Fully 3D-printed tortoise-like soft mobile robot with muti-scenario adaptability

Soft robotic systems are well suited to unstructured, dynamic tasks and environments, owing to their ability to adapt and conform without damaging themselves or their surroundings. These abilities are crucial in areas such as human-robot interaction, simplification of control system and weight reduction. At present, the existing soft mobile robots still have the disadvantages of single motion mode and application scenario, difficult manufacturing and low energy conversion efficiency. Based on the current shortcomings of soft robots, this paper designs and proposes a fully 3D-printed tortoise-like soft mobile robot with muti-scenarios adaptability. The robot uses a Bionic Tortoise Leg Actuator structure that enables simultaneous bending of the actuator in both directions, simplifying robot control and increasing the maximum bending angle achievable. In addition, a reconfiguration design solution has been proposed to enable the robot to implement two bionic modes for land and sea turtles, adapting to move on hard and soft surfaces and in water, enabling it to move in amphibious and complex environments. The performance of the pneumatic soft actuator is also improved by an improved Digital Light Processing method that enhances the maximum strain of the 3D printed soft material. The prototype was tested to give maximum movement speeds for different gaits and environments, demonstrating that the fully 3D printed tortoise-like soft-mobile robot designed in this paper is highly adaptable to multiple scenarios. The robot studied in this paper has a wide range of applications, with potential applications including navigation in a variety of domain environments, inspection of large underground oil and gas pipelines, and navigation in high temperature, high humidity and strong magnetic field environments or in military alert conditions.


Introduction
Mobile robots greatly expand people's space accessibility [1][2][3].Current mobile robots are dominated by metal-based material rigid robots connected by rigid connections, such as tracked mobile robots with high barrier-crossing capability [4], wheeled robots with fast movement [5], and legged mobile robots with multifunctionality and intelligent device integration [6].Mobile robots face unstructured environments that are more complex and dangerous than expected.When dealing with intricate scenarios, the weaknesses of traditional rigid mobile robots, such as bulky, heavy, single mode of motion, poor environmental interactivity, and high cost, become apparent [7].
Bioinspiration and biomimetics are areas that have been booming recently, providing solutions to many practical engineering problems [8].When people are confronted with complex and tricky tasks, organisms in nature may provide unexpected answers [9].The environment that nature provides to animals is complex and varied, and the ability of animals to adapt to their environment is astonishing.For traditional rigid mobile robots, they adapt to their environments through complex perception, feedback, and recognition systems [10][11][12].While most animals are soft-bodied, generate and transfer energy and motion through soft body structures and they use mechanical feedback from their interactions with the environment to adapt through their own compliance rather than antagonism [13].Therefore, it is meaningful to apply the principles of biology to mobile robots.Soft mobile robots have been proposed to take advantage of animal characteristics.
The locomotion modes of soft mobile robots are often inspired by the locomotion mechanisms of creatures, including crawling, swimming, flying, and legged locomotion [8,14].Soft mobile robots that use crawling locomotion mode are generally inspired by invertebrates (caterpillars, earthworms, inchworms, starfish, etc.) with soft bodies [15].Das et al designed and developed the peristaltic soft actuator (PSA) and a modular soft robot assembled from five PSAs, inspired by the contraction and diastole of the earthworm's antagonistic muscles and the friction squamate on the abdomen [16].Soft-mobile robots that imitate fish have a natural advantage over rigid robots in swimming locomotion.Snailfish is an animal that lives in the ocean depths around 8000 m.Inspired by the distributed skull and flapping pectoral fins of snailfish, Li et al developed a soft mobile robot for use in the deep ocean [17].Birds and flying insects are the inspiration for flying soft robot designs.Karásek et al developed a small programmable flying robot with autonomous motion based on the kinematic characteristics of fruit flies [18].Mobile robots with soft legs achieve legged locomotion through the deformation of soft legs.Muralidharan et al reported a novel fourgroup robot that demonstrated the ability to perform multiple gaits (e.g.walking and jumping) [19].It could run at speeds of up to two body lengths per second.
In terms of manufacturing, materials used in conventional robotic systems have Young's modulus in excess of the 1 GPa range.In contrast, soft robotic systems are typically manufactured using soft materials similar to the Young's modulus of natural organisms, about 10 4 to 10 9 Pa [20].Due to the usage of these soft materials, soft robots cannot be manufactured using traditional methods of rigid materials such as machining, joining and shear forming, posing a significant challenge to the processing and manufacturing of soft robots.In the initial stages of soft robot development, methods such as molding, film fabrication, shape deposition manufacturing and bonding were sufficient to manufacture soft robot systems due to their simple structure and single function.However, as the functionality of soft robots increased and researchers needed to design and manufacture soft structures in a variety of materials and sizes, the drawbacks of traditional manufacturing methods became apparent.3D printing emerged as a new manufacturing method that allows more freedom to design complex geometries than other manufacturing methods [21,22].And soft robots are usually composed of easily deformable substances such as fluids, gels and reactive polymers, all of which have to be compatible with 3D printing technology.In the field of soft 3D printing, the more commonly used 3D printing technologies are: fused deposition modeling (FDM), direct ink writing, selective laser sintering (SLS), inkjet printing (IP), stereo lithography appearance (SLA) and digital light processing (DLP).
Compared with rigid robots, pneumatic soft robots have proved their superiority in many fields and have been applied in practice.A number of explorations have been conducted by researchers for 3D printed soft pneumatic robotic systems in recent years.Yap et al used FDM method to print soft pneumatic actuators and characterized the performance of the actuators in various aspects, and demonstrated the potential applications of 3D printed actuators [23].Schaffner et al report a 3D printing platform for the seamless digital fabrication of pneumatic silicone actuators exhibiting programmable bioinspired architectures and motions [24].Xie et al have fabricated soft robots for pipe crawling by SLS, capable of working on pipes of various diameters, radii of curvature, inclined outer walls, as well as inner walls [25].Drotman et al used IP technology to design and fabricate a quadrupedal crawling robot with soft legs capable of rotating around two axes, enabling it to navigate through rough terrain [26].Peele et al used SLA technology to fabricate an artificial muscle antagonist system, enabling multi-degree of freedom flexion while enhancing mechanical properties [27].Zhang et al used DLP technology to fabricate the milli-meter scale soft pneumatic robots that enable navigation in confined areas or micro-scale object manipulation [28].
At present, the 3D printing technology commonly used in the manufacture of pneumatic soft robots has the characteristics of low manufacturing efficiency, high cost and insufficient flexibility of materials.Through experiments, we found that the application of traditional DLP-3D printing technology and the use of low-cost photosensitive polyurethane elastomer liquid can obtain low hardness, good tensile properties, while ensuring accuracy of more than 0.01 mm soft actuators.At the same time, we optimized the post-processing of the cured polyurethane elastomer soft actuators, solved the problems such as excessive surface adhesion limiting the large deformation of the soft actuator and internal cavity blockage.The complete manufacturing process proposed will provide some level of assistance for the manufacture of soft pneumatic actuators.
Since pneumatic soft robots are characterized by strong terrain adaptability.Several researchers have previously conducted bionic studies based on the amphibious reptile's ability to adapt to multiple environments, designing and building robots with specific advantages.Wu et al investigated a fully 3Dprinted amphibious soft robot with terrain adaptation and amphibious landing capabilities, capable of linear motion at 0.97 BL s −1 [29].Dortman et al present a method for controlling the gait of a soft-legged robot using a simple pneumatic circuit.Different gaits are generated based on the three degrees of freedom of the soft leg and motion is realized between the gaits [30].Faudzi et al designed Softamphibious robot based on thin and soft McKibben actuator so as to be able to move in complex environments.Although all of the above quadrupedal crawling robots are able to realize movement in complex environments, they still have problems such as complex control, single working mode, large size and manufacturing difficulties [31].In this paper, a fully 3D-printed tortoise-like soft mobile robot with mutiscenarios adaptability is developed by bionic terrapin as well as existing quadrupedal crawling soft robots based on their current problems sea turtle's movement pattern and based on DLP 3D printing technology.

Bioinspiration from tortoise's leg
The tortoise has lived on Earth as a reptile for millions of years.In the evolution process, due to the different living environment, the tortoise evolved to two morphologies: the land tortoise and the sea turtle.Land tortoises have thick, cylindrical limbs and are suitable for navigating on land and grass.Sea turtles have flat, flipper-like limbs that allow them to swim nimbly in the sea.Both land and sea turtles are generally amphibious and can adapt to both aquatic and terrestrial environments [32,33].
Both species of tortoises generate movement through their limbs in physical contact with the external environment.The legs of both land and sea turtles can be divided into two parts.During crawling, as shown in figure 1(a), Part I of the land tortoise's leg will swing back and forth parallel to the direction of motion, creating a stride, while Part II of the tortoise's leg will generate pressure downward perpendicular to the direction of motion, creating friction with the ground and converting the stride into a forward distance.As shown in figure 1(b), when the sea turtle swims in the water, Part I of the sea turtle's leg swings up and down perpendicular to the direction of motion to generate lifting force so that it does not sink, while Part II will swing back and forth parallel to the direction of motion like a boat paddle to generate a forward thrust [34].
To summarize the analysis of the turtle leg structure, it can be found that both sea turtles and land tortoises have legs that can be divided into two parts: Part I transmits motion and Part II generates motion through contact with the outside world.Both parts swing in the direction parallel to and perpendicular to the direction of motion.Therefore, a soft actuator that bends around both axes can be proposed to achieve such a movement pattern.

Design of bionic tortoise leg actuator (BTLA)
As shown in figures 2(a) and (b), the actuator designed to achieve tortoise movement is also divided into two parts in appearance, consisting of a doublechanneled pneumatic-network type actuator and a single-channeled pneumatic-network type actuator.If a space-rectangular coordinate system is established with the longest side of the actuator as the y-axis, the actuator will bend in both directions around the z-axis when the Part I double-chamber actuator is inflated, and in one direction around the x-axis when the Part II single-chamber actuator is inflated.
The bending of the two parts of the BTLA is synchronous, so that one channel of the doublechanneled actuator can be connected to the singlechanneled actuator to form a long channel, while the other channel is a short channel, as shown in the green box in figure 2(b).This ensures continuity of robot locomotion and allows for simpler robot control due to the reduction of one pneumatic circuit.
In addition, each of the BTLA's air cavities is trapezoidal in shape, and this design contributes to the maximum bending angle of the actuator and avoids collisions between the adjacent air cavities [35].
Figure 2(c) shows the deformation of the BTLA.When air pressure is applied in the long channel, the BTLA bends downwards and out of the page, producing 3D motion; when air pressure is applied in the short channel, the BTLA bends inwards towards the page.The deformation in this pattern simulates the movement of the land tortoise's legs considerably.
If the BTLA is rotated 90 degrees around the x-axis from figure 2(c), the deformation of BTLA is shown in figure 2(d).Part I of the BTLA will bend downwards around the y-axis and Part II will bend outwards around the page on the z-axis when air pressure is applied to the long channel; when air pressure is applied to the short channel, Part I of the BTLA will bend upwards around the x-axis; the deformation of the rotated BTLA simulates the motion of the sea turtle legs.In addition, Part II of the BTLA has a wide bottom surface area and has characteristics resembling the sea turtle's flippers.

Overall design of tortoise-like soft mobile robot
The tortoise-like soft mobile robot consists of four BTLAs, a shell, and connections between the shell and the BTLAs.The BTLAs are assembled to the   connection devices by interference fit, and the connection devices are bolted to the shell.The shell as the body (torso) of the robot is hollow inside.This design ensures that the robot can be floated on the water and avoid sinking, but also allows the air circuits to be positioned inside the torso, allowing for an untethered robot in the future.
According to the aforementioned, the interconversion of the land tortoise type configuration and the sea turtle type configuration can be achieved by simply changing the direction of the actuator, as shown in figure 3. The reconfiguration design solution simultaneously empowers the robot to move on hard surface (land tortoise locomotion mode), soft surface and water (sea turtle locomotion mode), Reproduced from [11], with permission from Springer Nature.enables movement in amphibious and complex environments.

Tortoise-like soft robot's locomotion gait design
The locomotion gait of a land tortoise is not the same as that of a sea turtle.As shown in figure 4(a), the left front leg and the right hind leg of a land turtle are in motion simultaneously, while the left hind leg and the right front leg are in motion at simultaneously; this gait can be referred to as diagonal gait.As shown in figure 4(c), when a sea turtle is swimming, the two hind legs of the tortoise will keep close to the body and remain motionless; the two front legs will be in motion at the same time; this gait can be called synchronous gait.
Several gaits have been developed based on the gait of land and sea turtles and the mechanism of the tortoise-like soft mobile robot, as shown in figure 5.The robot's straight-line gait in sea turtle type configuration is a synchronous gait as shown in figure 5(b).During a gait cycle, first the short channels of the four BTLAs will be inflated simultaneously (figure 5(b2)); subsequently the long channels of the BTLAs will be inflated simultaneously (figure 5(b3)).Therefore, the four actuators will deform synchronously.
In subsequent experiments, it has been found that the robot is more rapid if it is walking straight-line in synchronous gait in land tortoise type configuration (figure 5(c)).This is due to the fixed air pressure for driving the BTLA, and when the robot is in diagonal gait, only two legs (BTLA) generate backward friction against the ground for a time period.When the robot is in synchronous gait, however, although it does not move during the first half cycle (short channel inflated), during the second half cycle (long channel inflated), all four legs (BTLA) exert backward friction on the ground, resulting in a larger stride and hence a higher speed.
In order to enable the robot to possess greater navigational capability, the turning gait has also been developed, as shown in figure 5(d).If the RF actuator is not inflated during robot locomotion while the LH, RH, LF actuators are inflated simultaneously, the robot will turn right around the RF.Similarly, the right turn gait can be accomplished in the sea turtle type configuration.The principle of the left turn gait is similar to the right turn gait, where the LF actuator is not inflated during robot locomotion and the LH, RH and RF actuators are inflated simultaneously.
In order to more clearly illustrate the categories of each gait and the movement modes that can be accomplished, they are included in a table, as shown in.The different environments adaptive to each gait are illustrated in the subsequent chapters of the robot's testing.

Mathmatic model of BTLA
As shown in figure 6, The BTLA has two parts, Part II is a Pneumatic Network type structure with trapezoidal air cavity shape ((PN-T structure), and Part I consists of two such structures sharing one bottom surface to achieve bi-directional bending, as shown in a.It is assumed that these two structures of Part I do not affect each other during inflation, so only the Pneumatic Network type structure with single trapezoidal air cavity (PN-T structure) needs to be analyzed to model the entire BTLA.
The assumption of segmented constant curvature is to divide the PN-T structure into continuous small segments using the principle of differentiation.The bending deformation of the PN-T can be regarded as the connection of the individual cavities after bending, as shown in figure 6(b).Define the bending angle of a single air cavity as θ and the bending angle of the whole PN-T structure as φ .Since the bending degree of each air cavity is the same, then: where m is the number of cavities in PN-T structure.
The bending deformation of a single air cavity is shown in figure 6(c).According to the geometric relationship, the bending radius of curvature R is: where d is the chord length corresponding to the arc of a single air cavity after deformation.According to the Yeoh hyperelastic model, in the strain energy density function: where λ 1 , λ 2 , λ 3 is the main elongation ratio of the air cavity in length, width and height.Since hyperelastic materials are approximately incompressible, λ 1 λ 2 λ 3 = 1.When a single air cavity is deformed, it can be considered as a one-dimensional stretching and contraction force.Let λ = λ 1 = 1 λ2 , thus: So the strain energy density function of the Yeoh model for silicone like materials used can be rewritten as: ( Since the total bending angle of the PN-T structure can be derived from equation (1), the modelling of the PN-T can again be reduced to the analysis of the bending characteristics of a single air cavity.The geometric parameters of the single air cavity are shown in figure 7.
Assuming that during deformation of the air cavity is not considered its self-weight and is not subject to any external forces, it follows from the principle of virtual work that the sum of work done and energy stored in the system is 0 at any infinitesimal virtual displacement, the work done by the driving air pressure p is completely transformed into the energy stored after the deformation of the air cavity, i.e., where V c is the volume of the air cavity, and V m is the volume of the silicone like material.Since the silicon-like material is approximately incompressible, the volume of the material is the same both before and after deformation: The volume of air cavity after deformation is: where V is the total volume of the air cavity after deformation.Therefore, it can be approximated to obtain: The primary elongation ratio of a single air cavity in the length direction is: According to equation (10), it can be found that W is a one-variable function about θ.
Derivation of θ in equation ( 6) gives the relationship between the bending angle of a single air cavity and the input air pressure: To analyze the bending characteristics of the PN-T structure better, a rectangular coordinate system is established, and the bending curve is plotted as shown in figure 8.The end coordinates can be obtained as follows.
In equation ( 2), the chord length d can be equivalent to the total length of a single air cavity: After the modeling of the PN-T structure is obtained, the BTLA with three PN-T structures can be analyzed in an analogous way.In this paper, the BTLA in land tortoise type configuration will be analyzed as an example, because the BTLA in sea turtle type configuration is structurally the same as it, only the installation direction is different.
Two deformation parameters of the BTLA are significant, one is the deformation of the actuator in the horizontal direction, which can be called Stride.This parameter determines the step size of the robot during a motion cycle, which in consequence affects the speed of the robot.The other parameter is the deformation of the actuator in the vertical direction, which can be called Height.Height affects the pressure of the actuator on the ground and hence the friction of the ground on the actuator (i.e. the driving force of the robot movement).These two parameters are shown in figure 9.
When the air pressure p is applied in the short and long air channels respectively: In the equation ( 16), S is stride in figure 9. R 1 , R 2 are the bending radius of curvature for PN-T structures in one-channel part and two-channels part, which can be obtained in equations ( 2) and ( 13).φ 1, φ 2 are the bending angles in PN-T structures for one channel part and two channels part.L 1 is the length of one channel part in BTLA which can be obtain in equations ( 1) and (11).
When the short channel is inflated, the Height size is not influenced.When the long channel is inflated: where H is Height shown in figure 9.
Since the deformation of BTLA is in three dimensions, the end position coordinates are worth to be analyzed.After deriving the relationship between the input air pressure and the end position coordinates, the trajectory of the end of the BTLA can be obtained, which helps to evaluate the gait of the robot.
As shown in figure 10, establish a spacerectangular coordinate system on BTLA and determine point O as the origin position and point E as the end position.
When the air pressure in the short channel is p, the end position coordinates (x, y, z) can be expressed as: In the equation ( 18), R 1 , R 2 are the bending radius of curvature for PN-T structures in one-channel part and two-channels part.φ 1, φ 2 are the bending angles in PN-T structures for one channel part and two channels part.L 1 is the length of one channel part in BTLA.
When the air pressure in the long channel is p, one channel part of the BTLA bends so that z in the end coordinates is no longer zero.The end position coordinates (x,y,z) can be expressed as: In general, the mathematical model of BTLA is a process from the whole to the parts and back to the whole.Firstly, BTLA can be divided into three similar PN-T structures, each PN-T has several identical air cavities.According to the principle of virtual work and the strain energy density function of Yeoh model, the relationship between the input air pressure p and the bending angle A of a single air cavity can be obtained.Using the segmented constant curvature model, the relationship between the bending angle of the PN-T structure and the bending radius of curvature of the PN-T structure with the bending angle A of the single air cavity can be deduced.Finally, the Stride value, Height value and end position coordinates can be obtained according to the geometric parameters of BTLA, the mathematical modeling process of BTLA is shown in figure 11.The material used for printing was a photosensitive polyurethane elastomer, which after curing is a super-elastic material with a Shore hardness of 40 A and mechanical properties similar to those of silicone (Model: Smooth On, Dragon Skin 30).In order to accurately characterise the mechanical properties of this material, the stress-strain curve was obtained by uniaxial tensile testing of the photosensitive polyurethane elastomer using ISO 37 as the standard, as shown in figure 12. Furthermore, for stress-strain curves with an inflection point, the third-order Yeoh model is appropriate.Figure 12 shows the stressstrain curve obtained from an uniaxial tensile test of this material and the curve fitted with the Yeoh 3rd model.The strain energy density function is:  where I 1 is the first strain tensor invariant of the strain deviator, and J is the elastic volume ratio; when the material is considered incompressible, Figure 13 shows the exact process of top-down DLP 3D printing.As shown in figure 13(a), the model STL file is first imported into the software and key parameters are set.To control the printing accuracy of less than 0.1 mm, the single layer print thickness is set to 50 µm and the single layer exposure time is 8000 ms.As shown in figure 13(b), the printing platform is placed in a photosensitive siliconelike tank, with a distance of one print layer thickness reserved.The entire cross section of the print is cured using violet light at a wavelength of 405 nm through a lens.As shown in figure 13(c), after one layer is printed, the bi-directional vacuum scraper performs a reciprocating motion on the surface of the print piece, enhancing the accuracy of the print.The printing platform then moves down one layer thickness and the process is repeated as in figures 13(b) and (c) until the print is complete.Figure 4(d) shows the platform back in position and the BTLA samples.

Manufacturing and testing of BTLA
As shown in figure 14, after the overall print has been completed, the print is post-processed by first standing to pour out the liquid material from the internal cavity and then removing the external support.As shown in figure 14(a), the post-processing first requires the use of an air gun to clean the internal structure of any liquid material that has not been poured out.Subsequent cleaning by immersion using an ethanol solution is required.As shown in figure 14(b), for the structures designed in this paper, a complete cleaning with an ultrasonic device is also required during immersion.If the cleaning is not complete and the liquid material is still present, the secondary curing will result in blockage of the air cavity, which will affect the performance of the actuator.In this experiment, the ultrasonic cleaning temperature was set at 50 degrees and the time was

Finite element method (FEM) of BTLA
The FEM can integrate materials and structures to characterize BTLA.The finite element simulation using ANSYS Workbench resulted in different states of the actuators at different air pressures.
The Yeoh hyperelastic model parameters for the photosensitive silicone material used in the BTLA are imported into ANSYS Workbench, after which the basic procedure is essentially the same as above.The deformation results are shown in figure 15, after applying 5-30 KPa air pressure to the long and short channels of the BTLA, respectively.
In addition, the bending angles of each part of the actuator can be obtained in ANSYS Workbench, as well as the coordinates of the end positions.In the subsequent chapters the results of the mathematical modeling of the actuators, the finite element simulation results and the experimental results are in comparison.The characterization of the actuator results obtained using the FEA method considers the two main factors of large material deformations and the complexity of the structure with a high level of accuracy.17(a) shows the Stride value generated by the long channel inflation (S 1 ) versus air pressure.The graph shows that the mathematical model curve, although similar in trend, still differs numerically from the test measured values and the FEA data.In addition, the Stride value S1, which is generated when the long channel is inflated, has a maximum value at around 30 KPa, which is caused by the inward bending of the BTLA one channel part.Figure 17(b) shows the relationship between the Stride value (S 2 ) and the air pressure when the short channel is inflated, where the BTLA channel does not deform and therefore the value S 2 is greater than S 1 at the same air pressure.Figure 17(c) shows the relationship between the value of total Stride and air pressure.The total Stride is numerically equal to the sum of S 1 and S 2 .This physical quantity shows the relationship between the driving air pressure of the robot and the displacement of the movement in one motion cycle.

Testing of BTLA
Likewise, the measured values for Height (H) are plotted in the same graph with the values calculated from the finite element simulation data and the mathematical model, as shown in figure 17(d).Compared to the Stride values, the mathematical model error for Height is significantly larger than that for Stride, which is due to the fact that the PN-T structure in one channel of the BTLA is affected by the other two PN-T structures in both channels during the deformation process, and this effect is not negligible.
The end position coordinates of the BTLA are another important physical parameter that can help The variation pattern of the X, Y, Z values is similar to that of the Stride and Hight values.It is notable that in figure 18(c), the value of the FEA data is not zero when the short channel is inflated.This is due to the slight expansion deformation of the actuator in the Z-axis direction as the channel is inflated.Taking into account the deformation of the BTLA and its service life, around 30 KPa is used as the driving air pressure for the robot.
To illustrate more explicitly how the end position coordinates change at different air pressures, the end position data (including testing data, FEA data, and mathematical model data) for each air pressure can be plotted within a three-dimensional diagram, as shown in figure 19(a).The three-dimensional curve in the figure is actually the motion trajectory of the actuator during the deformation process.The curves for the Testing and FEA data are obtained by fitting the two sets of data.

Output force
The tortoise-like soft mobile robot moves through the friction between the ground and the BTLAs, which depends on the pressure of the actuators against the ground in the vertical direction.The robot, in addition, requires a thrust backwards through the actuators against the water when swimming in the water.The output force of the actuator is therefore also one of the parameters characterizing the performance of the actuator.For the sake of simplicity of testing, in this paper the two channel parts of the BTLA are fixed and the downward driving force of one channel part is tested, as shown in figure 20.
The BTLA output force at each air pressure is plotted in the figure 21(air pressure applied in the long channel).For a better representation of the output force F versus the air pressure p, a curve can be fitted using a polynomial of the fourth order:     For the goodness of fit, the value of R-square is equal to 0.995.Therefore, the correlation and confidence level of this fitted curve meets the requirements.

Permissible life
The limitations of 3D printed soft actuators exist mainly in terms of low tolerance to pressure.In this paper, a single inflation and deflation is specified as a cycle, and the permissible lifetime of BTLAs printed using DLP technology at different air pressures is tested.As shown in the figure, one set of tests was performed at 5 Kpa intervals at air pressures from 25 to 65 Kpa, for a total of nine sets of tests.Each set of tests is performed three times and the average value is taken.We stipulate that less than 30 Kpa is the low air pressure region, 30-45 Kpa is the working air pressure region, and more than 45 Kpa is the extreme air pressure region.As shown in figure 22, the lifetime of BTLA is close to infinity in the low air pressure region.At 35 KPa, the life of BTLA is 989 cycles, and in the extreme air pressure region, the life of BTLA decreases rapidly and is less than 500 cycles.sea turtle type configuration.SLA technology is used to manufacture the shell that serves as the robot's body, and the entire shell weighs approximately 45 grams.This technology provides high printing accuracy, speed, and low cost.The shells are interchangeable and can be changed to different materials and constructions as required.The BTLAs are attached to the SLA 3d-printed connection devices by means of an interference fit and the connection devices are then fixed to the shell using M2 type screws and nuts.By manually removing the screws and nuts and turning the mounting orientation of the BTLAs, it is feasible to change between sea turtle type and land tortoise type configurations.

Assembly and control of the robot
The control scheme for both worm-like soft mobile and tortoise-like soft mobile robots, as shown in figure 24, includes the control system and the pneumatic driving system.The Arduino IDE at the computer side sends the program to the Arduino Uno control board through the data line, and the control board transmits the signal to the relay, which controls the operation of the air pump and air solenoid valve to achieve robot movement.In addition, the control board and relays are powered by a 5 V battery, and a 12 V battery powers the air pump and air solenoid valve.Such a control system has the particular advantage that there are no electrical components on the body of the robots, only air pipes attached to the body, with an air source at the far end providing air pressure to power the actuators.Therefore, robots are more suitable for working in water or some other wet environment.Secondly, due to the absence of electrical equipment, the robot is not disturbed in strong magnetic environments.
For the five gaits of the tortoise-like soft mobile robot, each gait has only two movement cycles and the robot has four identical BTLAs.Therefore, it is critical to distinguish the inflation status of each air channel of the actuators.As shown in figure 25, a1-d2 represent the short channel of the robot LF, the long channel of LF, the short channel of LH, the long channel of LH, the short channel of RF, the long channel of RF, the short channel of RH, and the long channel of RH, respectively.Red indicates that air pressure is applied to this channel and white indicates that the air valve connected to this channel is closed.

Testing of the tortoise-like soft mobile robot
According to the control scheme in figure 24 and the inflation strategy of BTLAs in figure 25, Gait 1 (land tortoise type configuration, asynchronous gait), Gait 2 (sea turtle type configuration, synchronous gait), and Gait 3 (land tortoise type configuration, synchronous gait) in table 1 are tested on a smooth flat surface first.The smooth flat surface is made of tempered glass and has a measured dynamic friction factor of about 0.65 between it and the cured photosensitive polyurethane elastomer.For this robot, the air source used is also the one with a maximum output air pressure of 40 KPa.Considering the smaller volume of the air channel in the short channel of BTLA and the larger volume of the air channel in the long channel, the time ratio of the air pressure applied to the short channel and the long channel is set to 1:2. Figure 26 shows the tortoise-like soft mobile robot crawling on the smooth flat ground when using Gait 1, Gait 2, and Gait 3, respectively.The total inflation time in one cycle is set to 1.5 s, i.e., the air pressure

Right turning
Left turning applied to the short channel and the long channel is set to 0.5 s and 1 s respectively.As shown in figure 27, we measure the robot's velocity by tracking the coordinate change of a key point on the robot's body over multiple gait cycles.In the open-source video analytics software Tracker we use the fixed point of the robot's front leg as the tracking point, and based on the tracking point we build a Cartesian coordinate system to describe the real-time coordinates of the tracking point.
The total inflation time in one cycle has a large impact on the robot's speed, and figure 28 illustrates the speeds of the robot using Gait 1, Gait 2, and Gait 3, corresponding to different inflation times.From the figure, it can be concluded that the speed of the robot has a maximum value at a total inflation time of about 1500 ms in one cycle.
It is worth noting that when using Gait 3, the robot's velocity on smooth flat ground is greater than when using Gait 1 and Gait 2. Theoretically, the robot's speed should be maximal when using Gait 1 gait, because the robot has two legs moving forward and is always in motion regardless of the time period.While using Gait 2 and Gait 3, the robot does not move when the short channel of the four BTLAs is inflated; it only moves when the long channel is inflated.However, the air pressure applied to the two BTLAs drives the entire robot motion poorly, and the displacement in one cycle is smaller, which results in the robot not moving as fast as when using Gait 1 as opposed to when using Gait 3.And the reason why the robot's speed is less when using Gait 2 than when using Gait 1 is that the displacement generated by the robot in the sea turtle configuration in one motion cycle relies mainly on the Height value, while the displacement generated by the robot in the land tortoise type configuration in one motion cycle relies mainly on the total Stride value.According to the modeling and testing of BTLAs, the Stride value is greater than the Height value at the same air pressure.Thus, when the tortoise-like mobile robot crawls on a smooth flat surface, it has the greatest speed and the greatest motion capability when using the land tortoise type configuration and synchronized gait.
The capability of navigating in complex environments is the strength and advantage of the tortoise-like soft mobile robot.The robot does not depend on sophisticated sensor recognition system to control its adaptability to different environments but relies on its own compliance.Figures 29(a)-(c) shows the robot's locomotion in different unstructured scenarios, including stone paths, grass, and drainage outlet manhole covers, respectively (total inflation time in one cycle for the BTLAs is 1.5 s).For the stone path, there are many bumps on the surface of stone paths, and the crawling of soft robots will be limited to a certain extent.Because the motion mode can make part of the robot body leave the ground, the motion speed of robots on such rough ground can still be maintained at a high level.The grass corresponds to some soft surfaces, and the plants growing on the grass have a certain retardation to the movement of the robot.Tests found that the robot's maximum motion speed was reduced by an average of 20% when moving on grass with gait2 compared to moving on a smooth flat surface.At the same time, the test found that plants up to 32 mm in height did not affect the normal movement of the robot.The test on the drainage outlet manhole covers is mainly to verify the influence of a small area of the robot's impact point on the robot's motion speed.The test results show that the motion speed of the robot is almost unaffected by Gait2 mode.
Moreover, the robot possesses the ability to move in water (The test was conducted in standing water at a depth of 52 cm), as shown in figure 29(d), where the robot's small mass can float on the water surface and swim in the water through BTLAs.These tests validate the amphibious navigation capability of the tortoise-like soft mobile robot and expand its application scope.
Consistent with locomotion on smooth flat ground, using different gaits affects the speed and motion performance of the robot.Figure 31 shows the speed of the robot moving in different scenarios when using different gaits (total inflation time for one cycle for the BTLAs is 1.5 s).As can be seen from the testing results, the locomotion in complex scenarios is not identical to that on smooth flat ground, with the fastest speed and greatest locomotion capabilities when using Gait 2 (sea turtle type configuration, synchronized gait).Using Gait 2 when moving on complex terrains such as grass, the BTLAs lift up and over obstacles when the short channel is inflated, making the robot move more smoothly.In contrast, when using Gait 1 and Gait 3, the robot is in the land tortoise type configuration and the actuators do not lift upward over the obstacle, so the motion is stalled.It is worth noting that we still use tracker to measure the speed of the robot in different scenarios, in this set of experiments shown in the figure 30 we choose the  head of the robot as the tracking point and establish a coordinate system with the initial position of the robot's tail as the origin.
In addition, the robot is fastest when swimming in water using Gait 2. The reason for this is that the large bottom surface of the one-channel part of the BTLAs increases the contact area with the water and thus acquires more thrust from the water.In summary, the tortoise-like soft crawling robot performed the best locomotion when crawling on smooth land using synchronized gait (i.e.Gait 3) in the land tortoise type configuration.When crawling in unstructured and complex environments and swimming in water, the robot had the best locomotion in the sea turtle configuration using synchronized gait (i.e.Gait 2).This research also tested the motion capability of the tortoise-like soft mobile robot for left and right turning, as shown in figure 32.The gait of the robot is Gait 4 and Gait 5, and the total inflation time of the BTLAs in one cycle is 1.5 s.The characteristic of the robot turn is the basis of the robot's obstacle avoidance capability.Finally, figure 33 shows the testing of the robot's locomotion at the junction of two terrain environments to verify the robot's wilderness navigation performance.

Discussion
Manufacturing and navigation capabilities are difficult and challenging issues for soft mobile robots.
For the tortoise-like soft crawling robot proposed in this study, it can crawl on land as well as swim in water, achieving amphibious locomotion.This robot can optimize its locomotion performance in different environments and scenarios by reconfiguration (sea turtle type configuration and land tortoise type configuration) and selection of appropriate gait (synchronous gait and asynchronous gait).The robot has high environmental adaptability and can move quickly on smooth flat ground and water, as well as in environments such as rocky paths and grass, without avoiding small obstacles.In previous studies, there are many bionic soft quadruped robots similar to this robot, and although they overcome the disadvantage of poor environmental adaptation of rigid robots, most of them can only crawl on land, limiting their ability to reach space.Table 2 compares the tortoiselike robot in this study with other quadrupedal robots in following aspects.In comparison, our robot has made major improvements in the following main areas.First, we have fabricated a quadrupedal robot with smaller size and lighter mass through optimized 3D printing technology, which gives it the ability to enter into tight spaces such as the inside of a pipe.Second, the structural design of BTLA reduces the control input, which makes it less difficult to control.Finally, comparing with other quadruped crawling soft robots, we propose the Muti-mode working mode in this paper, which enables it to work in a variety of scenarios.In the future, after the optimization of the control system is realized, the autonomous selection of working modes in different scenarios will be realized.
In conclusion, our research has following highlights: 1.The BTAL structure is proposed.The BTLA is designed by combining a two-channel pneumaticnetwork type actuator and a single-channel pneumatic-network type actuator, which achieves simultaneous bending in both directions of the actuator and allows for simpler robot control due to the reduction of one pneumatic  circuit.In addition, each air cavity of the BTLA is trapezoidal, a design that helps to achieve the maximum bending angle of the actuator and to avoid collisions between adjacent air cavities.2. A reconfiguration design solution is proposed.
Reconfiguration allows the robot to implement two bionic modes.It also gives the robot the ability to move on hard surfaces (turtle-like locomotion mode), soft surfaces and water (turtle-like locomotion mode), allowing it to move in amphibious and complex environments.3. The prototype was tested in a variety of gaits and environments and the maximum speed of movement was given for different gaits and environments.It is demonstrated that the fully 3Dprinted tortoise-like soft mobile robot designed in this paper has strong muti-scenarios adaptability.
The research in this paper focuses on the design of the robot structure and the testing of the motion performance.Through the tests, we obtained the motion parameters of two modes transformed by reconfiguration and the corresponding three gaits.In the following work, we hope to integrate the sensing module so that the robot can automatically recognize the external environment and select its own working mode and gait.
For the tortoise-like soft mobile robot, three Potential application scenarios can be proposed with improvement and upgrade of the robot: 1. Navigate in various field environments.2. Navigate in large underground oil or gas pipelines 3. Navigation in high temperature, high humidity, and strong magnetic field environments or under military alert.

Figure 3 .
Figure 3. Reconfiguration of land tortoise type configuration and the sea turtle type configuration.

Figure 5 .
Figure 5. Tortoise-like soft robot's locomotion gait design.(a) Straight-line gait in land tortoise type configuration.(b) Straight-line gait in sea turtle type configuration.(c) Another straight-line gait in land tortoise type configuration.(d) Turning gait in land tortoise type configuration.

Figure 5 (
a) shows the robot's straight-line gait in land tortoise type configuration, which is a diagonal gait with LF, LH, RF and RH representing the left front leg, left hind leg, right front leg, and right hind leg of the robot respectively, i.e., the four BTLAs (figure 5(a1)).During a gait cycle, first, the short channels in the LF and RH actuators and the long channels in the LH and RF actuators are inflated (figure 5(a2)); then, first, the long channels in the LF and RH actuators and the short channels in the LH and RF actuators are inflated (figure 5(a3)).Therefore, the actuators of LF and RH are deformed asynchronously with the actuators of LH and RF.

Figure 6 .
Figure 6.(a) BTLA with three PN-T structure.(b) Bending deformation of PN-T structure.(c) Bending deformation of single air cavity.

Figure 7 .
Figure 7. Geometric parameters of a single air cavity in PN-T structure for BTLA.

Figure 9 .
Figure 9. Stride and Height in actuator deformation.

Figure 10 .
Figure 10.Space coordinate system, origin, and end position for BTLA.

4. 1 .
FabricationThis paper uses DLP 3D printing technology for the fabrication of the BTLA.The equipment used was a Top-down DLP 3D commercial printer (Model: Octavelight-R1).

Figure 11 .
Figure 11.The mathematical modelling process of BTLA.
4.3.1.Stride, height, and end position coordinates of BTLA Stride, Height, and end position coordinates are three physical parameters that characterize the deformation

Figure 16 (
c) shows the Height value of the BTLA at different air pressures.This value only relates to the one channel part of the BTLA, so only the long channel needs to be inflated.The Stride measured values are plotted in the same figure with the finite element simulation data and the values calculated by the mathematical model, as shown in figures 17(a)-(c). Figure

Figure 16 .
Figure 16.BTLA (In land tortoise type configuration).(a) Stride value S1 generated by long channel inflation.(b) Stride value S2 generated by short channel inflation.(c) Height value H generated by long channel inflation.

Figure 17 .
Figure 17.Comparison of the testing data with the FEA data and mathematical model for BTLA.(a) Stride value generated by long channel inflation versus air pressure.(b) Stride value generated by short channel inflation versus air pressure.(c) Total Stride versus air pressure.(d) Height value generated by long channel inflation versus air pressure.

Figure 18 .
Figure 18.Comparison of the testing data with the FEA data and mathematical model for the BTLA.(a) X value versus air pressure.(b) Y value versus air pressure.(c) Z value versus air pressure.

Figure 19 .
Figure 19.(a) Variation of end position coordinates at different air pressures in a 3D view.(b) Coordinate change curves for end positions.

Figure 21 .
Figure 21.Testing of output force versus air pressure and the fitted curve.

Figure 22 .
Figure 22.Testing of permissible lifetime versus air pressure.

Figure 23
shows the prototype of the tortoise-like soft mobile robot in land tortoise type configuration and L Sun et al 23.The prototype of the tortoise-like soft mobile robot in land tortoise type configuration and sea turtle type configuration.

Figure 24 .
Figure 24.The control scheme diagram for the testing of the robots' prototypes.

L Sun et al 25 .
The inflation status of each air channel in four BTLAs for the tortoise-like soft robot.

Figure 27 .
Figure 27.The trajectory of the tracking point of the robot obtained by tracker software.(a) Gait 1.(b) Gait 2. (c) Gait 3.

Figure 28 .
Figure 28.The speeds of the robot moving on the smooth flat ground using Gait 1, Gait 2, and Gait 3, corresponding to different inflation times.

Figure 29 .
Figure 29.The tortoise-like soft mobile robot navigation in different unstructured scenarios.(a) Stone paths.(b) Grass road.(c) Drainage outlet manhole covers.(d) Water pool.

Figure 30 .
Figure 30.The trajectory of the tracking point of the robot obtained by tracker software.(a) Stone paths.(b) Grass road.(c) Drainage outlet manhole covers.(d) Water pool.

Figure 31 .
Figure 31.Speeds of the robot moving in different scenarios when using different gaits.

Figure 32 .
Figure 32.The turning locomotion testing of the tortoise-like soft mobile robot.

L Sun et alFigure 33 .
Figure 33.Testing of the robot's locomotion at the junction of two terrain environments.

Table 1 .
Five gait patterns designed for tortoise-like mobile soft robots.

Table 2 .
Comparison of different quadrupedal robot in navigation capacity.