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Locomotion of inchworm-inspired robot made of smart soft composite (SSC)
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Bioinspiration & Biomimetics Bioinspir. Biomim. 9 (2014) 046006 (10pp)
doi:10.1088/1748-3182/9/4/046006
Locomotion of inchworm-inspired robot made of smart soft composite (SSC) Wei Wang1, Jang-Yeob Lee1, Hugo Rodrigue1, Sung-Hyuk Song1, Won-Shik Chu2 and Sung-Hoon Ahn1,2 1
Department of Mechanical and Aerospace Engineering, Seoul National University, Gwanak-Ro 566, Gwanak-gu, Seoul, Korea, 151-742 2 Institute of Advanced Machinery and Design, Seoul National University, Gwanak-Ro 566, Gwanak-gu, Seoul, Korea, 151-742 E-mail: [email protected] Received 1 July 2014, revised 1 August 2014 Accepted for publication 26 August 2014 Published 7 October 2014 Abstract
A soft-bodied robot made of smart soft composite with inchworm-inspired locomotion capable of both two-way linear and turning movement has been proposed, developed, and tested. The robot was divided into three functional parts based on the different functions of the inchworm: the body, the back foot, and the front foot. Shape memory alloy wires were embedded longitudinally in a soft polymer to imitate the longitudinal muscle fibers that control the abdominal contractions of the inchworm during locomotion. Each foot of the robot has three segments with different friction coefficients to implement the anchor and sliding movement. Then, utilizing actuation patterns between the body and feet based on the looping gait, the robot achieves a biomimetic inchworm gait. Experiments were conducted to evaluate the robot’s locomotive performance for both linear locomotion and turning movement. Results show that the proposed robot’s stride length was nearly one third of its body length, with a maximum linear speed of 3.6 mm s−1, a linear locomotion efficiency of 96.4%, a maximum turning capability of 4.3 degrees per stride, and a turning locomotion efficiency of 39.7%. S Online supplementary data available from stacks.iop.org/BB/9/046006/mmedia Keywords: inchworm-inspired robot, shape memory alloy, smart soft composite (Some figures may appear in colour only in the online journal) 1. Introduction
zirconate titanate, and pneumatics, to provide the driving force of the robot. Soft morphing robots based on biomimetic principles are capable of continuous locomotion in harmony with their environments. Without making use of traditional mechanical components, they can be built to be lightweight and capable of a diverse range of locomotion. The advantages of soft-bodied robots are reflected in their large and complex deformation, compact architecture, lightweight robot structure, and their control method based on body morphology [2]. In recent studies, various underwater soft robots have been developed, including one by Mazzolai et al that mimics the arm structure of an octopus via a braided sleeve that uses SMA coils as transverse actuators for elongation deformation [3]. Villanueva et al used bioinspired SMA composite actuators to mimic the locomotion and appearance of a
In nature, soft tissues and organs comprise most of the mass of animals belonging to either invertebrate or chordate phyla. Since most of their bodies are comprised of soft elements, these animals to have a strong ability to adapt to a variety of living environments, even in unexpected situations. In order to replicate the versatility found in living creatures, soft robots were developed using of a combination of soft materials and stiff components. Soft robotics has benefited greatly from advances in materials science, new manufacturing technologies, biomechanics, and computational simulations [1]. Recent research in the field of soft robotics focuses on the application of soft or compliant materials combined with smart actuators, such as shape memory alloys (SMAs), lead 1748-3182/14/046006+10$33.00
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© 2014 IOP Publishing Ltd Printed in the UK
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Figure 1. (a) An inchworm. (b) Side view of an inchworm and (c) sketch of its main muscular structures.
jellyfish [4]. Kim et al proposed a bionic marine turtle flipper using an SMA-actuated smart soft composite (SSC) structure capable of coupled bending and twisting locomotion [5, 6]. Marchese et al developed a soft-bodied fish robot with fluidic elastomer actuators to perform rapid escape responses [7]. Some studies have been conducted on robots that mimic the behavior of caterpillars and worms, such as a caterpillarinspired robot developed by Lin et al that is actuated by SMA coil actuators installed in a soft body capable of rolling locomotion [8]. Seok et al used an SMA-coil-actuated, braided mesh tube with a fixed volume by applying Pascal's principle to mimic the peristaltic locomotion of an earthworm [9]. A pneumatically actuated quadrupedal soft robot made of silicone and capable of multiple gaits was developed by Shepherd et al [10]. A few pneumatic robot hands made of either silicone or granular materials have also been developed [11, 12]. A few studies have been conducted on inchworm-based robots that use the inchworm’s distinctive locomotion pattern. Koh et al built an inchworm robot named Omegabot, which was made of SMA springs and smart composite microstructures (SCM). It could move in only one direction and had a stride length of around 1/6 of its body length [13]. Using a similar principle, a centimeter-scale, motor-actuated inchworm robot with bidirectional claws was designed by Lee et al [14]. This robot also moved in a single direction and had a similar stride length. Ueno et al [15] developed an inchworm robot capable of two-way movement by using electroconjugate fluid (ECF) to produce body deformation and suction at the robot’s feet. However, this robot was connected to an external ECF tank and required high voltage. Using glass fiber reinforced plastic, Kim et al [16] built an inchworm robot capable of one-directional movement with a very small stride of 1/24 of its body length. These inchwormbased robots have small stride lengths, and most are only capable of unidirectional movement. In this study, a soft, morphing, inchworm-inspired robot made of SSCs was designed and fabricated to be both thin and
lightweight. This was done by combining three materials to form an SSC: SMA wires, polydimethylsiloxane (PDMS), and a thin polyvinyl chloride (PVC) plate. SMA-based SSCs are capable of large deformation although they are small, lightweight, and noise-free. In order to replicate the functions of a living inchworm, the robot was divided into three functional parts, consisting of the body and both the front and back feet, to generate the required deformation at different steps of each stride. This soft inchworm-inspired robot is capable of large-stride, two-way, linear locomotion and of turning in either direction. Its locomotion efficiency was also evaluated and analyzed.
2. Biological analysis The caterpillar has a pressurized-fluid-column-form coelom comprising its head, thorax, and abdomen. It is a proficient crawler through the use of its front true legs and its welldeveloped foot-like organs called prolegs. Caterpillars have a very complex muscular system since they only have longitudinal and oblique muscle fibers in their abdomens, and they lack circumferential muscles [17]. For soft animals without skeletons, muscles play a central role in defining the shape of body movements [18]. Caterpillar muscles have long sarcomeres, where each thick filament is surrounded by 10–12 thin filaments that are quite different from skeletal muscles [19]. A constitutive model of the muscle structure of the tobacco hornworm caterpillar, a family member of the inchworm, was developed by Dorfman et al [21] and showed that the main longitudinal muscles of this arthropod had a nonlinear pseudo-elastic stress-deformation response, and can thus be considered to be nonlinear pseudo-elastic composites [20]. An inchworm is a kind of caterpillar of the geometer moth that has only two or three pairs of prolegs at its rear end and true legs at its front. Other types of caterpillars have prolegs located all along their body. The different body parts and locations of the different leg types of an inchworm are 2
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Figure 2. Locomotion of an inchworm for one stride. Figure 3. Conceptual design of body-bending structure: (left to right) right deviated bending, neat bending, and left deviated bending. (a) Oblique view. (b) Top view. (c) A-A section view.
shown in figure 1. Figure 1 also shows a real inchworm with its longitudinal muscles contracted (top left) and a cross section of its abdomen showing its main muscle structure (top right). The contraction of the longitudinal muscle fibers leads to a bending deformation of the body of the inchworm, which results in a shortening of its overall length. Then, by immobilizing the true legs and prolegs alternately, it uses a looping gait for locomotion. If the longitudinal muscle fibers are actuated symmetrically, then the inchworm undergoes a linear locomotion, but if it contracts its longitudinal muscle fibers asymmetrically, then the body undergoes a nonsymmetric deformation, which results in a turning locomotion using one of the feet as an anchor. Nonetheless, for both the linear and turning movements, the locomotion sequence of an inchworm is the same and can be divided into two stages: an anchor-pull locomotion and an anchor-push locomotion, as shown in figure 2.
Figure 4. Conceptual design of feet segment. (a) Status without
actuation. (b) Convex status by actuating SMA 2. (c) Concave status by actuating SMA 1.
3. Robot design figure 3, actuating all four SMA wires induces a symmetrical bending deformation of the body. Actuating only the pair of SMA wires located on one side of the body results in a deviation angle of the body of φ, as shown in figure 3 on the left and on the right. To achieve a large deviation angle of the body, the robot was designed with a large width. With this configuration, the actuation of all SMA wires is used to obtain linear locomotion, while the actuation of only one of the pair of SMA wires is used for turning locomotion. Generally, inchworm locomotion is based on the anchormotion crawling principle, where the legs are used for anchoring. In order to complete a stride, an inchworm needs to use its front and back legs sequentially for anchoring during body contraction and stretching. The design of the anchor-motion mechanism of the robot is very important for producing inchworm-like locomotion. To enable the robot’s feet to change states between holding and sliding on smooth ground, the feet are designed segmentally, as shown in figure 4. There are three segments for each foot; two side segments are covered with polyimide (PI) film to obtain a low
3.1. Locomotion principle
As described in the last section, the body of the inchworm is an isotropic soft material and the muscle tissues of its abdomen are longitudinal fibers used for linear contraction. Therefore, based on the morphology of the inchworm, SMA wires are selected to implement the function of the longitudinal fibers of the inchworm, and PDMS is used to create the body of the inchworm robot since it is soft, isotropic, and bonds well with the SMA wires. Referring to the sketch of the inchworm muscle structure shown in figure 1, the contraction of the longitudinal muscle fibers generate different deformations of the abdomen, such as bending and turning, depending on which muscle fibers are contracted. The robot structure was designed to be thin in order to obtain a large deformation, with two pairs of parallel SMA wires placed symmetrically on each side of the robot along the axial plane of the body. In order to imitate the locomotion patterns of the inchworm, the SMA wires can be actuated using different patterns to obtain different deformation patterns. As shown in the center of 3
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Figure 5. (a) Structure comparison between the robot structure and an inchworm. (b) Locomotion sequence of inchworm-inspired robot with an ideal stride length of λ .
friction force with the ground, and the middle segment is silicone to gain a high friction force with the ground. Figure 4 shows the two SMA wires, named SMA 1 and SMA 2, embedded on the top and bottom portions of the robot’s feet. Actuating SMA 1 leads to a concave shape, resulting in the middle high-friction segment touching the ground, while actuating SMA 2 deforms the structure into a convex shape, resulting in the two low-friction segments touching the ground. The front and rear feet alternate between low and high coefficients of friction (COF) to generate a friction difference, which prevents the robot from sliding in one direction during the upward stroke of the body and in the other direction during the downward stroke. Figure 5(a) shows the robot’s structure compared with an inchworm. Both are divided into three parts, referred to as the body, the middle section, and the feet (at both ends). Figure 5(b) shows the deformation of the robot throughout each stride, with the stride length denoted as λ , which corresponds to the forward distance achieved by accomplishing a complete cycle combining the anchor-pull and anchor-push motions. The transition in foot shape between the two motions is shown in the middle.
Figure 6. Overall robot structure and its components. Table 1. Parameters of robot structure.
Robot parameter
Value
Robot structure dimension (mm) Body structure dimension (mm) Feet structure dimension (mm) Robot structure weight (g)
196 L × 140 W × 4 T 158 L × 140 W × 4 T 140 L × 8 W × 4 T 63.0
L, W, and T: length, width, and thickness.
sections with different friction coefficients. Both ends of the foot were covered by PI film to reduce the COF. A PVC plate with a thickness of 0.4 mm was used to reduce the weight of the overall structure, enhance its stability, and to allow the structure to obtain a larger and faster recovery stroke. The edges of the PVC plate were embedded in the PDMS matrix to couple them, but the center region wasn’t embedded in PDMS, thus reducing the weight of the structure. The carbon rods were used to maintain the intended shape of the matrix during the linear and turning locomotion of the robot and to separate the deformation of the body and the feet. The PDMS has a transition area with a thickness of 1 mm between the foot and body to further decouple the deformation of the body and the feet. The specific parameters of robot structure are summarized and shown in table 1.
3.2. Robot architecture
SMA wires were used as the active components, and were embedded in the matrix eccentrically to obtain large bending deformation. The stiffness of the host structure, the effective bendable length, the eccentricity of the SMA wires, and their dimensions influence the bending properties of the structure. The robot structure was designed as a thin, rectangular shape with a structure size of 196 × 140 × 4 mm (length × width × thickness). Figure 6 shows the detailed design of the overall structure. In this figure, the eight SMA wires are gathered in four different groups: SMA-front (SMA-front-1 and SMAback-2), SMA-back (SMA-back-1 and SMA-front-2), SMAleft (SMA-left-1 and SMA-left-2), and SMA-right (SMAright-1 and SMA-right-2). The actuation of a group refers to actuating both corresponding SMA wires simultaneously. The SMA wires in each group were connected in series, such that they are simultaneously actuated. The forward and backward directions were defined arbitrarily, as the locomotion is the same in both directions. The robot foot was segmented into
3.3. Materials and fabrication
The chosen silicone is PDMS (Dow Corning Sylgard 184), since it is highly flexible. It is also highly stable since its elasticity isn’t affected by temperature changes, it has high shear stability, high thermal stability, and dielectric stability [21, 22]. The SMA wires used in this research are FLEXINOL (Ni: 55 wt%, Ti: 45 wt%, Dynalloy, US). They have diameters of 152 um for the feet and of 203 um for the body. The PVC plate was cut by a laser machine (M-300 laser platform, universal Laser Systems, Australia) with rectangular 4
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Table 2. Material properties of SMA [23].
Table 3. Material properties of PDMS (Sylgard 184).
Parameter
Value
Parameter
Value
Martensite Young’s modulus Austenite Young’s modulus Martensite start temperature Martensite finish temperature Austenite start temperature Austenite finish temperature SMA wire diameter SMA initial strain
E m = 23.2 GPa E a = 49.5 GPa Ms = 77 °C M f = 42 °C As = 81 °C A f = 106 °C 152 um, 203 um εini = 3∼4%
PDMS Young’s modulus PDMS specific gravity Useful temperature range Poisson’s ratio
1.8 MPa (25 °C ) 1.03 (25 °C ) −45 °C to 200 °C 0.45
holes along the sides to prevent delamination with the PDMS matrix. The main material properties of SMA and PDMS are listed in tables 2 and 3, respectively. To assemble and build the structure, an acrylonitrile butadiene styrene (ABS) mold is built using a three-dimensional printer (Dimension 768 SST, Stratasys, USA) that positions the components within the matrix while the PDMS cures. First, the SMA wires are positioned within the mold and prestrained by 3–4%. Second, the PVC plate is positioned in the mold. Third, the PDMS solution with a weight ratio of 10:1 monomer and hardener is mixed, degassed in a vacuum casting pump, and poured into the mold. The assembly is then placed in an oven at a temperature of 58 °C for 10 h to cure the PDMS. This temperature was chosen because it is below the actuation temperature of the SMA wires. After the curing process, the specimen is taken out of the oven and the ABS mold is removed. The PI film is then glued at the feet.
Figure 7. Schematic diagram of control process.
Figure 8. Current patterns for linear locomotion during two periods.
4. Experimental method 4.1. Control unit
with rectangular waves for the forward locomotion, is illustrated in figure 8. In this figure, two strides of 15 s each are applied for a period of 30 s, as illustrated in the time period shown in light grey; the waiting time to allow cooling of the SMA wires in the feet before they are actuated in the other direction is shown in dark grey. When actuating the SMA wires (SMA-front or SMA-back), both of the feet deform in the opposite direction to provide contact with the low-friction segment of the feet on one side of the robot and the highfriction segment on the other side. So when either is actuated, the locomotion is restricted to only one direction. The SMA wires in the body also need to maintain maximum deformation for a few seconds for the feet to change their shapes. By switching the sequence of actuation for the SMA-front and SMA-back wires, the direction of locomotion can be inverted. SMA-left and SMA-right are used to bend the body part, while the PVC plate is used to help the shape recovery. Figure 9 (middle) shows the robot at different steps of the locomotion, with the shape of each foot shown on the left and right. The robot was actuated to move forward and then backward for five strides, totaling 75 s each. The results showed that the effective average stride length was 54 mm
The experiments were conducted on a flat, horizontal rubber mat at room temperature. Through experimentation, the actuating currents for the 152- and 203 um-diameter SMA wires embedded in the SSC were determined to be 550 mA and 1000 mA, respectively. The setup for the control process of the inchworm robot is shown in figure 7. The CompactRIO 9024 and NI 9264 modules (National Instruments, USA) were used to regulate the current, and Labview 2012 was used to input the current patterns. Using this setup, the current patterns, including the actuation time and the magnitude of the currents for each channel, were set individually, with two channels used to actuate the SMA wires in the feet and two channels for the SMA wires in the body, for a total of four channels. A digital camera was used to record the locomotion of the robot, and the displacements of the robot were measured visually using a ruler. 4.2. Linear locomotion
For the linear locomotion of the robot, all four SMA wires in the body were actuated simultaneously. The actuation pattern, 5
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Figure 11. Turning locomotion for forty periods, turning angle of 90
degrees.
5. Results and discussion 5.1. Friction coefficient test
Figure 9. Linear locomotion for one period. The back and front view
show the configuration of the feet at each step throughout the stride.
A brief study on an inchworm, conducted to provide background on both the morphology and locomotion of the inchworm, was used as the basis for the design of an inchworm robot. For the design of the robot’s feet, the real inchworm has true legs and well-developed gripping prolegs to grip surfaces. For the robot built in this research, the overall locomotion principle of the robot is a looping gait that relies on a principle similar to that of the inchworm; however, rather than using true legs and prolegs to grip the locomotion surface, we used alternating low- and high-friction feet segments to implement the locomotion. Since the difference in friction between the segments of the feet plays a crucial role, an experiment was conducted to measure the static and dynamic COF of the material used in the low- and high-friction segments of the feet. This experiment was conducted according to the ASTM D 1894 standard, using a tensile testing machine (5948 MicroTester, Instron, US) with a friction fixture (2810-005, Instron, US). The COF of the PDMS and PI film structures to the rubber material were tested three times each, and the results are shown in figure 12. From the results, one can see that the static and dynamic COFs of PDMS-rubber (1.22 and 0.56) are approximately four and nine times of those of PI-rubber (0.30 and 0.06), respectively.
Figure 10. Current patterns for left-turning locomotion during two
periods.
during ten periods, with a total distance of 540 mm in 150 s and a corresponding average speed of 3.6 mm s−1.
4.3. Turning locomotion
Just like the muscle fibers in the abdomen of the inchworm, an asymmetrical contraction of the SMA wires can be used to produce a turning locomotion. For the turning locomotion, the SMA wires were actuated on only one side of the body. Therefore, the turning locomotion is done by using the same pattern as the linear locomotion, but by actuating only SMAleft or SMA-right. The current patterns for the left-turning locomotion during two periods are shown in figure 10. Forty strides with a left-turning locomotion were completed by actuating only SMA-left, to obtain a total turn of 90 degrees equaling 2.3 degrees per stride. The resulting locomotion of the forty combined strides is shown in figure 11.
5.2. Locomotion efficiency analysis 5.2.1. Linear locomotion efficiency analysis. To achieve
locomotion, the feet change from being used as anchors to sliding, depending on whether the high-friction or lowfriction segment of the foot is in contact with the ground. However, some sliding may occur in the anchored feet, which reduces the overall stroke length of the robot. The schematic of the robot’s linear locomotion for one stride is shown in figure 13, with the loss in stroke length due to slipping of the anchored feet shown as a 2 and b 2 . For the anchor-pull 6
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Based on this ideal stride length, the linear locomotion efficiency of the robot can be expressed as in (3): ηlinear =
λ eff λ ideal .
(3)
Using the results obtained in section 4.2, the effective stride length was calculated to be 54 mm, and the ideal stride length of the robot during the ten periods was 56 mm. The resulting linear locomotion efficiency is 96.4%, as in (4): ηlinear =
54 = 96.4%. 56
(4)
5.2.2. Turning locomotion efficiency analysis. The turning
locomotion efficiency is calculated by considering the deformation of the robot during the stride of the turning locomotion. As shown in figure 14, during the anchor-pull process of a left-turning stride, the clockwise rotation angle of the rear foot and the anticlockwise rotation sliding angle of the front foot are assumed to be α1 and α2 . In the following anchor-push process, the anticlockwise rotation angle of the front foot and the clockwise rotation sliding angle of the rear foot are assumed to be β2 and β1. Therefore, the effective turning angle, θeff , can be calculated as in (5):
Figure 12. COF of PDMS and PI films to rubber material.
θ eff = α1 − β1 = β2 − α2.
(5)
In the ideal turning locomotion, the sliding angle of the anchored feet should be zero (that is, α2 = β1 = 0 ). Then, the ideal turning angle for each stride of θ ideal can be calculated as in (6), where φ is the deviation angle of the body, as shown in figure 14: θ ideal = α1 = β2 = φ .
Then, the efficiency of the turning locomotion can be expressed as in (7):
Figure 13. Schematic of robot real linear locomotion. (Top to bottom) Initial, transitional, and final positions.
ηturning =
process, the forward displacements of the rear foot and the sliding displacement of the front foot are assumed to be a1 and a 2 . In the ensuing anchor-push process, the forward displacements of the front foot and the sliding displacement of the rear foot are assumed to be b 2 and b1. Therefore, the effective stride length, λ eff , can be calculated from either the displacement of the front foot or the displacement of the back foot, as in (1): λ eff = a1 − b2 = b1 − a 2 .
θ eff . θ ideal
(7)
Using the results obtained in section 4.3, the average turning angle was calculated to be 2.3 degrees per stride, and the ideal turning angle was calculated to be 10.8 degrees per stride. The turning locomotion efficiency was calculated to be 21.3%, as in (8): ηturning =
2.3° = 21.3%. 10.8°
(8)
In order to improve the robot’s turning locomotion efficiency, the experiments were repeated with the same robot, where the low- and high-friction segments of the feet were interchanged by removing the PI film from the two sides of the feet and attaching a single PI film to the middle section of the feet. These changes are shown in figure 15. Using the same method, a left-turning motion was tested, taking 21 strides to complete a 90 degree turn, so the average turning angle of the robot was determined to be 4.3 degrees per stride. Also, the ideal turning angle was measured to be 10.8 degrees
(1)
Ideally, there would be no slip in the anchored feet, which means that both a 2 and b 2 would be equal to zero. The resulting stride length would be maximal for the robot’s contraction, and this ideal stride length, λ ideal , can be calculated as in (2), where L relax and L contract are the relaxed and contracted length of the robot structure: λ ideal = L relax − L contract .
(6)
(2)
7
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Figure 14. Schematic of the robot’s left-turning stride. (a) From top to bottom are initial, transitional, and final positions of the robot, and the
red circles and blue circles denote the high- and low-friction segments that are in contact with the ground. (b) Corresponding top-view schematic. The dotted shape denotes the previous position.
Figure 15. Schematic of the robot’s real left-turning stride with inverted feet configuration. (a) From top to bottom are initial, transitional, and final positions of robot’s three-dimensional structures. (b) Corresponding top-view schematic.
8
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per stride. The turning locomotion efficiency was calculated to be 39.7%, as shown in (9), which is nearly double that of the previous configuration: ηturning =
4.3° = 39.7%. 10.8°
measured in (10), will increase, resulting in better turning efficiency. The turning locomotion of the modified robot was tested, and the results indicated that the turning efficiency was increased to 39.7%, which is nearly double that of the previous results.
(9)
6. Conclusion
5.3. Mechanical analysis
The schematic of the real turning locomotion of the robot for one stride is shown in figure 14. During the anchor-pull stage of the turning locomotion, the friction force generated at the high-friction feet should be enough to prevent any sliding, while the low-friction feet generate a minimal friction force. This would generate an optimal turning angle, but if the difference in friction force is not large enough, the highfriction feet will also slide. The same situation occurs for the anchor-push motion. In figure 14(b), during the anchor-pull locomotion motion, the O1 segment should be fixed without any sliding locomotion, and the lower friction contact points are expected to rotate with respect to the expected fixed region. The high friction contact region has a big friction, FH , but also has a small friction moment due to a very short moment arm, L H ; if the region is a point, the friction moment will be zero. To the contrary, the lower friction contact points have small frictions of FL1 and FL2 , but they have nonignorable friction moments to the expected fixed region due to their very long moment arms of L L1 and L L2 . The turning moment in the turning process can be calculated as in (10):
In this study, an inchworm-inspired biomimetic robot was built using an SMA-based SSC structure capable of mimicking the looping gait of an inchworm for both linear and turning locomotion. Based on the different functions of the inchworm, the robot is comprised of three segments, referred to as the body and the feet. The robot achieved a stride length of 54 mm, which is nearly a third of its body length, with a linear speed of 3.6 mms−1 a linear locomotion efficiency of 96.4%, a turning stride angle of 4.3 degrees, and a turning linear locomotion efficiency of 39.7%. The turning locomotion efficiencies of the robot with two different feet configurations were compared to determine the better solution. The reported linear stride length per body length and the stride turning angle is much higher than that reported in other studies. This robot could be useful in rescue and reconnaissance missions where humans or larger robots are not capable of access. Furthermore, since this structure is simple, lightweight, and quiet, its principles could also be applied to other applications where flexibility and large deformation are required, such as wearable devices or other types of smart structures. Future work will focus on improving the mobility of the robot using an independent control system.
2
M = FH ⋅ L H −
∑FLi ⋅ L Li.
(10)
i=1
In this case, the resultant force moment will not be big enough to prevent sliding during the turning locomotion. The same situation happens during the anchor-push stage, with the fixed region being O2 . For this configuration, the feet with high friction do not generate enough friction force to prevent sliding. To resolve this issue, the design of the feet was changed by giving the two side segments on each foot a high friction coefficient, and the middle segment a low friction coefficient. The design of the feet was changed to obtain a longer moment arm for the high-friction segments, leading to a larger moment to prevent sliding of the anchored foot during turning locomotion. The effect of the change in feet design on the locomotion is shown in figure 15. During the anchor-pull stage of the turning locomotion, the anchored region centered on O1′ should be fixed without any sliding locomotion, and the lower friction contact points are expected to rotate with respect to the expected fixed region. Using this design, the friction force acting on the nonanchored, highfriction foot segment, is reduced to half, as denoted by FH′ . However, it benefits from a longer moment arm equivalent to the width of the robot, w , which is much larger than the L H from the previous configuration. The same situation occurs during the anchor-push stage, with the O2′ segment being fixed. Following this, the resultant force moment, as
Acknowledgments This research was supported by the Converging Research Center Program through the Ministry of Science, ICT, and Future Planning, Korea (No. 2013K000371), the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. NRF-2010-0029227), and the third stage of the Brain Korea 21 Plus Project in 2013.
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[15] Ueno S, Takemura K, Yokota S and Edamura K 2012 An inchworm robot using electro-conjugate fluid IEEE Int. Conf. on Robotics and Biomimetics 1017–22 [16] Kim M S, Chu W S, Lee J H, Kim Y M and Ahn S H 2011 Manufacturing of inchworm robot using shape memory alloy (SMA) embedded composite structure Int. J. Precis. Eng. Manuf. 12 565–8 [17] Lin H T, Slate D J, Paetsch C R, Dorfmann A L and Trimmer B A 2011 Scaling of caterpillar body properties and its biomechanical implications for the use of a hydrostatic skeleton The Journal of Experimental Biology 214 1194–204 [18] Trueman E R 1975 The Locomotion of Soft-Bodied Animals (London: Edward Arnold Press) [19] Rheuben M B and Kammer A E 1980 Comparison of slow larval and fast adult muscle innervated by the same motor neurone The Journal of Experimental Biology 84 103–18 [20] Dorfmann A, Trimmer B A and Woods W A 2007 A constitutive model for muscle properties in a softbodied arthropod Journal of the Royal Society Interface 4 257–69 [21] Schneider F, Fellner T, Wilde J and Wallrabe U 2008 Mechanical properties of silicones for MEMS J. Micromech. Microeng. 18 065008 [22] Rodrigue H, Bhandari B, Han M W and Ahn S H 2014 A shape memory alloy–based soft morphing actuator capable of pure twisting motion J. Intell. Mater. Syst. Struct. 1045389–4536008 [23] Wang G and Shahinpoor M 1997 Design, prototyping and computer simulations of a novel large bending actuator made with a shape memory alloy contractile wire Smart Mater. Struct. 6 214
[5] Kim H J, Song S H and Ahn S H 2013 A turtle-like swimming robot using a smart soft composite (SSC) structure Smart Mater. Struct. 22 014007 [6] Ahn S H, Lee K T, Kim H J, Wu R Z, Kim J S and Song S H 2012 Smart soft composite: an integrated 3D soft morphing structure using bend-twist coupling of anisotropic materials Int. J. Precis. Eng. Manuf. 13 631–4 [7] Marchese A D, Onal C D and Rus D 2014 Autonomous soft robotic fish capable of escape maneuvers using fluidic elastomer actuators Soft Robotics 1 75–87 [8] Lin H T, Leisk G G and Trimmer B 2011 GoQBot: a caterpillar-inspired soft-bodied rolling robot Bioinsp. Biomim. 6 026007 [9] Seok S, Onal C D, Wood R, Rus D and Kim S 2010 Peristaltic locomotion with antagonistic actuators in soft robotics IEEE Int. Conf. on Robotics and Automation (ICRA) 1228–33 [10] Shepherd R F, Ilievski F, Choi W, Morin S A, Stokes A A, Mazzeo A D, Chen X, Wang M and Whitesides G M 2011 Multigait soft robot Proc. of the National Academy of Sciences 108 20400–3 [11] Deimel R and Brock O 2013 A compliant hand based on a novel pneumatic actuator Proc. of the IEEE Int. Conf. on Robotics and Automation (ICRA) 2047–53 [12] Deimel R and Brock O 2014 A novel type of compliant, underactuated robotic hand for dexterous grasping Robotics: Science and Systems (RSS) (Berkeley, USA 12–16 July 2014) [13] Koh J S and Cho K J 2009 Omegabot: biomimetic inchworm robot using SMA coil actuator and smart composite microstructures (SCM) Int. Conf. on Robotics and Biomimetics 1154–59 [14] Lee D, Kim S, Park Y L and Wood R J 2011 Design of centimeter-scale inchworm robots with bidirectional claws IEEE Int. Conf. on Robotics and Automation 3197–204
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Locomotion of inchworm-inspired robot made of smart soft composite (SSC)
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Bioinspiration & Biomimetics Bioinspir. Biomim. 9 (2014) 046006 (10pp)
doi:10.1088/1748-3182/9/4/046006
Locomotion of inchworm-inspired robot made of smart soft composite (SSC) Wei Wang1, Jang-Yeob Lee1, Hugo Rodrigue1, Sung-Hyuk Song1, Won-Shik Chu2 and Sung-Hoon Ahn1,2 1
Department of Mechanical and Aerospace Engineering, Seoul National University, Gwanak-Ro 566, Gwanak-gu, Seoul, Korea, 151-742 2 Institute of Advanced Machinery and Design, Seoul National University, Gwanak-Ro 566, Gwanak-gu, Seoul, Korea, 151-742 E-mail: [email protected] Received 1 July 2014, revised 1 August 2014 Accepted for publication 26 August 2014 Published 7 October 2014 Abstract
A soft-bodied robot made of smart soft composite with inchworm-inspired locomotion capable of both two-way linear and turning movement has been proposed, developed, and tested. The robot was divided into three functional parts based on the different functions of the inchworm: the body, the back foot, and the front foot. Shape memory alloy wires were embedded longitudinally in a soft polymer to imitate the longitudinal muscle fibers that control the abdominal contractions of the inchworm during locomotion. Each foot of the robot has three segments with different friction coefficients to implement the anchor and sliding movement. Then, utilizing actuation patterns between the body and feet based on the looping gait, the robot achieves a biomimetic inchworm gait. Experiments were conducted to evaluate the robot’s locomotive performance for both linear locomotion and turning movement. Results show that the proposed robot’s stride length was nearly one third of its body length, with a maximum linear speed of 3.6 mm s−1, a linear locomotion efficiency of 96.4%, a maximum turning capability of 4.3 degrees per stride, and a turning locomotion efficiency of 39.7%. S Online supplementary data available from stacks.iop.org/BB/9/046006/mmedia Keywords: inchworm-inspired robot, shape memory alloy, smart soft composite (Some figures may appear in colour only in the online journal) 1. Introduction
zirconate titanate, and pneumatics, to provide the driving force of the robot. Soft morphing robots based on biomimetic principles are capable of continuous locomotion in harmony with their environments. Without making use of traditional mechanical components, they can be built to be lightweight and capable of a diverse range of locomotion. The advantages of soft-bodied robots are reflected in their large and complex deformation, compact architecture, lightweight robot structure, and their control method based on body morphology [2]. In recent studies, various underwater soft robots have been developed, including one by Mazzolai et al that mimics the arm structure of an octopus via a braided sleeve that uses SMA coils as transverse actuators for elongation deformation [3]. Villanueva et al used bioinspired SMA composite actuators to mimic the locomotion and appearance of a
In nature, soft tissues and organs comprise most of the mass of animals belonging to either invertebrate or chordate phyla. Since most of their bodies are comprised of soft elements, these animals to have a strong ability to adapt to a variety of living environments, even in unexpected situations. In order to replicate the versatility found in living creatures, soft robots were developed using of a combination of soft materials and stiff components. Soft robotics has benefited greatly from advances in materials science, new manufacturing technologies, biomechanics, and computational simulations [1]. Recent research in the field of soft robotics focuses on the application of soft or compliant materials combined with smart actuators, such as shape memory alloys (SMAs), lead 1748-3182/14/046006+10$33.00
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© 2014 IOP Publishing Ltd Printed in the UK
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Figure 1. (a) An inchworm. (b) Side view of an inchworm and (c) sketch of its main muscular structures.
jellyfish [4]. Kim et al proposed a bionic marine turtle flipper using an SMA-actuated smart soft composite (SSC) structure capable of coupled bending and twisting locomotion [5, 6]. Marchese et al developed a soft-bodied fish robot with fluidic elastomer actuators to perform rapid escape responses [7]. Some studies have been conducted on robots that mimic the behavior of caterpillars and worms, such as a caterpillarinspired robot developed by Lin et al that is actuated by SMA coil actuators installed in a soft body capable of rolling locomotion [8]. Seok et al used an SMA-coil-actuated, braided mesh tube with a fixed volume by applying Pascal's principle to mimic the peristaltic locomotion of an earthworm [9]. A pneumatically actuated quadrupedal soft robot made of silicone and capable of multiple gaits was developed by Shepherd et al [10]. A few pneumatic robot hands made of either silicone or granular materials have also been developed [11, 12]. A few studies have been conducted on inchworm-based robots that use the inchworm’s distinctive locomotion pattern. Koh et al built an inchworm robot named Omegabot, which was made of SMA springs and smart composite microstructures (SCM). It could move in only one direction and had a stride length of around 1/6 of its body length [13]. Using a similar principle, a centimeter-scale, motor-actuated inchworm robot with bidirectional claws was designed by Lee et al [14]. This robot also moved in a single direction and had a similar stride length. Ueno et al [15] developed an inchworm robot capable of two-way movement by using electroconjugate fluid (ECF) to produce body deformation and suction at the robot’s feet. However, this robot was connected to an external ECF tank and required high voltage. Using glass fiber reinforced plastic, Kim et al [16] built an inchworm robot capable of one-directional movement with a very small stride of 1/24 of its body length. These inchwormbased robots have small stride lengths, and most are only capable of unidirectional movement. In this study, a soft, morphing, inchworm-inspired robot made of SSCs was designed and fabricated to be both thin and
lightweight. This was done by combining three materials to form an SSC: SMA wires, polydimethylsiloxane (PDMS), and a thin polyvinyl chloride (PVC) plate. SMA-based SSCs are capable of large deformation although they are small, lightweight, and noise-free. In order to replicate the functions of a living inchworm, the robot was divided into three functional parts, consisting of the body and both the front and back feet, to generate the required deformation at different steps of each stride. This soft inchworm-inspired robot is capable of large-stride, two-way, linear locomotion and of turning in either direction. Its locomotion efficiency was also evaluated and analyzed.
2. Biological analysis The caterpillar has a pressurized-fluid-column-form coelom comprising its head, thorax, and abdomen. It is a proficient crawler through the use of its front true legs and its welldeveloped foot-like organs called prolegs. Caterpillars have a very complex muscular system since they only have longitudinal and oblique muscle fibers in their abdomens, and they lack circumferential muscles [17]. For soft animals without skeletons, muscles play a central role in defining the shape of body movements [18]. Caterpillar muscles have long sarcomeres, where each thick filament is surrounded by 10–12 thin filaments that are quite different from skeletal muscles [19]. A constitutive model of the muscle structure of the tobacco hornworm caterpillar, a family member of the inchworm, was developed by Dorfman et al [21] and showed that the main longitudinal muscles of this arthropod had a nonlinear pseudo-elastic stress-deformation response, and can thus be considered to be nonlinear pseudo-elastic composites [20]. An inchworm is a kind of caterpillar of the geometer moth that has only two or three pairs of prolegs at its rear end and true legs at its front. Other types of caterpillars have prolegs located all along their body. The different body parts and locations of the different leg types of an inchworm are 2
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Figure 2. Locomotion of an inchworm for one stride. Figure 3. Conceptual design of body-bending structure: (left to right) right deviated bending, neat bending, and left deviated bending. (a) Oblique view. (b) Top view. (c) A-A section view.
shown in figure 1. Figure 1 also shows a real inchworm with its longitudinal muscles contracted (top left) and a cross section of its abdomen showing its main muscle structure (top right). The contraction of the longitudinal muscle fibers leads to a bending deformation of the body of the inchworm, which results in a shortening of its overall length. Then, by immobilizing the true legs and prolegs alternately, it uses a looping gait for locomotion. If the longitudinal muscle fibers are actuated symmetrically, then the inchworm undergoes a linear locomotion, but if it contracts its longitudinal muscle fibers asymmetrically, then the body undergoes a nonsymmetric deformation, which results in a turning locomotion using one of the feet as an anchor. Nonetheless, for both the linear and turning movements, the locomotion sequence of an inchworm is the same and can be divided into two stages: an anchor-pull locomotion and an anchor-push locomotion, as shown in figure 2.
Figure 4. Conceptual design of feet segment. (a) Status without
actuation. (b) Convex status by actuating SMA 2. (c) Concave status by actuating SMA 1.
3. Robot design figure 3, actuating all four SMA wires induces a symmetrical bending deformation of the body. Actuating only the pair of SMA wires located on one side of the body results in a deviation angle of the body of φ, as shown in figure 3 on the left and on the right. To achieve a large deviation angle of the body, the robot was designed with a large width. With this configuration, the actuation of all SMA wires is used to obtain linear locomotion, while the actuation of only one of the pair of SMA wires is used for turning locomotion. Generally, inchworm locomotion is based on the anchormotion crawling principle, where the legs are used for anchoring. In order to complete a stride, an inchworm needs to use its front and back legs sequentially for anchoring during body contraction and stretching. The design of the anchor-motion mechanism of the robot is very important for producing inchworm-like locomotion. To enable the robot’s feet to change states between holding and sliding on smooth ground, the feet are designed segmentally, as shown in figure 4. There are three segments for each foot; two side segments are covered with polyimide (PI) film to obtain a low
3.1. Locomotion principle
As described in the last section, the body of the inchworm is an isotropic soft material and the muscle tissues of its abdomen are longitudinal fibers used for linear contraction. Therefore, based on the morphology of the inchworm, SMA wires are selected to implement the function of the longitudinal fibers of the inchworm, and PDMS is used to create the body of the inchworm robot since it is soft, isotropic, and bonds well with the SMA wires. Referring to the sketch of the inchworm muscle structure shown in figure 1, the contraction of the longitudinal muscle fibers generate different deformations of the abdomen, such as bending and turning, depending on which muscle fibers are contracted. The robot structure was designed to be thin in order to obtain a large deformation, with two pairs of parallel SMA wires placed symmetrically on each side of the robot along the axial plane of the body. In order to imitate the locomotion patterns of the inchworm, the SMA wires can be actuated using different patterns to obtain different deformation patterns. As shown in the center of 3
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Figure 5. (a) Structure comparison between the robot structure and an inchworm. (b) Locomotion sequence of inchworm-inspired robot with an ideal stride length of λ .
friction force with the ground, and the middle segment is silicone to gain a high friction force with the ground. Figure 4 shows the two SMA wires, named SMA 1 and SMA 2, embedded on the top and bottom portions of the robot’s feet. Actuating SMA 1 leads to a concave shape, resulting in the middle high-friction segment touching the ground, while actuating SMA 2 deforms the structure into a convex shape, resulting in the two low-friction segments touching the ground. The front and rear feet alternate between low and high coefficients of friction (COF) to generate a friction difference, which prevents the robot from sliding in one direction during the upward stroke of the body and in the other direction during the downward stroke. Figure 5(a) shows the robot’s structure compared with an inchworm. Both are divided into three parts, referred to as the body, the middle section, and the feet (at both ends). Figure 5(b) shows the deformation of the robot throughout each stride, with the stride length denoted as λ , which corresponds to the forward distance achieved by accomplishing a complete cycle combining the anchor-pull and anchor-push motions. The transition in foot shape between the two motions is shown in the middle.
Figure 6. Overall robot structure and its components. Table 1. Parameters of robot structure.
Robot parameter
Value
Robot structure dimension (mm) Body structure dimension (mm) Feet structure dimension (mm) Robot structure weight (g)
196 L × 140 W × 4 T 158 L × 140 W × 4 T 140 L × 8 W × 4 T 63.0
L, W, and T: length, width, and thickness.
sections with different friction coefficients. Both ends of the foot were covered by PI film to reduce the COF. A PVC plate with a thickness of 0.4 mm was used to reduce the weight of the overall structure, enhance its stability, and to allow the structure to obtain a larger and faster recovery stroke. The edges of the PVC plate were embedded in the PDMS matrix to couple them, but the center region wasn’t embedded in PDMS, thus reducing the weight of the structure. The carbon rods were used to maintain the intended shape of the matrix during the linear and turning locomotion of the robot and to separate the deformation of the body and the feet. The PDMS has a transition area with a thickness of 1 mm between the foot and body to further decouple the deformation of the body and the feet. The specific parameters of robot structure are summarized and shown in table 1.
3.2. Robot architecture
SMA wires were used as the active components, and were embedded in the matrix eccentrically to obtain large bending deformation. The stiffness of the host structure, the effective bendable length, the eccentricity of the SMA wires, and their dimensions influence the bending properties of the structure. The robot structure was designed as a thin, rectangular shape with a structure size of 196 × 140 × 4 mm (length × width × thickness). Figure 6 shows the detailed design of the overall structure. In this figure, the eight SMA wires are gathered in four different groups: SMA-front (SMA-front-1 and SMAback-2), SMA-back (SMA-back-1 and SMA-front-2), SMAleft (SMA-left-1 and SMA-left-2), and SMA-right (SMAright-1 and SMA-right-2). The actuation of a group refers to actuating both corresponding SMA wires simultaneously. The SMA wires in each group were connected in series, such that they are simultaneously actuated. The forward and backward directions were defined arbitrarily, as the locomotion is the same in both directions. The robot foot was segmented into
3.3. Materials and fabrication
The chosen silicone is PDMS (Dow Corning Sylgard 184), since it is highly flexible. It is also highly stable since its elasticity isn’t affected by temperature changes, it has high shear stability, high thermal stability, and dielectric stability [21, 22]. The SMA wires used in this research are FLEXINOL (Ni: 55 wt%, Ti: 45 wt%, Dynalloy, US). They have diameters of 152 um for the feet and of 203 um for the body. The PVC plate was cut by a laser machine (M-300 laser platform, universal Laser Systems, Australia) with rectangular 4
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Table 2. Material properties of SMA [23].
Table 3. Material properties of PDMS (Sylgard 184).
Parameter
Value
Parameter
Value
Martensite Young’s modulus Austenite Young’s modulus Martensite start temperature Martensite finish temperature Austenite start temperature Austenite finish temperature SMA wire diameter SMA initial strain
E m = 23.2 GPa E a = 49.5 GPa Ms = 77 °C M f = 42 °C As = 81 °C A f = 106 °C 152 um, 203 um εini = 3∼4%
PDMS Young’s modulus PDMS specific gravity Useful temperature range Poisson’s ratio
1.8 MPa (25 °C ) 1.03 (25 °C ) −45 °C to 200 °C 0.45
holes along the sides to prevent delamination with the PDMS matrix. The main material properties of SMA and PDMS are listed in tables 2 and 3, respectively. To assemble and build the structure, an acrylonitrile butadiene styrene (ABS) mold is built using a three-dimensional printer (Dimension 768 SST, Stratasys, USA) that positions the components within the matrix while the PDMS cures. First, the SMA wires are positioned within the mold and prestrained by 3–4%. Second, the PVC plate is positioned in the mold. Third, the PDMS solution with a weight ratio of 10:1 monomer and hardener is mixed, degassed in a vacuum casting pump, and poured into the mold. The assembly is then placed in an oven at a temperature of 58 °C for 10 h to cure the PDMS. This temperature was chosen because it is below the actuation temperature of the SMA wires. After the curing process, the specimen is taken out of the oven and the ABS mold is removed. The PI film is then glued at the feet.
Figure 7. Schematic diagram of control process.
Figure 8. Current patterns for linear locomotion during two periods.
4. Experimental method 4.1. Control unit
with rectangular waves for the forward locomotion, is illustrated in figure 8. In this figure, two strides of 15 s each are applied for a period of 30 s, as illustrated in the time period shown in light grey; the waiting time to allow cooling of the SMA wires in the feet before they are actuated in the other direction is shown in dark grey. When actuating the SMA wires (SMA-front or SMA-back), both of the feet deform in the opposite direction to provide contact with the low-friction segment of the feet on one side of the robot and the highfriction segment on the other side. So when either is actuated, the locomotion is restricted to only one direction. The SMA wires in the body also need to maintain maximum deformation for a few seconds for the feet to change their shapes. By switching the sequence of actuation for the SMA-front and SMA-back wires, the direction of locomotion can be inverted. SMA-left and SMA-right are used to bend the body part, while the PVC plate is used to help the shape recovery. Figure 9 (middle) shows the robot at different steps of the locomotion, with the shape of each foot shown on the left and right. The robot was actuated to move forward and then backward for five strides, totaling 75 s each. The results showed that the effective average stride length was 54 mm
The experiments were conducted on a flat, horizontal rubber mat at room temperature. Through experimentation, the actuating currents for the 152- and 203 um-diameter SMA wires embedded in the SSC were determined to be 550 mA and 1000 mA, respectively. The setup for the control process of the inchworm robot is shown in figure 7. The CompactRIO 9024 and NI 9264 modules (National Instruments, USA) were used to regulate the current, and Labview 2012 was used to input the current patterns. Using this setup, the current patterns, including the actuation time and the magnitude of the currents for each channel, were set individually, with two channels used to actuate the SMA wires in the feet and two channels for the SMA wires in the body, for a total of four channels. A digital camera was used to record the locomotion of the robot, and the displacements of the robot were measured visually using a ruler. 4.2. Linear locomotion
For the linear locomotion of the robot, all four SMA wires in the body were actuated simultaneously. The actuation pattern, 5
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Figure 11. Turning locomotion for forty periods, turning angle of 90
degrees.
5. Results and discussion 5.1. Friction coefficient test
Figure 9. Linear locomotion for one period. The back and front view
show the configuration of the feet at each step throughout the stride.
A brief study on an inchworm, conducted to provide background on both the morphology and locomotion of the inchworm, was used as the basis for the design of an inchworm robot. For the design of the robot’s feet, the real inchworm has true legs and well-developed gripping prolegs to grip surfaces. For the robot built in this research, the overall locomotion principle of the robot is a looping gait that relies on a principle similar to that of the inchworm; however, rather than using true legs and prolegs to grip the locomotion surface, we used alternating low- and high-friction feet segments to implement the locomotion. Since the difference in friction between the segments of the feet plays a crucial role, an experiment was conducted to measure the static and dynamic COF of the material used in the low- and high-friction segments of the feet. This experiment was conducted according to the ASTM D 1894 standard, using a tensile testing machine (5948 MicroTester, Instron, US) with a friction fixture (2810-005, Instron, US). The COF of the PDMS and PI film structures to the rubber material were tested three times each, and the results are shown in figure 12. From the results, one can see that the static and dynamic COFs of PDMS-rubber (1.22 and 0.56) are approximately four and nine times of those of PI-rubber (0.30 and 0.06), respectively.
Figure 10. Current patterns for left-turning locomotion during two
periods.
during ten periods, with a total distance of 540 mm in 150 s and a corresponding average speed of 3.6 mm s−1.
4.3. Turning locomotion
Just like the muscle fibers in the abdomen of the inchworm, an asymmetrical contraction of the SMA wires can be used to produce a turning locomotion. For the turning locomotion, the SMA wires were actuated on only one side of the body. Therefore, the turning locomotion is done by using the same pattern as the linear locomotion, but by actuating only SMAleft or SMA-right. The current patterns for the left-turning locomotion during two periods are shown in figure 10. Forty strides with a left-turning locomotion were completed by actuating only SMA-left, to obtain a total turn of 90 degrees equaling 2.3 degrees per stride. The resulting locomotion of the forty combined strides is shown in figure 11.
5.2. Locomotion efficiency analysis 5.2.1. Linear locomotion efficiency analysis. To achieve
locomotion, the feet change from being used as anchors to sliding, depending on whether the high-friction or lowfriction segment of the foot is in contact with the ground. However, some sliding may occur in the anchored feet, which reduces the overall stroke length of the robot. The schematic of the robot’s linear locomotion for one stride is shown in figure 13, with the loss in stroke length due to slipping of the anchored feet shown as a 2 and b 2 . For the anchor-pull 6
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Based on this ideal stride length, the linear locomotion efficiency of the robot can be expressed as in (3): ηlinear =
λ eff λ ideal .
(3)
Using the results obtained in section 4.2, the effective stride length was calculated to be 54 mm, and the ideal stride length of the robot during the ten periods was 56 mm. The resulting linear locomotion efficiency is 96.4%, as in (4): ηlinear =
54 = 96.4%. 56
(4)
5.2.2. Turning locomotion efficiency analysis. The turning
locomotion efficiency is calculated by considering the deformation of the robot during the stride of the turning locomotion. As shown in figure 14, during the anchor-pull process of a left-turning stride, the clockwise rotation angle of the rear foot and the anticlockwise rotation sliding angle of the front foot are assumed to be α1 and α2 . In the following anchor-push process, the anticlockwise rotation angle of the front foot and the clockwise rotation sliding angle of the rear foot are assumed to be β2 and β1. Therefore, the effective turning angle, θeff , can be calculated as in (5):
Figure 12. COF of PDMS and PI films to rubber material.
θ eff = α1 − β1 = β2 − α2.
(5)
In the ideal turning locomotion, the sliding angle of the anchored feet should be zero (that is, α2 = β1 = 0 ). Then, the ideal turning angle for each stride of θ ideal can be calculated as in (6), where φ is the deviation angle of the body, as shown in figure 14: θ ideal = α1 = β2 = φ .
Then, the efficiency of the turning locomotion can be expressed as in (7):
Figure 13. Schematic of robot real linear locomotion. (Top to bottom) Initial, transitional, and final positions.
ηturning =
process, the forward displacements of the rear foot and the sliding displacement of the front foot are assumed to be a1 and a 2 . In the ensuing anchor-push process, the forward displacements of the front foot and the sliding displacement of the rear foot are assumed to be b 2 and b1. Therefore, the effective stride length, λ eff , can be calculated from either the displacement of the front foot or the displacement of the back foot, as in (1): λ eff = a1 − b2 = b1 − a 2 .
θ eff . θ ideal
(7)
Using the results obtained in section 4.3, the average turning angle was calculated to be 2.3 degrees per stride, and the ideal turning angle was calculated to be 10.8 degrees per stride. The turning locomotion efficiency was calculated to be 21.3%, as in (8): ηturning =
2.3° = 21.3%. 10.8°
(8)
In order to improve the robot’s turning locomotion efficiency, the experiments were repeated with the same robot, where the low- and high-friction segments of the feet were interchanged by removing the PI film from the two sides of the feet and attaching a single PI film to the middle section of the feet. These changes are shown in figure 15. Using the same method, a left-turning motion was tested, taking 21 strides to complete a 90 degree turn, so the average turning angle of the robot was determined to be 4.3 degrees per stride. Also, the ideal turning angle was measured to be 10.8 degrees
(1)
Ideally, there would be no slip in the anchored feet, which means that both a 2 and b 2 would be equal to zero. The resulting stride length would be maximal for the robot’s contraction, and this ideal stride length, λ ideal , can be calculated as in (2), where L relax and L contract are the relaxed and contracted length of the robot structure: λ ideal = L relax − L contract .
(6)
(2)
7
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Figure 14. Schematic of the robot’s left-turning stride. (a) From top to bottom are initial, transitional, and final positions of the robot, and the
red circles and blue circles denote the high- and low-friction segments that are in contact with the ground. (b) Corresponding top-view schematic. The dotted shape denotes the previous position.
Figure 15. Schematic of the robot’s real left-turning stride with inverted feet configuration. (a) From top to bottom are initial, transitional, and final positions of robot’s three-dimensional structures. (b) Corresponding top-view schematic.
8
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per stride. The turning locomotion efficiency was calculated to be 39.7%, as shown in (9), which is nearly double that of the previous configuration: ηturning =
4.3° = 39.7%. 10.8°
measured in (10), will increase, resulting in better turning efficiency. The turning locomotion of the modified robot was tested, and the results indicated that the turning efficiency was increased to 39.7%, which is nearly double that of the previous results.
(9)
6. Conclusion
5.3. Mechanical analysis
The schematic of the real turning locomotion of the robot for one stride is shown in figure 14. During the anchor-pull stage of the turning locomotion, the friction force generated at the high-friction feet should be enough to prevent any sliding, while the low-friction feet generate a minimal friction force. This would generate an optimal turning angle, but if the difference in friction force is not large enough, the highfriction feet will also slide. The same situation occurs for the anchor-push motion. In figure 14(b), during the anchor-pull locomotion motion, the O1 segment should be fixed without any sliding locomotion, and the lower friction contact points are expected to rotate with respect to the expected fixed region. The high friction contact region has a big friction, FH , but also has a small friction moment due to a very short moment arm, L H ; if the region is a point, the friction moment will be zero. To the contrary, the lower friction contact points have small frictions of FL1 and FL2 , but they have nonignorable friction moments to the expected fixed region due to their very long moment arms of L L1 and L L2 . The turning moment in the turning process can be calculated as in (10):
In this study, an inchworm-inspired biomimetic robot was built using an SMA-based SSC structure capable of mimicking the looping gait of an inchworm for both linear and turning locomotion. Based on the different functions of the inchworm, the robot is comprised of three segments, referred to as the body and the feet. The robot achieved a stride length of 54 mm, which is nearly a third of its body length, with a linear speed of 3.6 mms−1 a linear locomotion efficiency of 96.4%, a turning stride angle of 4.3 degrees, and a turning linear locomotion efficiency of 39.7%. The turning locomotion efficiencies of the robot with two different feet configurations were compared to determine the better solution. The reported linear stride length per body length and the stride turning angle is much higher than that reported in other studies. This robot could be useful in rescue and reconnaissance missions where humans or larger robots are not capable of access. Furthermore, since this structure is simple, lightweight, and quiet, its principles could also be applied to other applications where flexibility and large deformation are required, such as wearable devices or other types of smart structures. Future work will focus on improving the mobility of the robot using an independent control system.
2
M = FH ⋅ L H −
∑FLi ⋅ L Li.
(10)
i=1
In this case, the resultant force moment will not be big enough to prevent sliding during the turning locomotion. The same situation happens during the anchor-push stage, with the fixed region being O2 . For this configuration, the feet with high friction do not generate enough friction force to prevent sliding. To resolve this issue, the design of the feet was changed by giving the two side segments on each foot a high friction coefficient, and the middle segment a low friction coefficient. The design of the feet was changed to obtain a longer moment arm for the high-friction segments, leading to a larger moment to prevent sliding of the anchored foot during turning locomotion. The effect of the change in feet design on the locomotion is shown in figure 15. During the anchor-pull stage of the turning locomotion, the anchored region centered on O1′ should be fixed without any sliding locomotion, and the lower friction contact points are expected to rotate with respect to the expected fixed region. Using this design, the friction force acting on the nonanchored, highfriction foot segment, is reduced to half, as denoted by FH′ . However, it benefits from a longer moment arm equivalent to the width of the robot, w , which is much larger than the L H from the previous configuration. The same situation occurs during the anchor-push stage, with the O2′ segment being fixed. Following this, the resultant force moment, as
Acknowledgments This research was supported by the Converging Research Center Program through the Ministry of Science, ICT, and Future Planning, Korea (No. 2013K000371), the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. NRF-2010-0029227), and the third stage of the Brain Korea 21 Plus Project in 2013.
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