Selective Variable Stiffness Flexible Manipulator for Dexterous In-Hand Manipulation

Abstract

Adaptive grasping and dexterous manipulation of random objects in unstructured environments have broad practical significance. Compared with traditional rigid manipulators, flexible manipulators possess better adaptability and safety, and thus are widely used in industrial, agricultural, and medical fields. However, since flexible manipulators are typically made of soft materials, their stability and dexterity are always limited. To make up for the deficiencies of existing flexible manipulators, this research proposes a variable stiffness flexible element driven by rope and evaluates its performance by finite element simulation and experimental methods. Based on the Fin Ray Effect, the flexible element is then assembled into a novel adaptive flexible manipulator, which can selectively regulate its local stiffness by driving a set of ropes. The flexible manipulator not only has multiple contact modes but also has good self-adaptability when interacting with the external environment. We also establish an integrated experimental platform and control system for in-hand manipulation and conduct quantitative in-hand manipulation experiments to obtain the mapping relationship between the driving input and the displacement of manipulated objects. Finally, we apply the flexible manipulator to daily charging tasks where the charging head can be rotated on demand. The manipulator has a broad application potential in real-world scenarios such as smart homes. In addition, the selective stiffness regulation methods proposed in this study provide a new approach to enhancing the multi-functionality of soft robotic structures.

Keywords

bionic structure flexible manipulator variable stiffness rope drive in-hand manipulation

Introduction

With the rapid development and application of robotics, people have put forward higher requirements for the stability and dexterity of the end-effector. In order to achieve the in-hand manipulation function of robots, common design methods include friction mechanisms or additional mechanical structures. Among them, the methods utilizing friction mechanisms usually involve the re-regulation of the surface friction of the manipulator, which is related to the friction coefficient and normal load. Therefore, friction mechanism-based methods usually have one or more contact surfaces with variable friction, relying on the difference in friction between the surfaces to realize the movement of objects in the hand.^5–7 Friction mechanism-based methods can control the contact and interaction between the manipulator and the object, thus effectively realizing a variety of in-hand manipulation actions. However, the friction mechanism-based method suffers from limited accuracy, complex design, and high cost. On the other hand, adding mechanical structure is a new design idea, such as adding the linkage structure^8–11 or the pneumatic drive mechanism.^12–15 The additional mechanical structure can increase the degrees of freedom and reconfigure the grasping configuration, which enhances the movement space and flexibility of the manipulator. Compared with the method based on the friction mechanism, this method has better response speed and accuracy, but the manipulation structure becomes more complex. To address the limitations of traditional in-hand manipulation design approaches, we propose an innovative design strategy: achieving in-hand manipulation functionality through bionic variable stiffness methods.

Variable stiffness flexible manipulators have good compliance when in contact with objects while, at the same time, showing strong stability and load-bearing capacity in performing tasks. Jamming mechanisms, smart materials, and rope drives are common variable stiffness methods. Among them, the variable stiffness methods based on jamming mechanisms utilize the interaction between different parts of the manipulator. According to the working principle, they can be classified into two categories: one is to change the stiffness with the help of jamming of granules such as rice grains and coffee grains, which is known as the granular jamming method;^16–19 the other is to design an interference layer in the manipulator, that is, to change the stiffness by utilizing the antagonistic effect between the interference layer and the driving layer, which is called the layer jamming method.^20–24 Methods based on jamming mechanisms have the advantage of being simple in design, safe, and reliable, but they usually require activation with the aid of a vacuum, which can increase the cost and complexity of the system. In addition, it requires a sealing membrane, and air leakage can be a challenge. The smart material-driven based method can obtain a larger range of stiffness variation, which utilizes the mechanical properties of certain materials that are easily affected by the external stimulus. Commonly used smart materials in variable stiffness manipulators include low melting point alloys,^25–27 shape memory alloys,^28–31 and dielectric elastomers.^32,33 It is worth mentioning that since smart materials take a certain amount of time to respond to external stimuli, this leads to the disadvantage of slow response speed. Compared with the first two variable stiffness methods, the rope-driven method is to control the expansion and contraction of the rope to realize stiffness change, which has significant advantages such as simple modeling and fast response speed,^34–36 but at the same time, the method also has problems such as the small adjustable range.

Aiming at the prevailing shortcomings of traditional flexible manipulators in terms of stability and dexterity, this study proposes a selective variable stiffness flexible manipulator based on the rope-driven method, which can rely on the variable stiffness method to achieve delicate in-hand manipulation of translating and rotating objects (Fig. 1). Inspired by the working mechanism of muscle fibers in octopus tentacles, we first propose a variable stiffness bionic flexible element. Then, we conduct uniaxial compression experiments on the flexible element to investigate the effects of major structural parameters on its performance and cross-validate it with the help of finite element simulation. Second, based on the Fin Ray Effect, we assemble flexible elements with different structural parameters to form a novel adaptive flexible robotic finger. The results of both finite element simulations and contact experiments show that the manipulator has variable stiffness while maintaining its original compliance. Finally, we establish an integrated experimental platform and control system for the flexible manipulator and conduct quantitative in-hand manipulation experiments to obtain the mapping relationship between the rope pulling length and the movement of the manipulated object. In addition, we apply the variable stiffness flexible manipulator to the charging task, demonstrating the potential of future intelligent robots in the field of smart homes and also expanding the scope of application of flexible manipulators.

FIG. 1.

The proposed selective variable stiffness flexible manipulator is rotating the ball inside the hand.

Methods and Design

Bionic principles

Octopus is a common mollusk, and the muscles in its tentacles can be categorized into three main types according to the direction in which they are arranged: transverse muscles (TM), longitudinal muscles (LM), and oblique muscles (OM).³⁷ All muscles are regulated by a centrally located nerve cord (NC). By regulating the contraction and release of the TM fibers, octopuses can adjust the stiffness of their tentacles (Fig. 2a). Inspired by the working mechanism of octopus muscle fibers, we design a variable stiffness bionic flexible element. The element uses a rope to simulate the TM fibers of the octopus, and the stiffness of the element is regulated by varying the pulling length of the rope, resulting in better adaptability and stability of the whole structure.

FIG. 2.

Bionic principle and structural design of the flexible element. (a) The working mechanism of octopus muscle fibers (TM, transverse muscles; LM, longitudinal muscles; OM, oblique muscles; NC, nerve cord). (b) The flexible element undergoes a large deformation upon external load (the rope is unactivated). (c) The flexible element undergoes a small deformation upon external load (the rope is activated).

Structural design of bionic flexible element

We extend a rope from the midpoint of the lower left edge of the flexible element to the midpoint of the upper right edge to fix it (i.e., between points A and B shown in Fig. 2). In the unactivated state of the rope, the flexible element undergoes a large deformation under external force, as shown in Figure 2b. Whereas, when the rope is in the activated state, the flexible element will undergo smaller deformation or almost no deformation when interacting with the outside world, as shown in Figure 2c. Therefore, the driving rope essentially realizes the change in overall stiffness by modulating the deformation of the flexible element.

Structural design of flexible finger

When a load is applied to a fin, the fin does not bend outward, but rather bends inward to resist the applied load. This phenomenon is known as the Fin Ray Effect.^38,39 From the previous description, we know that the bionic design based on rope actuation can effectively control the deformation mode and effective stiffness of the flexible element. Inspired by the Fin Ray Effect and the idea of modularity, we arrange and combine multiple flexible elements with different structural parameters in a regular manner, which together form an adaptive flexible finger. Each flexible finger includes several rope-driven channels that can independently control the deformation and local stiffness of the corresponding element.

Flexible manipulator system

In order to verify and quantify the in-hand manipulation function, we first assemble two flexible fingers to form a two-finger bionic flexible manipulator. Then, we design a bionic flexible manipulator system capable of intelligently regulating the structural stiffness, as shown in Figure 3a. This manipulator system is mainly composed of ropes, flexible manipulators, micro DC motors, a back-end robotic arm, and a control system. Among them, the rope is responsible for regulating the deformation mode and stiffness of the local element. The micro DC motor controls the movement of the rope and is responsible for providing the driving force. The flexible manipulator is assembled on the back-end robotic arm, and under the collaborative command of the control system, they work together to accomplish the expected operation tasks.

FIG. 3.

Structure of the flexible manipulator system and mechanical properties of the driving rope. (a) Bionic flexible manipulator system with intelligently adjustable structural stiffness. (b) Stress–strain curves of driving ropes under quasi-static tensile experiments. (c) Stress–strain curves of driving ropes under cyclic loading–unloading experiments.

To characterize the mechanical properties of the driving rope, we have conducted additional quasi-static uniaxial tensile experiments and cyclic loading–unloading experiments. Rigid ropes use common nylon materials. The results of the quasi-static uniaxial tensile experiments (Fig. 3b) demonstrate that the driving rope exhibits an excellent linear stress–strain relationship, and its stiffness (elastic modulus) is about 571 MPa. Fracture occurred at a load of 61.15 N, and the ultimate tensile strength calculated based on the effective load-bearing cross-sectional area reached approximately 216 MPa. During the cyclic loading–unloading experiments, all specimens underwent preloading treatment at a 10% stress level. The stress–strain curves obtained from the cyclic loading–unloading experiments are shown in Figure 3c. The periodic cyclic loading–unloading experimental data reveal the viscoelastic behavior characteristics of the material: each cycle forms the stress–strain curve with significant hysteresis effects. Meanwhile, the stress–strain curves during the unloading phase exhibit residual load phenomena when the strain returns to zero, which is mainly influenced by the plastic deformation of the driving rope during the loading process. Furthermore, after five complete loading–unloading cycles, the stress–strain curves of the drive rope basically tend to stabilize, and the subsequent curve almost overlaps the preceding ones. This indicates that the reorganization process of the internal structure of the driving rope is basically completed at this time, and the mechanical response enters a stable state.

Control systems

In order to realize the dexterous in-hand manipulation function, a matching in-hand manipulation control system is also designed. The control system mainly includes the main control board, electronic switches, micro DC motors, L298N motor driver modules, rigid ropes, and Dupont cables. The Arduino UNO is selected as the main control board in this study, which is responsible for generating and transmitting control commands. The micro DC motor can provide large torque with a speed of 16 revolutions per minute and a reduction ratio of 1030. The DC motor utilizes a multistage gear reduction, and it can provide a maximum rated torque of 6.3 N·cm.

The in-hand manipulation control system drives four ropes through four micro motors, thus realizing the regulation stiffness in four specific regions of the manipulator. The variable stiffness elements of the flexible manipulator are defined as the left 1 region, left 2 region, right 1 region, and right 2 region in turn (Fig. 3a). The specific working process is as follows (Fig. 4): After the program runs, the Arduino main control board sends out control signals and subsequently transmits them to the motor driver module. After receiving the control information, the driver module immediately drives the motors to turn and continuously provides power to them. Then, each motor separately drives the movement of the rope connected to it, thus being able to actively regulate the stiffness and deformation of the local area of the manipulator.

FIG. 4.

The working principle of the in-hand manipulation control system.

Results and Discussion

Simulation and experimentation of bionic flexible elements

The performance of variable stiffness bionic flexible elements is related to many structural parameters, so we analyze them by adjusting different structural parameters in finite element simulations. The analysis shows that the structural parameters that affect the mechanical properties of the elements are mainly the height (H) and the tilt angle (θ), as shown in Figure 5a. Therefore, we vary the height (H) and the tilt angle (θ) of the elements, and use Abaqus software to accordingly build 3D models with different structural parameters. Subsequently, we apply homogeneous compression loads to the elements and obtain the load–displacement curves under different structural parameters.

FIG. 5.

Finite element simulation and experiment results of the flexible element. (a) Finite element displacement contour in the unactivated state. (b) Uniaxial compression experiment in the unactivated state. (c) Finite element displacement contour in the activated state. (d) Uniaxial compression experiment in the activated state. (e) Effective stiffness of the flexible element with different angles (rope unactivated; EXP value, experimental value; Cal value, simulation calculated value). (f) Effective stiffness of the flexible element with different heights (rope unactivated). (g) Effective stiffness of the flexible element with different angles (rope activated). (h) Effective stiffness of the flexible element with different heights (rope activated).

The heights (H) of the flexible elements are set to 20 mm, 25 mm, 30 mm, and 35 mm, while the tilt angles are set to 5°, 8°, 11°, and 14°, and the thickness is 20 mm. Thermoplastic polyurethane rubber (TPU83A) is selected as the base material to 3D print the prototype. The software analysis shows that the first-order Mooney–Rivlin model fits the strain–stress curve of the fabricated material (TPU83A) well. In order to simulate the mechanical properties of the elements more realistically, the hyperelastic material is chosen for the model, and the first-order Mooney–Rivlin model is used for the strain potential (C10 = 0.018, C01 = 2.834, D1 = 0.035). At the same time, we apply a fixed boundary condition to the lower surface of the element (Fig. 5), while a uniform displacement is applied to the upper surface. It should be noted that the other surfaces of the element are always kept free. In addition, the meshing is done with C3D8R with an approximate size of 1 mm. At the same time, we use the connector settings to constrain the length of the element diagonal, so that its length is always constant. The element diagonal is shown as the dashed line in Figure 5c. In the finite element simulation, we sequentially apply a uniform displacement of 3 mm to different elements, and the displacement contours are shown in Figure 5a and c.

In order to verify the accuracy of the finite element simulation results, prototypes of flexible elements with different structural parameters are fabricated and subjected to uniaxial compression experiments. The process of the compression experiment is shown in Figure 5b and d. Based on the load–displacement curves obtained by simulation and experiment, we calculate the effective stiffness of the flexible elements with different structural parameters (Fig. 5e–h). It is worth mentioning that the rope-driven bionic variable stiffness-based design significantly enhances the overall stiffness and stability of the element, with higher heights and angles producing higher stiffness changes. For example, at an angle of 14° and a height of 20 mm, the addition of a rope will increase the stiffness by more than 10 times. In addition, since the ropes used in the experiments are not rigid ropes in the full sense, there are some errors in the experimental and simulation results.

Simulation and experimentation of flexible finger

In order to simulate the contact experiments between the finger and external objects, we build a regular hemisphere model with large stiffness. Same as the flexible elements, the model of the manipulator finger is also made of hyperelastic material, while the model of the regular hemisphere is made of linear elastic material. In the finite element simulation, we fix the bottom surface of the robotic finger while applying a uniform lateral displacement to the hemisphere to simulate its gradual contact. The finite element results show (Fig. 6a and c) that the local stiffness of the finger in contact with the object is significantly improved, while the intrinsic self-adaptation behavior of the Fin Ray structure remains unchanged in the unactivated region.

FIG. 6.

Analysis of the characteristics of variable stiffness flexible fingers and grasping experiments. (a) Displacement contour of finite element simulation (rope is unactivated). (b) Results of contact experiment (rope is unactivated). (c) Displacement contour of finite element simulation (rope is activated). (d) Results of contact experiment (rope is activated). (e) The contact experiment platform for the flexible finger. (f) Results of finite element simulations and contact experiments for the flexible finger (FEM, finite element method; EXP, experiment). (g) Results of the grasping experiments (rope is unactivated). (h) Results of the grasping experiments (rope is activated).

We design and construct a contact experimental platform for the bionic flexible finger (Fig. 6e). The experimental platform mainly consists of a vise, a frame, a motion stage, a force sensor, and a signal acquisition device. The vise fixes the position of the flexible robotic finger. One end of the frame is connected to the motion stage, and the other end is connected to the rigid hemisphere. The S-type sensor utilized in the experiment features a measurement range of 50 N and a resolution of 0.05% of its full-scale range, enabling high-sensitivity force measurement data acquisition. A signal acquisition device is then used to record the output signals from the force sensors and transfer the collected data to a computer for further processing and analysis.

In the contact experiment, the hemispheres gradually contact and squeeze the flexible finger, and the experimental process is shown in Figure 6b and d. Analyzing the experimental data collected by the force sensor, we obtain the nearly linear mapping relationship between the contact force applied to the robotic finger and its displacement (Fig. 6f). In addition, the finite element simulation of the flexible finger is basically consistent with the experimental results within the error allowance. We find the contact stiffness of the flexible finger is approximately doubled when the driving rope is activated, proving the concept of the selective stiffness regulation.

To quantify the grasping capability of the variable stiffness manipulator, we also carry out grasping comparison experiments under two conditions: the drive rope is unactivated and the drive rope is activated (Fig. 6g and h). We find that the stabilized grasping force of the gripper is increased by approximately 40–50% after the rope is activated. Additionally, it should be particularly noted that since the gripper is integrated into a linear rail platform (Fig. 3a), the effective size range of graspable objects primarily depends on the travel length of the rail. In this study, the effective travel length of the rail used is 55 mm, so the gripper’s effective grasping size range is 0–55 mm.

Quantitative in-hand manipulation

In this section, we utilize the selective variable stiffness finger to achieve more flexible in-hand manipulation tasks. By precisely controlling the stiffness of different elements, the manipulator has multiple variable stiffness modes (Supplementary Video S1), such as unilateral variable stiffness and bilateral variable stiffness, so that the in-hand manipulation of objects can be achieved. In order to quantitatively evaluate the in-hand manipulation capability of the flexible manipulator, we test the relationship between the rope pulling length and the displacement (translation and rotation) of the manipulated object. We first fabricate regular spheres and hexagonal prisms as manipulated objects by fused deposition molding. Figure 7a demonstrates the in-hand manipulation of translational objects using a mode that only adjusts the stiffness of the left 1 region; Figure 7c shows another set of translational object manipulations using a mode that adjusts the stiffness of both the left 1 and right 1 regions. Figure 7e illustrates an in-hand rotating object manipulation, where the mode employed is to adjust the stiffness of the left 1 region and the left 2 region sequentially; and in Figure 7g, the mode employed is to adjust the stiffness of the left 1 and the right 1 regions at the same time. To obtain better results, we set the friction coefficients of the left and right finger surfaces of the manipulator to have a certain difference when performing the rotation manipulation. The experimental results show that the bionic flexible manipulator we designed is able to realize the translation or rotation operation of the object through multiple variable stiffness modes (Supplementary Video S2), which is difficult to be realized in the traditional way. Based on the experimental data, we also establish the mapping relationship between the rope pulling length and the translational and rotational displacements of the manipulated object, which can be used to guide the practical application of the in-hand manipulation at a later stage (Fig. 7b, d, f, and h).

FIG. 7.

Results of the quantitative in-hand manipulation experiments. (a) Translation of the object (adjusting only the left 1 region). (b) Curve of the relationship between the rope pulling length and the amount of translation of the manipulated object (adjusting only the left 1 region). (c) Translation of the object (adjusting the left 1 and the right 1 regions at the same time). (d) Curve of the relationship between the rope pulling length and the amount of translation of the manipulated object (adjusting the left 1 and the right 1 regions at the same time). (e) Rotation of the object (adjust the left 1 region first and then adjust the left 2 region). (f) The relationship curve between the rope pulling length and the rotation of the operated object (adjust the left 1 region first and then adjust the left 2 region). (g) Rotating the object (adjusting the left 1 and right 1 regions at the same time). (h) The relationship curve between the rope pulling length and the rotation of the operated object (adjusting the left 1 and right 1 regions at the same time).

Adaptive in-hand manipulation

In order to verify the adaptive ability of our designed bionic flexible manipulator to different objects in unstructured environments, we conduct adaptive experiments for in-hand manipulation (Supplementary Video S3). In this section, we select common objects such as headphones, pen caps, and book clips as manipulated objects. Based on the experimental results, we know that the flexible manipulator can perform both translational manipulation on objects of different shapes, such as headphones, and effectively perform rotational manipulation on objects such as pen caps (Fig. 8). The bionic flexible manipulator can both smoothly grasp common objects and dexterously perform in-hand manipulation on objects with different qualities and different shapes. The adaptive experiments of in-hand manipulation further demonstrate the good generality and adaptability of our proposed manipulator.

FIG. 8.

The results of the adaptive experiments for in-hand manipulation. (a) Translational manipulation of the earphone. (b) Translational manipulation of the clip. (c) Rotational manipulation of the pen cap. (d) Rotational manipulation of the clip.

Practical application

In the previous sections, we demonstrate the operability and adaptiveness of the flexible manipulator. Therefore, flexible manipulators have a vast potential for real-life applications, such as assisting in the charging of common items such as laptops and Bluetooth headsets or aiding in the precise docking of sockets and plugs (Fig. 9). In order to further validate the potential of the manipulator in practical applications, we apply it to the charging task, especially the docking process between the charging cable interface and the charging slot. Currently, the mainstream charger interfaces are flat design or straight angle design. This design requires one to precisely adjust the position and attitude of the charging cable to ensure that the charging interface can be correctly and smoothly inserted into the charging slot. Accomplishing this maneuver is notoriously difficult for most current robot hands. Here, we show the application of the selective variable stiffness flexible manipulator to the charging task to ensure that the charging task is completed successfully. The working process of using the manipulator to adjust the position and attitude of the charging interface is shown in Figure 9 and Supplementary Video S4, which is mainly divided into the following three steps: Step 1: The rear-end robotic arm drives the flexible manipulator to move, so that the manipulator stably grasps the charging cable with the interface. Step 2: The in-hand manipulation control system issues commands to control the manipulator to adjust the interface of the charging cable to a suitable position and attitude. Step 3: Programming and controlling the movement of the rear-end robotic arm, so that it drives the charging interface close to the charging slot and finally inserts it successfully into the charging slot.

FIG. 9.

Potential application scenarios for flexible manipulators and the process of assisted charging tasks.

The experimental results of applying the in-hand manipulation function during the charging process are shown in Figure 10. Figure 10a demonstrates that the charging task is not successfully completed when the position and attitude of the charging interface are not adjusted. In contrast, Figure 10b demonstrates that the charging interface is successfully inserted into the charging slot after the position and attitude of the charging interface are adjusted with the help of a flexible manipulator. It can be observed through the detail drawings (Fig. 10b 1–5) that the interface is precisely adjusted to a horizontal position by the manipulator from its initial position. Once the charging cable interface was adjusted to the correct position, the charging task was completed with the help of the rear-end robotic arm.

FIG. 10.

Practical application of the in-hand manipulation function. (a) Charging failure (position and attitude of the charging interface are not adjusted). (b) Charging success (position and attitude of the charging interface are adjusted within the manipulator hand).

Conclusion

With the rapid development of artificial intelligence and human–computer interaction, it is urgently hoped that the new generation of robots can have hands with the same dexterity as human beings. The adaptability and safety of flexible manipulators make them expected to become a new generation of end-effectors, but the existing flexible manipulators generally have poor stability and insufficient dexterity. To make up for the shortcomings of existing flexible manipulators and inspired by the working mechanism of muscle fibers of octopus tentacles, this article proposes a variable stiffness bionic flexible element. Meanwhile, a novel bionic flexible manipulator is successfully designed on the basis of the flexible element. The flexible manipulator not only has variable local contact stiffness but also effectively realizes dexterous in-hand manipulation.

This article focuses on the design principles, structural parameters, performance characterization, and applications of a selective variable stiffness bionic flexible manipulator, aiming to provide theoretical and practical support for the design and development of future flexible manipulators. We evaluate in detail the effects of the structural parameters on the performance of the bionic flexible element by finite element simulations and experiments. On this basis, we introduce the Fin Ray Effect and the modular design concept, and propose a novel adaptive flexible finger. Subsequently, we establish an in-hand manipulation control system for the bionic flexible manipulator and achieve fine manipulation of a sphere and a hexagonal prism. The flexible manipulator can both smoothly grasp common objects in life and perform in-hand manipulation on objects of different shapes and weights. Finally, we successfully apply the flexible manipulator’s in-hand manipulation function to daily charging tasks. The flexible manipulator proposed in this article realizes in-hand manipulation by local stiffness regulation, instead of by adding complex mechanical structures, which provides an important reference for the design and delicate operation of future soft robots. In our future work, we plan to introduce tactile sensing technology to further enhance the intelligence level and sensing ability of this bionic flexible manipulator,^40–42 so as to realize more accurate and efficient grasping and manipulation functions.

Authors’ Contributions

B.G.: Investigation, formal analysis, methodology, writing—original draft, and writing—review and editing. Z. Zhao: Conceptualization, methodology, writing—review and editing, resources, and supervision. Z. Zhang: Investigation, formal analysis, and validation. H.L.: Supervision, funding acquisition, and project administration.

Footnotes

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This work was supported by the National Natural Science Foundation of China (Grant No. 12372162) and the Fundamental Research Funds for the Central Universities (Grant No. 2024CX06021).

Supplemental Material

References

Laschi

, Mazzolai

, Cianchetti

. Soft robotics: Technologies and systems pushing the boundaries of robot abilities. Sci Robot, 2016; 1(1):eaah3690; doi: 10.1126/scirobotics.aah3690

, Li

, Gao

, et al. Advances in flexible robotic manipulator systems—Part II: Planning, control, applications, and perspectives. IEEE/ASME Trans Mechatron, 2024; 29(3):1680–1689; doi: 10.1109/TMECH.2024.3359334

Guo

, Li

, Fang

, et al. Encoded sewing soft textile robots. Sci Adv, 2024; 10(1):eadk3855; doi: 10.1126/sciadv.adk3855

Fang

, Chow

MCK

, Ho

JDL

, et al. Soft robotic manipulator for intraoperative MRI-guided transoral laser microsurgery. Sci Robot, 2021; 6(57):eabg5575; doi: 10.1126/scirobotics.abg5575

Spiers

, Calli

, Dollar

. Variable-friction finger surfaces to enable within-hand manipulation via gripping and sliding. IEEE Robot Autom Lett, 2018; 3(4):4116–4123; doi: 10.1109/LRA.2018.2856398

Delhaye

, Schiltz

, Crevecoeur

, et al. Fast grip force adaptation to friction relies on localized fingerpad strains. Sci Adv, 2024; 10(3):eadh9344; doi: 10.1126/sciadv.adh9344

Teeple

, Aktas

, Yuen

, et al. Controlling palm-object interactions via friction for enhanced in-hand manipulation. IEEE Robot Autom Lett, 2022; 7(2):2258–2265; doi: 10.1109/LRA.2022.3143578

, Liang

, Gao

, et al. A linkage-driven underactuated robotic hand for adaptive grasping and in-hand manipulation. IEEE Trans Automat Sci Eng, 2024; 21(3):3039–3051; doi: 10.1109/TASE.2023.3273721

, Baron

, Clark

, et al. Systematic object-invariant in-hand manipulation via reconfigurable underactuation: Introducing the RUTH gripper. Int J Robot Res, 2021; 40(12–14):1402–1418; doi: 10.1177/02783649211048929

10.

Rahman

, Carbonari

, D’Imperio

, et al. A dexterous gripper for in-hand manipulation. in: 2016 IEEE International Conference on Advanced Intelligent Mechatronics (AIM). IEEE: Banff, AB, Canada; 2016; pp. 377–382; doi: 10.1109/AIM.2016.7576796

11.

Rojas

, Ma

, Dollar

. The GR2 gripper: An underactuated hand for open-loop in-hand planar manipulation. IEEE Trans Robot, 2016; 32(3):763–770; doi: 10.1109/TRO.2016.2562122

12.

Zhu

, Lu

, Zheng

, et al. A soft-rigid hybrid gripper with lateral compliance and dexterous in-hand manipulation. IEEE/ASME Trans Mechatron, 2023; 28(1):104–115; doi: 10.1109/TMECH.2022.3195985

13.

Zhou

, Yi

, Chen

, et al. BCL-13: A 13-DOF soft robotic hand for dexterous grasping and in-hand manipulation. IEEE Robot Autom Lett, 2018; 3(4):3379–3386; doi: 10.1109/LRA.2018.2851360

14.

Pagoli

, Chapelle

, Corrales

, et al. A soft robotic gripper with an active palm and reconfigurable fingers for fully dexterous in-hand manipulation. IEEE Robot Autom Lett, 2021; 6(4):7706–7713; doi: 10.1109/LRA.2021.3098803

15.

Abondance

, Teeple

, Wood

. A dexterous soft robotic hand for delicate in-hand manipulation. IEEE Robot Autom Lett, 2020; 5(4):5502–5509; doi: 10.1109/LRA.2020.3007411

16.

S-Q

, Li

W-H

, Li

J-H

, et al. Tuning stiffness with granular chain structures for versatile soft robots. Soft Robot, 2023; 10(3):493–503; doi: 10.1089/soro.2021.0218

17.

Jiang

, Yang

, Chen

, et al. A variable stiffness gripper based on differential drive particle jamming. Bioinspir Biomim, 2019; 14(3):e036009; doi: 10.1088/1748-3190/ab04d1

18.

Yamane

, Wakimoto

. Development of a flexible manipulator with changing stiffness by granular jamming. In: 2017 24th International Conference on Mechatronics and Machine Vision in Practice (M2VIP). IEEE: Auckland; 2017; pp. 1–5; doi: 10.1109/M2VIP.2017.8211491

19.

Ranzani

, Cianchetti

, Gerboni

, et al. A soft modular manipulator for minimally invasive surgery: Design and characterization of a single module. IEEE Trans Robot, 2016; 32(1):187–200; doi: 10.1109/TRO.2015.2507160

20.

Crowley

, Zeng

, Su

H-J

. A 3D printed soft robotic gripper with a variable stiffness enabled by a novel positive pressure layer jamming technology. IEEE Robot Autom Lett, 2022; 7(2):5477–5482; doi: 10.1109/LRA.2022.3157448

21.

Xue

, Jin

, Jian

, et al. Origami-based flexible robotic grippers via hard-soft coupled multimaterial 3D printing. Soft Robot, 2025; doi: 10.1089/soro.2024.0166

22.

Sun

, Chen

, Han

, et al. A soft gripper with variable stiffness inspired by pangolin scales, toothed pneumatic actuator and autonomous controller. Robot Comput Integr Manuf, 2020; 61:101848; doi: 10.1016/j.rcim.2019.101848

23.

DCF

, Wang

, Ouyang

, et al. A reconfigurable variable stiffness manipulator by a sliding layer mechanism. In: 2019 International Conference on Robotics and Automation (ICRA). IEEE: Montreal, QC, Canada; 2019; pp. 3976–3982; doi: 10.1109/ICRA.2019.8793571

24.

Al Abeach

LAT

, Nefti-Meziani

, Davis

. Design of a variable stiffness soft dexterous gripper. Soft Robot, 2017; 4(3):274–284; doi: 10.1089/soro.2016.0044

25.

, Liu

, Chen

, et al. A miniaturized variable stiffness soft manipulator with a customizable LMPA pattern. IEEE Robot Autom Lett, 2023; 8(9):5704–5711; doi: 10.1109/LRA.2023.3300241

26.

Wang

, Chen

, Zuo

. Flexible manipulator with low-melting-point alloy actuation and variable stiffness. Soft Robot, 2022; 9(3):577–590; doi: 10.1089/soro.2020.0143

27.

Shintake

, Schubert

, Rosset

, et al. Variable stiffness actuator for soft robotics using dielectric elastomer and low-melting-point alloy. In: 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE: Hamburg, Germany; 2015; pp. 1097–1102; doi: 10.1109/IROS.2015.7353507

28.

Wang

, Yu

, Abrego Serrano

, et al. Shape memory alloy-based soft finger with changeable bending length using targeted variable stiffness. Soft Robot, 2020; 7(3):283–291; doi: 10.1089/soro.2018.0166

29.

Aksoy

, Shea

. Multistable shape programming of variable-stiffness electromagnetic devices. Sci Adv, 2022; 8(21):eabk0543; doi: 10.1126/sciadv.abk0543

30.

Wang

, Ahn

S-H

. Shape memory alloy-based soft gripper with variable stiffness for compliant and effective grasping. Soft Robot, 2017; 4(4):379–389; doi: 10.1089/soro.2016.0081

31.

Jeon

, Le

, Jeong

, et al. Towards a Snake-like flexible robot with variable stiffness using an SMA spring-based friction change mechanism. IEEE Robot Autom Lett, 2022; 7(3):6582–6589; doi: 10.1109/LRA.2022.3174363

32.

Imamura

, Kadooka

, Taya

. A variable stiffness dielectric elastomer actuator based on electrostatic chucking. Soft Matter, 2017; 13(18):3440–3448; doi: 10.1039/C7SM00546F

33.

Guo

, Liu

, et al. Review of dielectric elastomer actuators and their applications in soft robots. Adv Intell Syst, 2021; 3(10):2000282; doi: 10.1002/aisy.202000282

34.

Sui

, Zhao

, Wang

, et al. Design of a bio-inspired extensible continuum manipulator with variable stiffness. J Bionic Eng, 2025; 22(1):181–194; doi: 10.1007/s42235-022-00213-0

35.

Ham

, Han

, Park

Y-J

. Soft gripper using variable stiffness mechanism and its application. Int J Precis Eng Manuf, 2018; 19(4):487–494; doi: 10.1007/s12541-018-0059-2

36.

Kim

Y-J

, Cheng

, Kim

, et al. A stiffness-adjustable hyperredundant manipulator using a variable neutral-line mechanism for minimally invasive surgery. IEEE Trans Robot, 2014; 30(2):382–395; doi: 10.1109/TRO.2013.2287975

37.

Kier

, Stella

. The arrangement and function of octopus arm musculature and connective tissue. J Morphol, 2007; 268(10):831–843; doi: 10.1002/jmor.10548

38.

Shan

, Birglen

. Modeling and analysis of soft robotic fingers using the fin ray effect. Int J Robot Res, 2020; 39(14):1686–1705; doi: 10.1177/0278364920913926

39.

Manoonpong

, Rajabi

, Larsen

, et al. Fin ray crossbeam angles for efficient foot design for energy—Efficient robot locomotion. Adv Intell Syst, 2022; 4(1):2100133; doi: 10.1002/aisy.202100133

40.

Tang

, Li

, Zhang

, et al. Digital channel-enabled distributed force decoding via small datasets for hand-centric interactions. Sci Adv, 2025; 11(4):eadt2641; doi: 10.1126/sciadv.adt2641

41.

Lepora

. The future lies in a pair of tactile hands. Sci Robot, 2024; 9(91):eadq1501; doi: 10.1126/scirobotics.adq1501

42.

Suresh

, Qi

, Wu

, et al. NeuralFeels with neural fields: Visuotactile perception for in-hand manipulation. Sci Robot, 2024; 9(96):eadl0628; doi: 10.1126/scirobotics.adl0628

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.00 MB

23.13 MB

22.50 MB

24.08 MB

21.12 MB