 105.15 3 0.05 [39]\n315 300 1100 3.67 0.01 [S5]\n200 80 850 10.62 0.48 [44]\n82 10 110 11 0.48 [45]\n200§ 5 25 5 0.67 [46]\n60 25 80 3.2 0.40 [S6]\nPJS\n355 5.56 10 1.80 0.40 [S7]\n84 18 186 10.33 0.33 [S8]\n160 21 71 3.38 0.37 [47]\n108 19.23 57.47 2.99 0.40 [48]\n100§ 6.90 58 8.41 0.05 [49]\n60 12.50 95 7.60 0.04 [S9]\n100§ 45 474 10.53 0.04 [50]\nPCM\n150 30.96 1369.86 44.24 0.03 [28]\n150§ 13.15 477.05 36.28 0.06 [S10]\n85 33.33 415.45 12.46 0.07 [51]\n100§ 59.6 145.6 2.44 1 [S11]\n220 80 220 2.75 0.50 [37]\n360 40 312.5 7.81 0.20 [S12]\n200 60 93.33 1.55 0.33 [S13]\nSAM\n115 100 200 2 1 [52]\n700§ 50 200 4 0.17 [53]\n1300§ 2.40 6.50 2.71 0.50 [35]\n135 11.63 27.78 2.39 1 [36]\nThis\nSAM 920 23.94 542.47 22.66 1.06\nwork\nAnnotation: MLS: mechanical locking structure; PJS: pneumatic jamming system; PCM: phase-change material; SAM: synergistic and antagonistic mechanism.\n§ Estimated length\nComment #1.1\nAdditional limitations of the proposed mechanical design include:\n1.1 Coupling between stiffness and manipulator length: The system modulates stiffness through antagonistic cable pulling, which shortens the entire structure (ΔL). This inherently couples stiffness with posture, limiting independent control of impedance and workspace.\nResponse #1.1\nWe thank the reviewer for pointing out this important design consideration. We fully acknowledge that the coupling between stiffness modulation and length variation (ΔL) is an inherent trade-off in antagonistic tendon-driven systems. However, this coupling is not merely a limitation—it is also a necessary mechanism to achieve large-scale stiffness modulation. Specifically, without structural shortening, the amount of elastic energy that can be stored through cable antagonism is significantly limited, resulting in only marginal changes in stiffness. In contrast, our design embraces this coupling by enabling the tensegrity skeleton to geometrically shorten under antagonistic loading, thereby increasing internal energy storage and enabling a high stiffness tuning ratio.\nModification #1.1\nTo alleviate your concern, we have fully discussed this part in the Discussion. On Page 14,\n“One structural trade-off of our stiffness modulation strategy is the coupling between stiffness and manipulator length: antagonistic cable actuation shortens the trunk while increasing its stiffness. This trade-off is intrinsic to many tendon-driven designs, yet crucial—without structural shortening, the elastic energy that can be modulated remains limited, resulting in a narrow stiffness range. In our design, we utilize this shortening behavior to achieve high stiffness ratios, enabled by the geometric reconfiguration of the tensegrity skeleton.\nTo address workspace concerns, we integrate the BRT into a mobile electric wheelchair platform. The wheelchair’s mobility compensates for any length loss at high stiffness states, allowing the user to reposition the robot as needed and maintain full access to their environment.”\nComment #1.2\n1.2 Orientation-dependent gravity compensation: The use of reinforcing springs to maintain alignment appears tuned for a specific mounting configuration. It is unclear how the system performs when mounted vertically or in mobile, orientation-varying applications, raising concerns about generalizability.\nResponse #1.2\nWe would like to thank you for your valuable suggestions. In response to your suggestions, we have conducted comparative experiments on the vertical configuration. As depicted in Fig. 2B and S3, the introduction of reinforcing springs can improve the resistance of the BRT to gravity, whether placed horizontally or vertically.\nModification #1.2\nTo alleviate your concern, we have added Fig. S3 in the Supplementary Information and made modifications in Section 2.1 of the Manuscript. On Page 6,\n“The arrangement of reinforcing springs is also equally effective in minimizing the influence of gravity when placed in vertical directions (Fig. S3).”\nFig. S3. Effects of gravity on vertically arranged BRTs with and without reinforcing springs.\n1.3 Limited adaptability to payload variation: The stiffness adjustment is not dynamically decoupled from geometry or actuation mode, which may reduce robustness in tasks involving variable object dynamics or interactions.\nResponse #1.3\nThank you for your valuable comments. We agree that the stiffness modulation in our design is coupled to the geometry through antagonistic actuation; however, as discussed in Response 1.1, this coupling is an essential mechanism for achieving large-scale stiffness variation. Rather than limiting robustness, it provides the BRT with adaptive mechanical intelligence—allowing the structure to dynamically redistribute tension and stabilize under changing payloads.\nWe have experimentally validated this adaptability in diverse manipulation scenarios. In the low-stiffness state, the BRT demonstrates excellent shape-morphing ability to navigate and interact safely within cluttered environments (Fig. 3G). In the high-stiffness state, it supports a wide range of payloads—from 0.07 kg to 2.17 kg—without loss of stability or control accuracy (Fig. 3H). These results confirm that the structural coupling dose not compromise robustness when interacting with objects of varying mass or dynamics.\nFurthermore, to mitigate workspace reduction during high-stiffness configurations, the BRT is integrated into a mobile electric wheelchair platform. The wheelchair’s motion compensates for the geometric shortening that occurs during antagonistic contraction, preserving overall reachability and functional range. This synergy enables the user to perform practical daily tasks such as opening cabinet doors, retrieving items from refrigerators, and watering plants (Fig. 6), illustrating robust real-world adaptability.\nModification #1.3\nTo emphasize the mutual promotion between the BRT and the wheelchair, we have made modifications in the Section 2.4. On Page 11,\n“To demonstrate the practical utility and assistive potential of our BRT, we integrated it into an electric wheelchair equipped with a control module via human-machine interface (HMI)56. Embedding the variable-stiffness robotic arm into the wheelchair system substantially expands its functional capabilities beyond mobility support. The ability to tune stiffness not only improves task versatility, including delicate manipulations and stable load-bearing actions, but also ensures safer interactions in human-centered environments compared to the integration of rigid robotic arms (Table S3). Moreover, the wheelchair’s mobility naturally complements the BRT’s structural behavior: it compensates for the modest geometric shortening accompanying high-stiffness actuation, thereby preserving workspace and ensuring that the end-effector remains within reach of target objects.”\nComment #2\n2. Lack of Modeling and Control Contribution\nDespite claims of dynamic adaptability and task versatility, the modeling and control aspects of this work remain underdeveloped and do not meet the standards expected for publication in Nature Communications.\nWe sincerely appreciate the reviewer’s feedback regarding modeling and control. In response, we have significantly strengthened both aspects in the revised manuscript. On the modeling side, we have included a static model of the tensegrity skeleton in Supplementary Notes S2 and S5, which provides quantitative insight into the mapping between structural geometry, stored elastic energy, and stiffness modulation. Building upon this foundation, we have now added new modeling content in Supplementary Information. Please refer to our Response 2.2 for details. On the control side, we have developed and implemented a vision-based control strategy to enhance trajectory tracking and task accuracy. This system utilizes onboard camera feedback and joystick input to guide the robotic trunk through pre-programmed or user-defined trajectories. The controller compensates for structural nonlinearities and external disturbances, ensuring smooth and robust manipulation in both constrained and dynamic environments. Please refer to our Response 2.1 for details.\nComment #2.1\n2.1 No Control-Theoretic Innovation\nThe system operates entirely under open-loop kinematic control using joystick inputs.\nThere is no discussion or implementation of dynamic modeling, trajectory planning, impedance/admittance control, or adaptive learning strategies, techniques that are well-established in robotic manipulation.\nThe “control model” referenced in Fig. S11 is not formulated mathematically nor validated experimentally.\nResponse #2.1\nThank you for your invaluable comments. In the previous version, our robotic trunk was capable of assisting individuals in performing diverse tasks. In this open-loop control, we use the inverse solution of the proposed mechanical model to determine the length variation of the cables. The accuracy of this mechanical model has been shown in Fig. S11. Meanwhile, the effectiveness of this open-loop control is also demonstrated in the manual trajectory tracking of Fig. 5D.\nAdditionally, in response to your suggestions, we have applied a camera mounted on the robotic gripper as a visual sensor to integrate vision-based control strategies into the BRT, ensuring it to implement grasping behaviors more accurately.\nModification #2.1\nTo alleviate your concern, we have revised this part in the Section 2.4. On Page 12,\n“Upon joystick movement, the system first calculates length variations across the six cable groups based on an inverse solution of the mechanical model, then translates these into actuation commands for the servo systems (Fig. S15).”\n“Subsequently, vision-based control strategies are integrated. When an object enters the camera’s field of view, the robotic arm can automatically align with the center of the object, thereby enhancing grasping accuracy (Fig. S16, Video S7).”\nVideo S7. Vision-based control strategy for assisting in precisely grasping objects.\nComment #2.2\n2.2 No Generalizable Modeling Framework\nThe stiffness estimation is based on an empirical analysis of nonlinear spring elongation and elastic energy accumulation. While visually intuitive, this method lacks analytical formulation and does not generalize to other designs or conditions.\nThere is no attempt to derive reduced-order models, continuum approximations, or tensegrity statics that would support broader reuse or theoretical insight.\nResponse #2.2\nWe sincerely appreciate your suggestions and the opportunity to provide a more detailed clarification on this point. In our study, the stiffness estimation is not obtained through an empirical analysis of nonlinear spring elongation and elastic energy accumulation. We construct a mechanical model, and the modeling process is as follows. First of all, the structural deformation of the components—including rigid frames, elastic springs, and tensioned cables—is expressed using generalized coordinates, i.e., q. This formulation allows for a unified representation of both the rigid and elastic elements. Based on the generalized coordinates, we derive 7\nthe mechanical model of the system in accordance with the principles of tensegrity statics. To enable a direct and meaningful comparison with experimental measurements, we replicate experimental loading conditions in our theoretical analysis. Specifically, an external force (Mg) is applied to the distal end of the BRT in the same manner as in the experimental procedure. Using the derived mechanical model, we then calculate the corresponding deformation response of the structure. Finally, the equivalent stiffness of the robotic system is determined according to the relationship K = Mg / Δh, where Δh is the resulting displacement. This calculation yields the stiffness values presented in Fig. R1, which serve as the theoretical counterpart to the experimental data.\nFig. R1. Stiffness evaluation.\nModification #2.2\nTo further clarify our work, we have supplemented the revised manuscript with a comprehensive description of the system’s static modeling process in the Supplementary Information. On Page 7,\n“Based on the finite element method, all nodes of the system of BRT are numbered. Then, according to the mapping relationship between the local node numbers of each component and the global degree of freedom numbers, the generalized force , gravity , and external force vector of each element are superimposed onto the generalized f𝑒orce , gravit𝑒y , and external force vector 𝑒 of the system. Here, as 𝑓𝑘 𝑔𝑘 𝑝𝑘\nlubricating oil is applied at the cable-frame contact points to minimize frictional effects, friction is not 𝑓 𝑔 𝑝\nexplicitly incorporated into the mechanical model. Therefore, the static equilibrium equation of the system is further established.\n(S28)\nwhere can be calculated by assemblTing the the generalized force vector of every element:\n𝛷𝑞𝜆−𝑓(𝑞)−𝑔−𝑝 = 0\n. The system gravity force vector and the system external force vector are obtained in a similar 𝑓(𝑞) 𝑓(𝑞) =\nwa𝑛y: 𝑒 , . The term physically represents the control force vector applied to ⋃𝑘=1𝑓𝑘 𝑔 𝑝\nthe clustered 𝑛cable𝑒s [S3].” 𝑛 𝑒 T\n𝑔 = ⋃𝑘=1𝑔𝑘 𝑝 = ⋃𝑘=1𝑝𝑘 𝛷𝑞𝜆\nComment #2.3\n2.3 No Sensor Integration or Feedback\nThe robot lacks onboard sensing (e.g., cable tension, force, proprioception, or vision), precluding feedback control or autonomous adaptability.\nThis directly contradicts the claims of adaptability and safe interaction (e.g., in the egg-drop test or during human-robot assistance).\nWithout sensing and feedback, the system behavior is limited to predefined actuation patterns, with no capacity for reactive decision-making or robustness to uncertainty.\nThank you for your invaluable comments. In terms of soft robots, their adaptability and safety of interaction are due to the passive flexibility of their structures, rather than active control. The minimum stiffness of our robotic trunk is merely 23.94 N/m, which is the fundamental reason for ensuring the adaptability and safety of robotic system interaction. Although we believe that the current robotic trunk has good adaptability and safety, we also agree with the reviewer’s suggestion to enhance system functionality by introducing onboard sensors. Consequently, we have integrated a camera as vision sensors in our robotic system. The vision-based control strategies can effectively improve the fault tolerance of individual operations, ensuring the BRT to implement grasping behaviors more accurately. Specifically, individuals only need to move the distal end of the robotic trunk to a position where the camera can capture the object, and the remaining fine alignment is fully automated.\nModification #2.3\nTo alleviate your concern, we have revised this part in the Section 2.4. On Page 12,\n“Subsequently, vision-based control strategies are integrated. When an object enters the camera’s field of view, the robotic arm can automatically align with the center of the object, thereby enhancing grasping accuracy (Fig. S15, Video S7).”\nFig. S15. Vision-based control strategy for BRTs. (A) Automatic alignment between our robotic trunk and an object without operating the joystick to control the BRT. (B) Quantitative results of automatic tracking effect at the end of the BRT. (C) Vision-based control strategy assists in precise grasping of objects.\nVideo S7. Vision-based control strategy for assisting in precisely grasping objects.\n3. Concerns on Application Relevance and Justification\nThe integration of the BRT into a wheelchair platform with a human-machine interface is well executed and visually compelling. However, the system appears to be developed primarily for demonstration purposes, rather than to address a clearly defined assistive need or user-driven challenge. The work lacks a comparison with alternative solutions, such as existing lightweight robotic arms, which could also be mounted on a wheelchair with similar or better functional outcomes. As such, the superiority or necessity of the proposed system is not convincingly justified.\nResponse #3\nThank you for your comments. We compare the differences between our robotic arm and rigid robotic arms in integrating into a wheelchair, as shown in Table S3. First, the invariable rigidity, substantial mass, and lack of compliance of rigid robotic arms raise safety concerns during physical human–robot interaction. As an example, JACO robotic arm has a mass of approximately 6.00 kg, while its maximum payload capacity is only 1.50 kg [S15]. This low payload-to-mass ratio limits efficiency. Meanwhile, its rigidity increases the risk of injury in the event of unintended or imprecise movements. Since rigid arms are unforgiving in collisions, their safe operation demands highly accurate perception systems and precise control algorithms to prevent accidental contact with the user—requirements that can be relaxed when using soft robotic systems due to their inherent compliance. The other challenge arises when rigid robotic arms are used to manipulate objects at greater distances from the wheelchair. As the cantilever length increases, the resulting overturning moment on the wheelchair increases, potentially compromising stability. For the patients with reduced balance control, this situation can lead to hazardous events such as tipping or falls.\nIn our study, we address these challenges by leveraging the advantageous properties of tensegrity structures, which combine lightweight design, structural compliance, and large-scale stiffness modulation. By integrating this robotic trunk into a wheelchair platform, we showcase both its safety and functional versatility in assisting users with a diverse range of activities, thereby validating its practical effectiveness in real-world assistive scenarios.\nModification #3\nTo alleviate your concern, we have added Table S3 in the Supplementary Information and made modifications in the Section 2.4. On Pages 11,\n“To demonstrate the practical utility and assistive potential of our BRT, we integrated it into an electric wheelchair equipped with a control module via human-machine interface (HMI)56. Embedding the variable-stiffness robotic arm into the wheelchair system substantially expands its functional capabilities beyond mobility support. The ability to tune stiffness not only improves task versatility, including delicate manipulations and stable load-bearing actions, but also ensures safer interactions in human-centered environments compared to the integration of rigid robotic arms (Table S3). Moreover, the wheelchair’s mobility naturally complements the BRT’s structural behavior: it compensates for the modest geometric shortening accompanying high-stiffness actuation, thereby preserving workspace and ensuring that the end-effector remains within reach of target objects.”\nLength Mass Overturning Carrying\nReference Stiffness\n(m) (kg) moment (N/m) capacity (kg)\n[S14] 0.80 12.97 51.88 1.00 High\n[S15] 0.90 6.00 27.00 1.50 High\nOur work 0.92 1.05 4.83 2.50 Low and High\n[S14] Tsui K, Yanco H, Kontak D, et al. Development and evaluation of a flexible interface for a wheelchair mounted robotic arm [C]//Proceedings of the 3rd ACM/IEEE International Conference on Human Robot Interaction. 2008: 105-112.\n[S15] Maheu V, Archambault P S, Frappier J, et al. Evaluation of the JACO robotic arm: Clinico-economic study for powered wheelchair users with upper-extremity disabilities [C]//2011 IEEE International Conference on Rehabilitation Robotics. IEEE, 2011: 1-5.\nComment #4\nMinor Comments\nIt is also unclear whether long-term reliability concerns, such as cable creep, spring fatigue, or material degradation, have been assessed or mitigated.\nResponse #4\n1. The concerns of cable creep:\nWe appreciate your comments and the opportunity to clarify this point. In response to the reviewer’s concerns regarding the cable creep, we have conducted dedicated experiments to characterize its impact. Since cable creep refers to the time-dependent elongation of the cable under sustained tensile loading, we maintain a 200 mm cable under a constant tensile force of 20 N for 30 minutes to evaluate this effect. During this period, the cable exhibits an elongation of 0.45 mm due to creep (Fig. R2), corresponding to only 0.22% of its original length. Furthermore, since the robotic trunk requires increased stiffness during operation, the cable forces can reach approximately 100 N. To replicate this condition, we subject a 200 mm cable to a constant tensile force for 10 minutes. The resulting creep elongation is measured to be 0.58% of the original length. Taken together, these results indicate that the magnitude of cable creep in our system is minimal. For this reason, the effect of creep is not explicitly considered in the initial design and control framework. However, we acknowledge that long-term creep will accumulate and impact system reliability over extended operation. Consequently, in the revised manuscript, we highlight cable creep as a current limitation in the Discussion section and identify it as a focus for future work. Specifically, we will attempt to address this limitation through the integration of adaptive tensioning mechanisms, which would further enhance the durability and robustness of tensegrity-based robotic trunks.\n2. The concerns of spring fatigue:\nTwo types of springs are used, and the corresponding dimension are 1 mm-5 mm-30 mm (connecting spring) and 1 mm-5 mm-50 mm (reinforcing spring). When the robot is contracted, the stretch length of the springs reaches their maximum. Subsequently, we use a tensile testing machine to cyclically stretch the springs to their maximum length. After 500 cycles, the length comparison of the springs is shown in Fig. R3. The consistency of the spring’s length before and after stretching indicates that the springs in the robotic system has favorable fatigue resistance.\nFig. R3. Comparison of spring lengths after cyclic stretching.\n3. The concerns of material degradation:\nIn addition to both cables and springs, the rigid frames manufactured by 3D printing are made of aluminum alloy, which has strong bending rigidity. Notably, these frames did not deform or be deformed throughout the entire experiments.\n4. The concerns of stress hysteresis:\nAdditionally, we also discover that stress hysteresis phenomenon occurs in cables after stretching, and this directly impacts the predictive accuracy of theoretical models. However, accurately modeling stress hysteresis in the cables is challenging, since it requires solving complex nonlinear mechanical equations that are difficult to derive and computationally intensive to implement. In this study, we adopt a practical approach to mitigate the effect of stress hysteresis on our BRT by pre-processing the cables prior to their integration. To show the effectiveness of this approach, we use a mechanical testing machine to subject the cables to repeated stretching cycles before installation. As showcased in Fig. S1A, the hysteresis effect is particularly pronounced during the initial tension stage (N < 100). If such untreated cables are installed C\ndirectly into the system, repeated actuation will gradually elongate them, reducing their actuation efficiency and degrading system performance over time. Conversely, after a high number of stretching cycles (N > 500), the hysteresis effect is substantially diminished, as shown in Fig. S1B. Subsequently, C\nwe quantitatively compare the hysteresis behavior after the 1st and the 500th cycles. Following the first stretch, the cable exhibits an elongation of 11.41 mm (Fig. S1C). If such elongation caused by material hysteresis is neglected in the system’s theoretical model, the accuracy of model predictions will be significantly compromised. In contrast, after 500 pre-stretching cycles, the cable length variation due to 12\ncreep is reduced to only 0.04 mm—a negligible amount in terms of system performance. Therefore, to ensure consistent actuation and maintain model accuracy, all cables used in our robotic system undergo a pre-stretching process. This simple yet effective procedure substantially mitigates stress hysteresis-induced performance degradation and improves the reliability of the BRT over its operational lifespan.\nModification #4\nIn the revised version, we have added Fig. S1 in the Supplementary Information and fully revised this part in the Section 2.1 and Discussion. On Pages 5 and 15,\n“As shown in Fig. 2A, the BRT consists of three main sections: the basal, middle, and distal portions. The basal portion is a rigid disk with six prefabricated holes, through which six actuation cables (No. 1-6) are threaded. Notably, to avoid potential stress hysteresis issues during cable stretching, we pre-stretch the cables 500 times and then integrate them into the robotic system (Fig. S1).”\n“First, both cable creep and stress hysteresis may affect long-term reliability and model accuracy. Future designs may address this issue by incorporating an adaptive tensioning mechanism.”\nFig. S1. Characterization of stress hysteresis. (A) Initial stretching from cycles 1 to 100. (B) Stretching from cycles 401 to 500. (C) Comparison of force-displacement between the first and 500th cycles.\nComment #5\nThe human evaluation is limited to a single post-stroke participant. Broader user studies or a more systematic assessment would be needed to substantiate the assistive potential of the system.\nResponse #5\nWe thank the reviewer for this valuable comment. In our current study, we demonstrated the assistive capabilities of the BRT-enabled wheelchair through a longitudinal, one-week evaluation involving a post-stroke individual across multiple real-world scenarios (see Fig. 6, Videos S7-S9). While this provides important early evidence of practical utility, we fully acknowledge that a broader user study will be essential to more rigorously validate generalizability and clinical impact. However, due to the limited access to patient recruitment under current hospital collaboration agreements and funding constraints on multi-subject trials, the scope of human evaluation in this study remains limited. These practical challenges reflect typical barriers in early-stage translational research involving medical robotics. Looking ahead, we plan to expand our collaboration with rehabilitation centers to conduct larger-scale user studies. Additionally, we will explore the integration of intent recognition, shared autonomy, and personalized interfaces to improve user adaptability, autonomy, and long-term rehabilitation outcomes.\nTo alleviate your concern, we add the following descriptions in the Discussion.\nOn Page 15, “Lastly, promoting active user engagement is essential for improving long-term outcomes. Future developments will focus on systematic evaluation across diverse user populations and real-world conditions. In addition, future systems will explore intent recognition, shared autonomy, and personalized control interfaces to increase accessibility.”\nThe manuscript under consideration presents a novel cable-driven robotic trunk which leverages tensegrity structures and passive springs to provide continuously-variable stiffness over a large range. Importantly, the tensegrity structure and passive spring configuration is such that although the springs are close to linear, the macroscopic deformation behavior is highly nonlinear, and the variable stiffness is obtained by exploiting this nonlinearity. The authors describe their trunk design, study its behavior through modeling and a series of experiments, and demonstrate a real-world use case where the trunk is mounted on an electric wheelchair. The trunk design is novel and highly interesting, thoroughly evaluated with the presented experiments, and the paper is well written.\nOur Response:\nWe sincerely thank the reviewer for your thoughtful evaluation of our manuscript and for acknowledging the clarity of our novelty, engineering effort, and writing involved. We respectfully address each in our point-by-point responses below.\nComment #1\n1. I am missing a description of the overall size/weight of the trunk in the main text. This is important to interpret results such as length change, which is given in cm.\nResponse #1\nThank you for your suggestions. The descriptions have been modified in the revised manuscript.\nModification #1\nTo alleviate your concern, we have added these physical parameters in Section 2.1. On Page 5,\n“We propose a tensegrity-based BRT (length: 920 mm and weight: 1.05 kg) that achieves both dexterous morphing and powerful load-bearing capabilities through controlled cable interactions.”\nComment #2\n2. I am missing a description of how the cable attaches to the frames. Presumably the cables driving the distal portion are anchored at the most distal frame, pass through eyelets in 7 frames, before entering the cable sheath at the 9th frame?\nResponse #2\nThank you for your comments. There are two sets of cables (No. 1-3 and No. 4-6), and they actuate middle and distal portions, respectively. Cables 1-3 pass through the pre-fabricated holes located in the rigid frames of the middle portion. For cables 4-6, we apply sheaths to allow the cables to pass through pre-fabricated holes in the distal portion, bypassing the middle portion, as shown in Fig. S2.\nModification #2\nTo show the path of these cables passing through more clearly, we have added Fig. S2 and made modifications in Section 2.1. On Page 5,\n15\n“The middle and distal portions each contain nine identical rigid frames (denoted as Fi, i = 1,…,9), which are actuated by cables No. 1-3 and cables No. 4-6, respectively. Additionally, to prevent physical interference between these two sets of cables, cables No. 4-6 are enclosed in stiff sheaths, and pass through the pre-fabricated hole in the distal portion, bypassing the middle portion (Fig. S2, Video S1).”\nFig. S2. The route of cables 1 and 4 passing through.\nComment #3\n3. How does cable friction come into play? Would be pertinent to discuss what effect unmodelled friction would be expected to have on the trunk behavior.\nResponse #3\nWe would like to thank the reviewer for pointing out this issue. During deformation of robotic trunks, friction between cables and frames will reduce the achievable bending angle. In addition, repeated friction accelerates cable wear and may lead to premature failure under tension, thereby shortening service life. To mitigate these effects, lubricating oil is applied at the cable–frame contact points to reduce friction. The measured friction coefficients before and after lubrication are shown in Fig. S10. Since lubrication effectively minimizes frictional effects, friction is not explicitly incorporated into the model, which allowed for a reduction in model complexity.\nModification #3\nTo improve the accuracy of the description, we have added Fig. S10 and made modifications in Note S2 in Supplementary Information. On Pages 7 and 20,\nBased on the finite element method, all nodes of the system of BRT are numbered. Then, according to the mapping relationship between the local node numbers of each component and the global degree of freedom numbers, the generalized force , gravity , and external force vector of each element are superimposed onto the generalized f𝑒orce , gravit𝑒y , and external force vector 𝑒 of the system. Here, as 𝒇𝑘 𝒈𝑘 𝒑𝑘\nlubricating oil is applied at the cable-frame contact points to minimize frictional effects, friction is not 𝒇 𝒈 𝒑\nexplicitly incorporated into the mechanical model (Fig. S10). Therefore, the static equilibrium equation of the system is further established.\n(S28)\nwhere can be calculated by assembTling the the generalized force vector of every element:\n𝜱𝑞𝝀−𝒇(𝒒)−𝒈−𝒑 = 𝟎\n16\n𝒇(𝒒) 𝒇(𝒒) =\n. The system gravity force vector and the system external force vector are obtained in a similar wa𝑛y: 𝑒 , . The term physically represents the control force vector applied to ⋃𝑘=1𝒇𝑘 𝒈 𝒑\nthe clustered 𝑛cable𝑒s [S3]. 𝑛 𝑒 T\n𝒈 = ⋃𝑘=1𝒈𝑘 𝒑 = ⋃𝑘=1𝒑𝑘 𝜱𝑞𝝀\nFig. S10. Evaluation of friction coefficient during pulling cables.\nComment #4\n4. What is the natural frequency of the trunk for different stiffness configuration? And how does it change with end effector load? One problem frequently arising with soft systems is that they are susceptible to vibrations-is this an issue here? If so, how can it be circumvented? (e.g. you only have springs within the trunk, but no dampers).\nResponse #4\nThank you for your suggestions. To calculate the natural frequency of the robotic system, we first derived the corresponding mass matrix M and stiffness matrix K, and linearized the stiffness matrix at the equilibrium point of specific configurations. The natural frequency can be described.\n(R1)\nwhere, λ denotes the eigenvalue of equation .\nn 𝜔𝑛 = √𝜆𝑛\nAccording to the above method, the first-order natural frequency of robotic systems under different stiffness (𝑲−𝜆𝑴) = 0\nor end-effector load is showcased in Fig. R1. Theoretical results indicate that as the stiffness increases, the natural frequency of the robotic system slowly rises. In contrast, this frequency is not sensitive to changes in the end-effector load.\nAlthough vibration is common in these undamped robotic systems, the low natural frequency of our BRT will not cause such issue. For soft robotic systems with higher vibration frequencies, active control methods can be introduced to suppress vibration phenomena in practical applications.\nFig. R1. Effects of length variation and end-effector load on natural frequency.\n5. Fig 2: \"Reinforcing Spring\" label points to sheathed cable; should be pointing to purple spring.\nResponse #5\nThank you for kindly reminding us. We have modified Fig. 2A in the revised manuscript.\nModification #5\nWe have revised the original description. On Page 23,\nFig. 2A. The trunk consists of basal, middle, and distal portions, each composed of multiple tensegrity frames connected via cables, connecting springs, and reinforcing springs. The cable sheath encases the internal cables to avoid physical interference between cables. A detailed schematic illustrates the connection between adjacent frames, where connecting springs (blue) and reinforcing springs (purple) enhance structural integrity.\nComment #6\n6. What is the reason for a 2 x 9 frame configuration? Presumably one could vary both the number of frames per portion and the number of different portions (using 3 cables per portion)?\nResponse #6\nThank you for your comments. The overall length of the robotic arm is determined in accordance with the geometric constraints and operational requirements imposed by the wheelchair’s dimensions. Specifically, the number of rigid frames directly influences the arm’s reach, maneuverability, and efficiency in assisting patient manipulations. If the number of frames is insufficient, the robotic arm will lack the necessary reach to interact effectively with the intended workspace, thus limiting its ability to perform patient-assistive tasks. Conversely, an excessive number of frames introduces structural redundancy, greatly increases system complexity, and may compromise control performance and energy efficiency, making it unsuitable for the intended application.\nThrough an analysis based on the physical dimension of a wheelchair and the anticipated distance to the objects of operation, an arrangement consisting of 18 frames offers an optimal balance between functionality and complexity. The stiffness modulation of robotic arms is achieved through the use of three tensioned cables per portion. When either the middle or the distal portion becomes excessively long, the time required for stiffness modulation increases due to the greater travel distance and inertia of the actuation mechanism. To address this and ensure rapid response in stiffness modulation, the frames are evenly divided into two portions. This configuration reduces the regulation time for each portion, enhances the precision of stiffness 18\ncontrol, and maintains the overall responsiveness of the robotic arm during patient-assistive tasks.\nComment #7\n7. It would be useful, though not required, if the authors could provide some intuition regarding the particular design of the tensegrity structure used in the trunk. Which properties are important (e.g. the resultant nonlinear macroscopic behavior)?\nResponse #7\nThank you for your suggestions. In natural systems such as an elephant trunk, active control of muscle tension facilitates the elastic energy within the tissue, enabling stiffness to be modulated. Reproducing this mechanism directly in artificial systems would require an impractically large number of active actuators, posing significant challenges in terms of weight, complexity, and energy consumption. In this study, we reveal that a comparable improvement in stiffness can be attained by utilizing the passive deformation capacity of elastic structural components. This insight positions tensegrity architectures—comprising a large number of interconnected elastic elements—as an ideal physical prototype for implementing bioinspired stiffness modulation in robotic systems.\nModification #7\nTo alleviate your concern, we have added the following descriptions in the Introduction. On Page 4,\n“In this study, we present a bionic robotic trunk (BRT) that leverages synergistic and antagonistic mechanisms to implement rapid and wide-range stiffness modulation (Fig. 1A). Inspired by the biomechanics of elephant trunks, which modulate internal stiffness through active tensioning of antagonistic muscles to redistribute elastic energy 3, our BRT adopts a cable-driven tensegrity skeleton—a lightweight and compliant architecture that can redistribute elastic energy via cable-induced deformation of struts and springs 41,42.”\nComment #8\n8. Fig 3 E+F: Is the stiffness a true exponential curve? Or is it just that it is well approximated by an exponential curve? If it is an approximation then I would suggest to make the language more precise. I would find it counterintuitive if linear springs + geometric nonlinearities were to produce an exponential relationship?\nResponse #8\nWe thank the reviewer for bringing this to our attention. In our study, we obtained the total elastic energy by accumulating the elastic energy of all springs. The mapping relationship between robotic energy and structural length is obtained through exponential function fitting.\nModification #8\nTo avoid this misunderstanding, we have revised the original description. On Page 8,\n“The total elastic energy accumulated in the structure is written as , which approximately increases exponentially with as shown by both experimental and theoretical curves in Fig. 𝑊E = Σ(𝑊E_c𝑖 +𝑊E_𝑟𝑖)\n3E.”\nΔ𝐿\n9. In images/video, I would recommend to make consecutive frames alternating colors, for improved legibility.\nResponse #9\nThank you for your suggestions. We have modified Fig. 2A, Fig. 2B, Fig. S4, and Video S1.\nModification #9\nTo improve the legibility, we have made consecutive frames alternating colors. On Page 23,\nFig. 2. Tensegrity-based design of the BRT.\nVideo S1. Composition and connection relationship of the BRTs.\n20"}, {"round": 2, "reviewer_comments": {"reviewer_1": "Thank you for the revision effort. The authors present a bio-inspired variable-stiffness continuum robot based on a tensegrity architecture, combined with synergistic and antagonistic stiffness regulation. The revised manuscript includes additional experiments, modeling analyses, and clarification in response to the first-round reviews. The engineering system is comprehensive and demonstrates a suite of manipulation and assistive tasks, including a proof-of-concept study with a post-stroke user.", "reviewer_2": "This is the second review round of the manuscript NCOMMS-25-50877-T.\nThe authors have provided thorough responses to the questions raised in the first review round, and have updated the manuscript accordingly. The updates largely address my concerns, but I have a couple of follow-up comments below.\nReviewer #1 was in the last round concerned with the novelty, scientific depth, and generalizability of the work, in particular given the top-tier venue. I agree with this concern and wonder if the publication might be better suited for a different venue. While the engineering effort of this work is commendable, the scientific value of advancing theory and generalization is harder to judge.\nI have some smaller comments to the replies to my (Reviewer #2) feedback from round 1:\n- Cable friction: understood that this is omitted for the sake of reducing model complexity. But what would be worth noting is that under the presence of friction, the tension in the cable will no longer be uniform along its length, which will in turn change the deformed shape.\n- I do not understand how the natural frequency can be independent of end effector load. The end effector load will be a (significant) part of the mass matrix, so an unchanged frequency would require a corresponding change in the stiffness which would in turn lead to a change in length that you say is not occurring. Please elaborate."}, "author_response": "Responses to Comments on Manuscript No. NCOMMS-25-50877A\nWe sincerely thank two reviewers for thoroughly reading our manuscript. The constructive comments and suggestions are fully addressed point-by-point in this letter. For the convenience of the reviewers, we marked the corresponding modifications in our revised manuscript in blue. We believe that the concerns raised by two reviewers have highlighted areas in need of further attention and our modifications have made the manuscript more suitable for publication in Nature Communications.\nReviewer #1\nThank you for the revision effort. The authors present a bio-inspired variable-stiffness continuum robot based on a tensegrity architecture, combined with synergistic and antagonistic stiffness regulation. The revised manuscript includes additional experiments, modeling analyses, and clarification in response to the first-round reviews. The engineering system is comprehensive and demonstrates a suite of manipulation and assistive tasks, including a proof-of-concept study with a post-stroke user.\nOur Response:\nWe appreciate your summary of the manuscript and encouraging comment.\nThis is the second review round of the manuscript NCOMMS-25-50877-T.\nThe authors have provided thorough responses to the questions raised in the first review round, and have updated the manuscript accordingly. The updates largely address my concerns, but I have a couple of follow-up comments below.\nOur Response\nThank you for the assistance provided in improving our manuscript. We sincerely hope that these revisions meet your requirements.\nReviewer #1 was in the last round concerned with the novelty, scientific depth, and generalizability of the work, in particular given the top-tier venue. I agree with this concern and wonder if the publication might be better suited for a different venue. While the engineering effort of this work is commendable, the scientific value of advancing theory and generalization is harder to judge.\nOur Response\nWe sincerely thank the reviewer for their continued engagement and thoughtful critique. we would like to highlight that this study does not merely present an engineering implementation, but rather introduces and experimentally validates a biomechanics-inspired structural principle—namely, a reconfigurable tensegrity-based robotic trunk that leverages antagonistic elastic energy redistribution to achieve continuous, wide-range stiffness modulation. This principle draws direct inspiration from the active stiffening behavior of elephant trunks and is implemented through a scalable tensegrity skeleton, offering a novel route to rapid and continuous stiffness tuning across a broad range (23.94 to 542.47 N/m at 1.06 Hz), without the need for dense actuator arrays or phase-changing materials. Our design translates a key biological insight into a physical system with tunable mechanical response, supported by modeling (Supplementary Information), experimental validation, and real-world assistive trials.\nReviewer #1 had initially raised concerns regarding novelty. In the revised submission, we addressed these through expanded modeling, comparative analysis, and validation. As noted in the latest comments, Reviewer #1 has acknowledged these points to be satisfactorily addressed. Therefore, we believe this interdisciplinary study—spanning bioinspired mechanics, soft robotics, and assistive human–machine integration—presents a meaningful contribution aligned with the scope of Nature Communications.\nI have some smaller comments to the replies to my (Reviewer #2) feedback from round 1:\nComment #1\nCable friction: understood that this is omitted for the sake of reducing model complexity. But what would be worth noting is that under the presence of friction, the tension in the cable will no longer be uniform along its length, which will in turn change the deformed shape.\nOur Response\nThank you for your invaluable comments. In the last round, we measured friction coefficients before and after lubrication, as illustrated in Fig. S10. Since lubrication effectively minimizes frictional effects, friction is not explicitly incorporated into the model, which allowed for a reduction in model complexity.\nSubsequently, the approximate consistency between theoretical and experimental results proves that ignoring cable friction in the model can still accurately predict the morphology of the robot, as shown in Fig. S11.\nFig. S11. Deformation comparison between experimental and theoretical results, including (A) contraction (length ranging from 0 to 30 cm) and (B) bending (angle ranging from 10 to 40°). (C)-(D) Quantitative comparison results of corresponding contraction and bending deformations.\nAlthough many efforts are made to reduce the effects of cable friction on model accuracy, we also agree with the reviewer’s opinion that the cable friction can introduce morphological discrepancies. Consequently, for future applications involving model-based control, it is essential to explicitly account for cable friction. Given the complexity of theoretical models, we would like to leverage data-driven approaches to compensate for errors arising from cable friction and other unmodeled factors.\nModification #1\nFirst, both cable creep and friction may affect long-term reliability and model accuracy. Future studies may address these issues by utilizing adaptive tensioning mechanisms and data-driven compensation methods.\nComment #2\nI do not understand how the natural frequency can be independent of end effector load. The end effector load will be a (significant) part of the mass matrix, so an unchanged frequency would require a corresponding change in the stiffness which would in turn lead to a change in length that you say is not occurring. Please elaborate.\nOur Response #2\nWe thank the reviewer for this thoughtful comment. In our previous response, we misunderstood your point and treated the end-effector load solely as an external force, which affects the robot’s configuration but does not modify its mass matrix. Under that assumption, the natural frequency would not be varied. According to your comments, we have considered the end-effector load directly into the mass matrix. Therefore, the natural frequency is influenced by both end effector load and the change in structural length, as illustrated in Fig. S15.\nModification #2\nOn Page 11,\nThe introduction of the robotic gripper has a decrease in the natural frequency of the BRT, as illustrated in Fig. S15.\nFig. S15. Effects of length variation and end-effector load on natural frequency.\n4"}, {"round": 3, "reviewer_comments": {"reviewer_1": "After reviewing the revised manuscript and the authors’ detailed responses, I acknowledge that substantial effort has been made to address most of the technical and experimental concerns raised in the first-round review. The revision adds meaningful enhancements, including expanded modeling details, improved comparative analyses, more systematic stiffness-modulation experiments, and clearer articulation of the biomechanical inspirations. Overall, the engineering system is well executed, and the additional experiments provide a more comprehensive picture of the trunk’s performance across dexterity, stiffness modulation, and assistive tasks.", "reviewer_2": "Thank you for your comments and edits to the paper. I have no further technical comments; I believe that as it stands the paper is complete and scientifically sound."}, "author_response": "Responses to Comments on Manuscript No. NCOMMS-25-50877B\nReviewer #1\nAfter reviewing the revised manuscript and the authors’ detailed responses, I acknowledge that substantial effort has been made to address most of the technical and experimental concerns raised in the first-round review. The revision adds meaningful enhancements, including expanded modeling details, improved comparative analyses, more systematic stiffness-modulation experiments, and clearer articulation of the biomechanical inspirations. Overall, the engineering system is well executed, and the additional experiments provide a more comprehensive picture of the trunk’s performance across dexterity, stiffness modulation, and assistive tasks.\nOur Response:\nWe sincerely thank the reviewer for the evaluation of our manuscript, and greatly appreciate the reviewer’s time and effort.\nReviewer #2\nThank you for your comments and edits to the paper. I have no further technical comments; I believe that as it stands the paper is complete and scientifically sound.\nOur Response\nWe sincerely thank the reviewer for the positive evaluation of our revised manuscript and for recommending its acceptance.\n1"}]

Decision letter