The novel design of the actuator with large force and a precise sensing output is fundamentally facilitated by the new origami-inspired actuating-sensing mode. Two main objectives are required by the origami-inspired actuator design. These involve using origami folding structures to generate robust contraction, extension, and passive bending instead of material inflation which lacks actuation linearity and strength. Also required is the use of origami folding structures to offer a deployable sensing mode instead of material inflation which couples bending and stretching motions. Based on these two objectives, this section investigates the origami-inspired design concept and mechanisms in detail as a general reference.

Origami, the ancient art of paper folding, has uses in geometrical space extension and smart programmable motion mechanisms, which have led to various applications in erospace engineering, architecture, and robotics. Taking inspiration from basic research on origami patterns (Buri and Weinand, 2008; Stavric and Wiltsche, 2014; Liu et al., 2015; Cai et al., 2016; Morgan et al., 2016; Wang et al., 2018), our design was developed based on the Yoshimura pattern (Buri and Weinand, 2008; Morgan et al., 2016). Unlike rigid origami (Stavric and Wiltsche, 2014; Cai et al., 2016), by allowing ridges’ distortion and slight facets’ deformation, utilizing its high foldability among units, the proposed design could offer multiple motion patterns and unique sensing modes simultaneously. Figures 2E–H plot the origami chamber in a natural state (no external force exerted on it), bending state (external force unevenly exerted on it), elongation state, and contraction state. In the linear states (no bending), the length of chamber h could be presented as h = 4 l ⁡ sin ( θ 2 ) , (1) where θ is the intersection angle of two facets of the origami design, which could also be presented as the intersection angle between ridges of optical waveguides. l is the geometrical length in the origami unit as labeled in Figure 2I. Maximum elongation length h max and h min could be achieved, { h max = 4 l h min = ( 2 n + 2 ) t , (2) where n is the numbers of origami units vertically and t is the wall thickness. As facts and ridges deform during actuation, which has a large effect on the minimum state, h min is calculated by adding the wall thickness of layers.

The output force generated at the cross section f is presented as f = P π r 2 , (3) where P is water pressure and r is the radius of the chamber cap (Figure 2K), which mainly depends on the design of origami parameters, illustrated in Figure 2J. The origami chamber could be fully deployed into a plate, as shown in Figure 2I. The cross-section of the actuator cap is a polygon which could be radially distorted under actuation. The perimeter of the actuator cross-section c is c = 3 ( m 1 + m 2 ) , (4) therefore, the radius of the cross-section under actuation could be approximated to r = c 2 π = 3 ( m 1 + m 2 ) 2 π . (5)

All states of the actuator, including contraction, elongation, and bending, could be sensed by three optical waveguides labeled with sensor A, B, and C on the surface of the origami. The unique mechanism of the sensor is introduced; as shown in Figure 2L, when the intersection angle θ becomes smaller, the upper and lower surface of the optical waveguide will have a higher contact area. This area provides a “shortcut” for the light, as the light can propagate straight toward the photodiode. In this case, the smaller the intersection angle θ , the larger the photodiode’s output will be. Relatively large facet deformation would happen on the maximum deploying and minimum folding states, which may have an effect on the relations of θ and photodiode’s output. This effect could be weakened by tuning the boundaries and thicknesses of ridges and walls to decrease the deformation on the facets. Therefore, by reading the signals from three sensors, i.e., θ a , θ b , θ c , we could obtain the pitch and roll angles of the actuator with the following models.

Considering the output force and motion are transmitted by the two caps of the actuator which are mounted on rigid parts, we assume these two caps as rigid plates. Hence, points a ' , b ' , c ' , as well as points a , b , c , are always in one plane, a ' ( − r , 0,0 ) ; b ' ( r 2 , − 3 r 2 , 0 ) ; c ' ( r 2 , 3 r 2 , 0 ) , (6) a ( x a , y a , z a ) ; b ( x b , y b , z b ) ; c ( x c , y c , z c ) , (7) where r is the radius of the actuator. The pitch angle α and roll angle β of actuator could be presented as { sin ⁡ α = | n x → . a ' a → | | n x → | . | a ' a → | = | n x → . b ' b → | | n x → | . | b ' b → | = | n x → . c ' c → | | n x → | . | c ' c → | sin ⁡ β = = | n y → . a ' a → | | n y → | . | a ' a → | = | n y → . b ' b → | | n y → | . | b ' b → | = | n y → . c ' c → | | n y → | . | c ' c → | , (8)

where n x → = ( 0,1,0 ) ; n y → = ( 1,0,0 ) , (9)

Vectors in three directions are { a ' a → = ( x a + r , y a , z a ) b ' b → = ( x b − r 2 , y b + 3 r 2 , z b ) , c ' c → = ( x c − r 2 , y c − 3 r 2 , z c ) (10)

Based on the consistent features of origami units, θ a = θ a ' = θ a ' ' = θ , (11) where θ a , θ a ' , θ a ' ' are the intersection angles between ridges of optical waveguides. Geometrically, we have | a ' a → | = 4 l ⁡ sin θ a 2 , (12)

Substituting (10) and (12) into (8), { sin ⁡ α = | y a | 4 l ⁡ sin θ a 2 = | y b + 3 r 2 | 4 l ⁡ sin θ b 2 = | y c − 3 r 2 | 4 l ⁡ sin θ c 2 sin ⁡ β = | x a + r | 4 l ⁡ sin θ a 2 = | x b − r 2 | 4 l ⁡ sin θ b 2 = | x c − r 2 | 4 l ⁡ sin θ c 2 . (13)

In Equation 13, θ a , θ b , θ c are the intersection angles between ridges of optical waveguides, which are achieved by sensor signals. l and r are constants decided by the origami design. Therefore, to get the pitch angle α and roll angle β of actuator, we need to calculate values of x a , y a .

In the top plane where sensor A, B, and C are evenly distributed, we have | a b → | = | b c → | = | c a → | = 3 r . (14)

By substituting (10) into (14), ( y b − y a ) 2 + ( x b − x a ) 2 = ( y c − y b ) 2 + ( x c − x b ) 2 = ( y c − y a ) 2 + ( x c − x a ) 2 = 3 r 2 . (15)

From Equations 13, 15, we will get the coordinate of a ( x a , y a , z a ) to substitute into (8). Therefore, { sin ⁡ α = | y a | 4 l ⁡ sin θ a 2 sin ⁡ β = | x a + r | 4 l ⁡ sin θ a 2 . (16)

From Equation 16, the bending angle of the actuator in pitch and roll directions could be calculated based on the output signals from sensor A, B, and C. The length of the actuator under contraction and elongation could be obtained with the same three signals. It is noted that slight deviation between the model and real circumstance may be generated in the maximum deploying and minimum folding states, as geometrical parameters of origami may vary due to the facets’ deformation. This deviation could be ignored as the working range of the actuator generally does not include these two states.

Fabrication of the SOSA actuator is considerably simplified with the following four steps: 1)

The soft origami actuator shown in Figure 3A is fabricated by injection molding with the following parameters: wall thickness t = 0.7   m m , number of origami pattern n = 2 , and origami structure parameters m 1 = 3.37 m m , m 2 = 22.37   m m , σ = 35.55 ∘ , h n a t u r a l = 13   m m . Polyurethane rubber materials (Hei-Cast 8400, Hardness 60 A) are chosen for their flexible but inflatable features to ensure the folding and deployment of the actuator.

A preliminary validation test for the feasibility of the actuating-sensing integrated mechanism was carried out. Based on the actuating and sensing concepts in Design Concept, Modeling, and Fabrication Process section, three groups of experimental conditions were set to do the comparison and validate the sensing mechanism under linear actuation: 1) Normal: one optical waveguide was placed as the proposed design; 2) Blocked: one waveguide has tinfoil placed between the upper and lower surface of the waveguide so that there is no “shortcut” when these two surfaces get closer; 3) Empty: the last waveguide path is empty.

During the test, the SOSA actuator was mounted at the photodiode side while the LED side could move axially. The actuator was actuated with water in and out to elongate and contract. The change lengths were measured by a laser distance sensor (HG-C1100, Panasonic) which was placed at the LED side.

The testing results are shown in Figure 4B, which indicate that the actuator could contract and elongate under actuation. Furthermore, according to the feedback of sensor signals, compared to the Empty (photodiode output is 0) and Blocked (photodiode output is constant) ones, only the Normal one returns efficient signals indicating the length change of actuators. Therefore, significant conclusions could be drawn that the actuating-sensing mechanism has been well justified.

The correlations of output force f and water pressure P were investigated in the isometric test. In the isometric state, the actuator length was a constant. Two caps were fixed to the experimental platform. We recorded the output force generated at the cap by increasing the inlet water pressure from 0 Kpa to 100 Kpa. Additionally, following the isometric tests’ procedure, three actuators (Figure 4C) with the same dimensions were tested, each repeated thrice, to validate the performance repeatability of actuator.

Figure 4D shows the results on the actuators’ natural length h = 13   m m . According to the experimental results, the performance repeatability of the SOSA actuator could be validated from two aspects. One is that good repeatability is shown in three repeated tests of each actuator. The other one is that good repeatability is shown in three actuators tests. In addition, a relatively good linearity between the output force and water pressure is presented, showing agreements with the model (3). Maximum force was achieved on higher water pressure P = 100   K p a compared to the traditional piston (Festo Pneumatic Cylinder (DSNU-16-25-P-A and Festo, 2020), force/weight = 50 N/0.1 Kg); the force to weight ratio of our proposed actuator is much larger reaching to 50 N / 0.01 Kg .

In the free space state, one cap of the actuator was fixed to the experimental platform, while the other cap was set in free space. The motion range of the actuator was tested by recording the relations between water pressure P and actuator length h . During the test, the length h and bending pitch α / roll  β angles were separately returned by the distance laser sensor and IMU for benchmarking to validate the accuracy of SOSA sensor under actuation.

The relations of length and pressure are shown in Figure 4E. Compared to the commercial soft actuator with nonlinear elastic materials which are hard to actuate under 50 Kpa (Yi et al., 2018), the SOSA actuator could easily complete the whole motion range using no more than 40 Kpa. Figure 4E plots the minimum, natural, and maximum length of the SOSA actuator, which indicates that it has a full travel distance of 15.3 mm, more than 100% its natural length. In this test, the sensor signals in detecting length were presented with a blue area. The test results show that the blue area (SOSA sensor) highly overlaps with the gray area (benchmark laser sensor). Significant conclusions could be drawn that the proposed SOSA actuator could obtain a large actuating force output in very low working pressure and high sensing accuracy. This excellent actuating-sensing performance means the SOSA actuator can be applied to more integrative and in harsh environment applications.

SOSA bend sensing tests were conducted in the experimental platform shown in Figure 4A. Different from the above tests, in this setup, a 6-DOF Inertial measurement unit (IMU) was mounted on the top cap of a photodiode tube to read the pitch and roll angles of the actuator with time varying for calibrating the SOSA sensor A, B, and C sensing accuracies. In this setup, one cap of the SOSA actuator was fixed on the platform, while the other cap was manually rotated to generate real-time varying bending motion. Test data could be captured by actuating the actuator, resulting in bending motions. The signals recorded by the optical-sensing actuator and IMU are shown in Figure 4F and Figure 4G, with the RMS error of pitch 2.2 ∘ and the RMS error of roll 2.63 ∘ . The results indicate that higher accuracy could be achieved compared to our previous work (Shen et al., 2016), showing relatively good following feedback which could totally satisfy the current application. Slight deviation was generated at the maximum deploying and minimum folding states due to the unmodeled facets deformation. This deviation will be decreased by improving the origami design and signal processing in the future.

The performance reliability of the actuator was validated with a cycling test. In this test, the actuator was required to complete 10,000 cycling movements in the full motion range with a frequency of 0.3 Hz. One cap of the actuator was fixed at the experimental platform, with the other one in free space. Firstly, water was pumped into the actuator, resulting in maximum elongation. Secondly, the water was drawn to maximumly contract the actuator. The cycling test was performed by repeating this process with a frequency of 0.3 Hz. Figure 4H shows the performance comparison of the actuator before test and after test, which indicates that the performance of the actuator was still maintained over 10,000 cycles. Therefore, the performance reliability of the actuator was validated. Further iterations on life span and endurance will be continued in future works.

The SOSA actuator design was applied for the underwater manipulator to showcase its performance. By using the SOSA actuators (Figure 5C) in complex underwater environments, the proposed actuators have the advantage of inherent compliance compared with conventional rigid-bodied robots. Better accuracy and a larger payload can also be achieved. The hybrid underwater manipulator, shown in Figure 5A, consists of two parts: one gripper and one joint. The gripper (Figure 5B) is actuated by one SOSA, which completes the opening and closing of gripper fingers by actuating axially. The maximum opening angle is 78 ∘ . Regarding the joint, its diameter and height are 108 mm and 114 mm, respectively. The joint has two sections, each section with three SOSAs mounted triangularly. In addition, two photodiode circuits are sealed inside the middle acrylic tubes. And two LED circuits are sealed in two tubes mounted on the top and bottom of the joint. These components, together with the hydraulic control system, are presented in Figure 5D and Figure 5E, which consists of eight valves, two pumps, and one control unit. For the sake of waterproofing and compactness, all the electronic components are put into acrylic tubes. Six actuators on the joint correspond to six valves, and each valve is connected with two coupled actuators. The remaining two valves are for the actuator on the gripper.

A series of tests were carried out to demonstrate the performance of the hybrid underwater manipulator. For the experimental setup, the hybrid underwater manipulator was mounted on a fixed platform and performed different tasks both onshore and underwater. In the on-shore test (Figure 6A), the manipulator was mounted vertically and controlled to grab a pen from an operator, rotate counterclockwise, and return the pen to the operator. In the underwater test (Figure 6B), the manipulator was controlled to perform one pick-and-place task of a cylindrical object. All these movements show high flexibility and high precision positioning, benefiting from the SOSA groups.

The gripper’s grasping force was tested for validating the large force output of the SOSA actuator. Figure 6A illustrates the experimental setup, where a force sensor (FSR400, Interlink Electronics) was mounted at the tip of the gripper. As shown in Figure 6D, the grasping force could reach 2.3 N when pressure was only 30 kPa. This force is large in this low actuation pressure, as force generated in this pressure is very limited for the conventional soft actuator (Polygerinos et al., 2015) and compliant gripper (Wang et al., 2013).

As illustrated in the last section, giving three critical angles, the orientation of one SOSA can be calculated. In the manipulator’s joint, the normal vector of each section is in parallel with the corresponding SOSA. In other words, one section’s orientation can be obtained by only one of the three SOSAs. This redundant sensing feedback mode could largely increase system robustness and accuracy. In order to validate the position feedback, an IMU was mounted on the top photodiode tube for benchmarking (Figure 6C). The test results were shown in Figure 6E and Figure 6F, exhibiting the RMS error of pitch in 1.34 ∘ and the RMS error of roll in 5.1 ∘ . The results show the same tendency with actuator bend sensing tests. As a short conclusion, this actuating-sensing mode with redundant sensing feedback could largely improve the robustness and accuracy of manipulations, which are offered by the SOSA actuators.