Layer jamming-based soft robotic hand with variable stiffness for compliant and effective grasping

: A novel variable stiffness soft robotic hand (SRH) consists of three pieces of layer jamming structure (LJS) is proposed. The mechanism is driven by the motor-based tendon along the surface of the pieces that connect to individual gas channel. Each LJS is optimised by adhering a thin layer of hot melt adhesive and overlapping the spring steel sheet as inner layer material. It can be switched between rigid and compliant independently. The structures of variable stiffness and tendon-driven lead to various deformation poses. Then the control system of SRH and the performance analysis of the LJS are introduced. Finally, the experiments are implemented to prove the superiority of the proposed LJS and the demonstrations show that the designed robotic hand has multiple configurations to successfully grasp various objects.


Introduction
The soft robotic hand (SRH) that is made up of soft material has an inherent advantage of high compliance and dexterity. The SRH is suitable for grasping fragile and irregular objects like glasses and fruits [1,2]. However, the common SRHs can only switch their configuration between the initial state and continuous curved state so that the single operation cannot adjust the grasping posture diversely and cannot change the actuation behaviour of the manipulator for specific grasping tasks [3,4]. Also, because of the common SRHs are lack of adequate impedance so that it has limited stiffness to sustain external forces [5]. Hence the variable stiffness structure of the robotic hand is the trend of researching [6]. The work presented here concentrates on the powerful and dexterous grasping in a variable stiffness SRH.
Recently, various mechanical of variable stiffness have developed, such as heat-sensitive material [7,8], magnetorheological (MR) or electrorheological (ER) fluid [9,10], low-melting-point alloys (LMPAs) [11] and jamming [12,13]. Among them, heat-sensitive materials include conductive polylactic acid (CPLA) [14], liquid metal, shape memory polymer (SMP) and so on, which are soft when heated and become stiff when cooled. However, heat-sensitive materials require enough heating time to activate. An SMP-based novel gripper [15] with variable stiffness in a finger joint, is proposed successively. However, the effect of the heat-sensitive materials requires time to action from one state to another rigidity state [15,16]. For the LMPA-based gripper [11], it also cannot respond to the desired state in real-time. For an SRH, the response time is a nonnegligible index, which is offline for most of the above mechanisms, limiting the practical application in services and industry.
The jamming structure has advantages such as simple structure and easy control, large variable stiffness range and rapid response [5]. The stiffness is often controlled by the air pressure difference between inside and outside of the membrane. A jamming structure can be divided into two types, granular jamming [17] and layer jamming. The former one needs a bigger substantial volume [5], so layer jamming is the more ideal structure, which consists of inner layers and external membrane. Jamming layers are loosely packed within the enclosed membrane, which is ductile without disturbing the compliance. Layers are jammed together firmly by the air pressure difference when vacuumed by vacuum pump so that the layers are shackled as a whole and exhibit stronger stiffness quickly [13].
The actuation section is the essential research point of the SRH and an effective and convenient actuation is an important structure for the robotic hand. Nowadays, various actuation techniques had been developed, such as pneumatic actuators [18,19], chemical reaction [20], the tendon-driven mechanism (TDM) [21,22], shape memory alloy actuators [23] and so on. As a physical actuation technique, the tendon-driven actuator pulled by motor-based TDM has better frequency response and power than the many other actuation mechanisms [24]. The power and the respond time of TDM are depended on the motor property and the transmission structure, so the upper limitation of the power and respond time are potential.
In this paper, a tendon-driven SRH with variable stiffness is proposed. The LJS varies the stiffness of the three pieces of actuator individually and the single tendon driver takes charge of the deformation. The structure of the paper is organised followed as the narration of the variable stiffness soft gripper's design principle and structure driven by tendon is arranged at first. Then the performance analysis of the SRH is described before the experiments of the prototype are represented. Finally, the conclusion and outlook about the variable stiffness SRH (VS-SRH) are expressed. Considering the manipulation skills of VS-SRH, it is feasible to practice skills learning from humans to robot-like [25] in the future. Sensors like a visual-tactile sensor with an algorithm [26] are also planned to integrate together.

Principle of LJS
LJS is the core component of VS-SRH. The soft robotic based on layer jamming achieves variable stiffness performance though changing the internal air pressure. When the air pressure is reduced, the normal force of the LJS and the friction between each layer are changed. They eventually lead to a change the stiffness of LJS.
There are some other variable stiffness methods, such as shape memory polymer or gallium-indium alloy. The methods realise variable stiffness by changing the state of the material. Therefore, they have to require enough time to absorb and release heat, and the efficiency is rather low. Comparing with the above variable stiffness methods, the LJS can be repeatedly used by way of pressurisation and depressurisation, so that the continuity of variable stiffness is better and can achieve faster response speeds.
However, LJS also has a shortcoming. The initial position of the LJS is not easy to restore when it performs a specific action. Moreover, the layers in the jamming structure are easy to be creased for the lack of stiffness in the axial direction. In order to overcome this shortcoming, the spring steel sheet (SSS), which is elastic in the radial direction but stiff in the axial direction, is used to insert into the LJS. It is beneficial to restore the initial position and increase the strength of LJS. Fig. 1 shows the internal structure of VS-SRH, which includes three pieces of LJS and tendon drive line. Three pieces of LJS are linked by crisscross overlapping end-to-end. The gas pipeline is independently connected to the inner gas-cavity of each LJS for flowing in-out gas. The linked structure is aimed to explore the flexibility and practicability of LJS and the cooperation between three gas controllers and a tendon controller. The tendon-driven line is linked from the top section of LJS to the bottom section of LJS, along with the surface of all sections. Hence, all the pulling force comes from the bottom section of LJS, turning the SRH to a different configuration. Fig. 2 shows the structure of VS-SRH, which includes jamming-based structure and fixed structure. Common printing paper is selected because of the paper is soft in the radial direction but tough in the axial direction. The manufacturing process of VS-SRH is described as follows:

Design and fabrication of VS-SRH
(1) Adhering the tight hot melt adhesive layer (whose thickness is about 0.1 mm and almost loss stickiness after solidification) to the surface of the paper to elevate the friction coefficient.
(2) Tailoring the processed paper into many little pieces with a uniform size of 9.8*3.5 cm.
(3) Creating a membrane inner cavity whose inner size is 11*3.8 cm by two thermoplastic polyurethanes (TPU) slices: heating two TPU slices paste together orderly and tightly on their top, right and left edge by the thermoplastic device. (4) Overlapping 18 pieces of papers flatly and adhering to the SSS, whose size is smaller than the paper sheets slightly to the underside of the overlapping paper sheets. (5) Putting the paper sheets and SSS into the membrane together through the bottom entrance, then closing the entrance with a thin gas pipeline inserting into by thermoplastic device and sealant. (6) Repeating from step (1) to step (5) for getting 3 same LJSs. (7) Crisscross overlapping 3 above LJSs end-to-end and attaching several plastic tubes on both sizes of LJSs for passing through a Kevlar string. (8) Fastening the end of LJSs to a clamping structure, and tying the above Kevlar string form LJSs to a roller which is connected to the motor mounted on clamping structure.
The proposed VS-SRH has some unique advantages (1) It is easy to change stiffness rapidly by combining multi-DOF LJS and tendon structure.
(2) It is easy to control by one motor and three channels of air pressure.
(3) It is flexible to realise many kinds of deformations and various grasping poses (like hooking, clamping and grasping).

Control principle of VS-SRH
The control of VS-SRH includes two parts: vacuum control for a variable stiffness of LJS and tendon-driven for deformation of LJS. The LJS turns to a rigid state as the gas cavity is in a vacuum state, while turns to a compliant state in the atmospheric pressure state. Fig. 3 shows the control principle of the variable stiffness of LJS. A micro-vacuum pump is used to pump out the internal gas of LJS. A 3/2 way solenoid valve is linked between the vacuum pump and LJS. When the solenoid valve is active on ports 2 and 3, the internal gas of LJS is vacuumed up and a rigid state is achieved. When the solenoid valve is active on ports 2 and 1, the atmospheric gas flows into the LJS, and compliant state is achieved. The vacuum degree is controlled by a solenoid valve. The vacuum degree can achieve −0.81 bar. As three LJSs are linked to a vacuum pump with an independent solenoid valve, the state of each LJS is controlled independently.
An STM32F407 chip is selected as an embedded CPU to generate PWM signals for VS-SRH. Stepping motor (CHR-GM20-20BY) mounted on the clamping structure is used to drive the rotation of the roller. The tendon drive line tied to the roller is pulled to make the VS-SRH be deformed. When adjusting the three values, vacuum pump and steeping motor, VS-SRH can be adjusted in too many states.

Friction-controlled variable flexible
The area moment of inertia J is a geometrical property of a flexible beam's cross-sectional area A, which describes the distribution of area about the arbitrary axis. The geometry of the beam's crosssectional shape influences J. The area moment of inertia for a sole rectangular cross-section yields [27]: where h represents the thickness of the beam and b represents the width of the beam structure. In fact, the stiffness depends on the sliding behaviour between the individual layers deeply, which means that the friction between the layers would also affect the stiffness of the LJS. It is the friction that enhances the bending resistance of the LJS and generates an effective area moment of inertia by limiting the relative sliding.
In order to produce effective J, it is essential to apply adequate pressure force F press outside the layers to suppress their relative movements. However, when the external loading force F load is applied on the tip of LJS, J will generate shear stress τ between the adjacent layers within the beam, which would compel the beam structure to generate bending deformation. Fig. 4 shows the distribution of shear stress over a simplified multi-layer beam structure consisting of three paper layers and a SSS overlapping on the top of paper layers. SSS generates restoring force F resist whose direction is in contrast or identical to the external loading force. Because of the shear stress produced from the SSS is tiny, the friction effect is ignored here where W is the shear force generated by F resu which is the resultant force of F load and F resist and S(y) is the first moment of the crosssectional area, zs is the distance from the neutral axis to the centroid of A(y). Among them, after stiffness variation, the SSS is anti-deformed. At this time, the F resu is equal to the sum of F load and F resist in the initial state. When SSS is deformed, the F resu is equal to the difference of F load and F resist in the curved state. According to the moment balance principle, the W can be equal to F resu , and the result yields According to (3), shear stress is a function of the distance y from the radial axis with its maximum value located in the neutral axis when y is 0.
Pressure force F press between layers must be large enough that the sliding between paper layers is absent. In order to guarantee the relative rest state, the stiction force σ fric due to F press should not be weaker than the maximum amount of shear stress τ max at the neutral axis. An ultimate state happens when τ max is equal to σ fric by lucky coincidence yields τ max = σ fric (4) According to mechanics principles, the σ fric is related to a given friction coefficient μ and the contact area A xz between the paper layers as (5) yields Based on the above analysis, the maximum external loading force F maxload can be calculated Equation (6) gives the conditions that the external loading force related to some parameters mainly includes the number and the effective size of the layers, the friction coefficient of the layers' surface and the pressure force around the membrane. The loading force can be increased through the following ways: (i) elevating the friction coefficient that the melt adhesive is attached into the paper layers in this project and (ii) improving the outside pressure, which can be achieved by increasing the air pressure difference between the inside and outside of the soft membrane. Furthermore, it is unavoidable that the crease appears when the layers switch between rigid and compliant state repeatedly. To decrease the negative effect of layers' crease, a piece of SSS is applied because of its appropriate stiffness coefficient and easily bending behaviour.

Stiffness performance comparison experiment
In LJS, the hot melt is covered on the surface of paper sheets, and a SSS is inserted into the papers to improve the stiffness performance. Therefore, in order to verify the feasible and effectiveness of these methods, the stiffness performance comparison experiment is performed. Three types of inner modes are employed to be compared: using paper sheets only (type-1), adhering a tight hot melt adhesive layer to paper sheets (type-2) and overlapping a SSS on the base of type-2 (type-3). All the tested LJSs have 17 layers of papers, and are manufactured in the same way when being clamped on a platform. Fig. 5a shows the experiment result when the LJSs are vacuumed up to maintain on the vertical state and curved state, respectively. A tautness meter is adopted to add different horizontal direction forces, including 1, 2, 3 and 4 N for every LJS. The deformation of type-1 is obviously enhanced with the increase of horizontal pull force. The deformation of type-3 is least, and the deformation of type-2 is in the second place among these types.
For the practical application, LJS should have excellent stiffness performance at a curved state. After being bent into 90°, the LJS is applied the same operation. It is obvious that the deformation of type-1 is most dangerous, and type-2 takes second place, and the type-3 is slightest, which is shown in Fig. 5b.
By adjusting the state of the vacuum pump, the vacuum degree can be adjusted. Fig. 5d is the result of LJSs' deformation with various inner modes in different vacuum degrees when LJSs are under 2N horizon pull force. It is stated that type-1 has the largest deformation, type-3 has minimum deformation, and type-2 on the second place. It is explained that with the increasing of vacuum degree, the LJS has better anti-deformed character.
In the above experiment, three comparison tests between type-1 and type-2 in Figs. 5a, b, d show that higher friction coefficient between the layers results to better effect of variable stiffness. In addition, with the increasing of the vacuum degree, the deform angle shrinks, representing the improvement of F maxload . As (6) shows, the friction coefficient μ and F press have a positive correlation to F maxload , which are coincident to the experimental results. Furthermore, the addition of the SSS theoretically increases the deformation resistance in an initial state and enhances the deformation recover in a curved state. The experimental results above show that the addition of the SSS can effectively optimise the performance of stiffness variation.

Deformation experiment
The VS-SRH can perform various states of deformation, which is realised by LJS and tendon drive method. For every LJS, it can be in a rigid state when the internal gas is vacuumed up and be the compliant state when the internal gas is filled with atmospheric gas. Through different combinations of three sections of LJS, the VS-SRH can perform different deformation pose. Fig. 6 shows various shapes of deformation pose, and the corresponding combination states of LJS are listed in Table 1. As Fig. 6a, all the vacuum action is close, and all the three LJSs are soft and deformable, then the VS-SRH is pulled by a tendon to achieve deformation pose. As Fig. 6b, the top section of LJS is vacuumed up, and the other two sections of VS-SRH are in the compliant state, then the VS-SRH is pulled to achieve the deformation pose. The other deformation poses are performed according to the three LJS's states in Table 1, in which number '1' represents that the LJS is on the rigid state, while '0' represents that the LJS is on the compliant state.
The deformation experiment results demonstrate that there are various deformation poses performed by controlling different states of three LJSs in the VS-SRH. It is proven that the proposed  variable stiffness method and tendon drive scheme are effective and feasible.

Grasping experiments
To verify the grasp performance of VS-SRH, a variety of objects are grasped. All the grasp operations include four steps: (i) selecting the vacuum pair according to the target object's features; (ii) driving the motor to pull the tendon so that the VS-SRH is deformed to wrap the objects tightly; (iii) vacuuming all the LJS to harden the structure; (iv) releasing the tendon and grasp up the target object. As shown in Figs. 7a-c, the top section of LJS is deformed to clamp up a goblet, screwdriver and glue box, respectively. Moreover, in Fig. 7d, a headset is hooked by the top section of LJS vertically, which is maintained in a rigid state steadily and in Figs. 7f, g and h, a lemon, an orange and a pear are wrapped up around by the top and middle sections of LJS. In Figs. 7e and j, all the sections of LJS deform and then stiffen together to wrap a hand cream bottle and a water bottle tightly. It is worth explaining that a flimsy paper cup can be grasped without happening obvious extrusion in Fig. 7i. The grasp experiment indicates that the VS-SRH is enable to hook, clamp, wrap and grasp according to the specific grasp task, outstanding the variety of it's grasp mode.
Moreover, as shown in Fig. 8, the total weight of the variable stiffness sections is 45 g, but it can hook up 800 g objects. This test reflects that the VS-SRH achieves powerful force to hook effortlessly and the structure has a commendable high payloadweight ratio, which is the prominent advantage of VS-SRH.

Conclusion
The proposed robotic hand consists of three pieces of LJS, which is driven by the motor-based tendon along the surface of the pieces. Each layer jamming that is optimised by adhering a thin layer of hot melt adhesive and overlapping the SSS can be switched between rigid state and compliant state independently. The theory analysis of layer jamming shows that the stiffness performance is relative to friction area, friction coefficient and vacuum degree. Meanwhile, the vacuum control for a variable stiffness of LJS and tendon-driven method for the deformation of VS-SRH are respectively described. The configurations of the structure would be deformed by the tendon in advance and the shape is maintained firmly when vacuuming the LJSs. It is the cooperation of the LJS and tendon that realises the deformation and grasping of the VS-SRH.
Finally, several experiments are implemented to prove the superiority of the proposed SRH. The experiments reveal that the final three-DOF structure realises multiple configurations when the LJSs are vacuumed to corresponding vacuum pairs previously. Furthermore, the structure enables the robotic hand with multiple grasping configurations and hooking the ability to pick up various shaped objects. Although the soft hand's total weight is light, it can hook up the objects far heavier than itself.
The proposed SRH, based on the integration of different functional components, provides a new solution to the soft manipulators. It is adaptable and effective for different grasping tasks. This study, through introducing stiffness modulation, enables the soft gripper to be adaptable to grasp objects with a larger range of weight and more varying shapes. Besides, the choice of using tendon for actuation and pneumatic for changing stiffness is motivated by the fact that more manipulation skills can be achieved for SRH. Future research will focus on optimising the design of the finger structure to integrate more sensors for perception and applying intelligent algorithms for manipulation.