Propulsion-Based Soft Robotic Actuation

The use of air propulsion to drive limb motion in soft robotics has been a largely untapped field even though the technology has been around since the 1700s. Air propulsion can generate greater degrees of motion in limb actuators compared to widely-experimented pneumatic actuators operating on expandable air channels, which are limited by air pressure input, minimum size and cyclic fatigue. To demonstrate the application of air propulsion in soft robotics motion, we developed a 3D-printed, tri-pedal, soft, air-driven robot that can perform biomimetic motions such as flexion and extension of limbs, crawling, rotation, grasping, kicking and picking of objects. To accomplish air-propelled actuation, milli-scale channels are incorporated throughout each limb that guides the pressurized air inflow to outlets of different directions. A Finite Element Model (FEM) approach to simulate the bending response of the limb due to varying pressure is proposed and evaluated. This study introduces the potential of using air propulsion as an alternate form of soft body actuation for longer cyclic lifespan and increased maximum air pressure input.


Introduction
Air propulsion has been around for centuries since John Wilkinson introduced the first air compressor prototype in 1762 [1].To date, this technology has matured and is ubiquitous in our daily lives, and can be found in jet planes, factory air compressors, gas powered pistons and so on.The working mechanism behind air propulsion lies in the creation of kinetic motion through directional exertion of pressurized air either through combustion or an air reservoir [2].Although air propulsion generates bending in soft flexible bodies during motion as an inevitable effect [3][4][5], there has been minimal investigation done into the use of air propulsion to create soft body locomotion to perform tasks.In this paper, we study and present air-propelled actuation methods in soft robotics, which is the use of pressurized air through mini-channels and out of an outlet, to generate bending and flexing motions in robotic limbs.
Pneumatic-actuated soft robotics have been a widely studied field recently, and their applications range from medical devices [6][7][8][9], to biomimetic robots [10,11] and artificial muscles [12,13].These pneumatic-actuated soft robots generally have customized and expandable internal air channels that results in overall locomotion when air is pumped in [7,14].However, there are several limitations with these pneumatic actuators.Firstly, the amount of input air pressure is highly limited by the strength of the polymeric material used [15].This factor restricts the speed and force of the actuation as air pressure has to be controlled.Secondly, due to the walls of the pneumatic actuators experiencing tensile stress and elastic deformation, there needs to be a minimum wall thickness to ensure durability.Additionally, the channel dimensions and geometry are determined by the resultant stiffness of the materials used in these actuators [7], therefore resulting in bulky sizes that they presently have [16].Thirdly, most of these soft actuators are made of hyper-elastic materials that are prone to hysteresis after multiple cycles of tension and relaxation, giving rise to compliance issues [7,[17][18][19].Thus, an alternate mean of utilizing pneumatic energy to drive such robots is required if size, speed, actuation and durability are to be addressed.
In this paper, we demonstrate the use of air propulsion as a mean to create locomotion in soft robotic limbs.The main aims of this study were to show that air propulsion technology can: (i) produce biomimetic motion; (ii) shrink down the size of actuators; (iii) circumvent durability issues in traditional pneumatic actuators; and (iv) generate enough actuating force to perform simple tasks.We also propose a finite element approach to model the bending of the robotic limb due to air propulsion.Section 2 presents the design of the air-driven robot, a finite element modeling approach and the experimental setup.Section 3 presents the results of the experiments and simulation while Sections 4 and 5 present some applications and discussion, respectively.The paper finally concludes in Section 6.

Design of Air-Driven Robot
The soft robot consists of 3 flexible limbs and 3 lateral thrusters printed using NinjaFlex ® [20], consisting of thermoplastic polyurethane, with a commercial 3D printer (Figure 1).The material properties of NinjaFlex ® can be found in Table 1.The total rapid prototyping time took around 4 h and each limb module was printed separately and later joined together.
are prone to hysteresis after multiple cycles of tension and relaxation, giving rise to compliance issues [7,[17][18][19].Thus, an alternate mean of utilizing pneumatic energy to drive such robots is required if size, speed, actuation and durability are to be addressed.
In this paper, we demonstrate the use of air propulsion as a mean to create locomotion in soft robotic limbs.The main aims of this study were to show that air propulsion technology can: (i) produce biomimetic motion; (ii) shrink down the size of actuators; (iii) circumvent durability issues in traditional pneumatic actuators; and (iv) generate enough actuating force to perform simple tasks.We also propose a finite element approach to model the bending of the robotic limb due to air propulsion.Section 2 presents the design of the air-driven robot, a finite element modeling approach and the experimental setup.Section 3 presents the results of the experiments and simulation while Sections 4 and 5 present some applications and discussion, respectively.The paper finally concludes in Section 6.

Design of Air-Driven Robot
The soft robot consists of 3 flexible limbs and 3 lateral thrusters printed using NinjaFlex ® [20], consisting of thermoplastic polyurethane, with a commercial 3D printer (Figure 1).The material properties of NinjaFlex ® can be found in Table 1.The total rapid prototyping time took around 4 h and each limb module was printed separately and later joined together.

Bulk Properties
Values Bulk Density 600 kg/m 3 Young's Modulus [21] 7.5 MPa Compressive Modulus [21] 20 MPa Specific Gravity 1.2 The limbs were designed to mimic simple flexion and extension motions.This requires two separate air channels to be incorporated side by side within each limb (Figure 2A).A CAD model of a limb and its cross sections are shown in Figure 2.Each channel started from the top of the limb where the air source was connected to, and runs continued to the bottom of the limb, ending in opposite directions (Figure 2B,C).The dimensions of the channel cross section were 2 mm × 1 mm throughout the limb and the wall thickness was around 1 mm.We observed that, below this wall thickness, the actuators walls became porous, resulting in ineffective air propulsion due to leakage.The limb actuators were also kept as thin as possible to maximize flexibility in the actuating plane.Additionally, to ensure optimal flexibility, the limbs had to be printed in the orientation where the cross section was parallel to the tabletop surface.Besides the air propelled limbs, the air-driven robot also consisted of three lateral thrusters (Figure 2D), which enabled the robot to perform quick rotation and to change its direction of travel.Similar to the actuating limb, the thrusters had two air channels

Bulk Properties Values
Bulk Density 600 kg/m 3 Young's Modulus [21] 7.5 MPa Compressive Modulus [21] 20 MPa Specific Gravity 1.2 The limbs were designed to mimic simple flexion and extension motions.This requires two separate air channels to be incorporated side by side within each limb (Figure 2A).A CAD model of a limb and its cross sections are shown in Figure 2.Each channel started from the top of the limb where the air source was connected to, and runs continued to the bottom of the limb, ending in opposite directions (Figure 2B,C).The dimensions of the channel cross section were 2 mm × 1 mm throughout the limb and the wall thickness was around 1 mm.We observed that, below this wall thickness, the actuators walls became porous, resulting in ineffective air propulsion due to leakage.The limb actuators were also kept as thin as possible to maximize flexibility in the actuating plane.Additionally, to ensure optimal flexibility, the limbs had to be printed in the orientation where the cross section was parallel to the tabletop surface.Besides the air propelled limbs, the air-driven robot also consisted of three lateral thrusters (Figure 2D), which enabled the robot to perform quick rotation and to change its direction of travel.Similar to the actuating limb, the thrusters had two air channels that pointed to opposite directions (Figure 2E).For input pressure large enough to overcome static friction, one lateral thruster was sufficient to achieve rotation, which reduced the number of pneumatic connection to 8 for 2 degrees of freedom (DOF) movement.
The flexion and extension of the limbs were attained through channeling the pressurized airflow into either of the two top inlets (Video S1).The greater the air pressure input, the larger the bending displacement of the limb was.Using all three air propelled limbs resulted in the crawling locomotion of the air-driven robot (Video S2).The input pressure needed to be controlled at around 3 bars to perform this crawling motion, where each gait cycle sequence started off with the extension of its frontal limb (Figure 3A), followed by the flexion of its right rear limb (Figure 3B) and lastly the flexion of the left rear limb (Figure 3C).The second movement locomotion demonstrated was the hopping of the air-driven robot (Video S3), which had greater velocity compared to crawling.To achieve this, the air pressure of 4 bars and above was used to generate more acceleration through the back-facing outlet of the frontal limb.These air-propelled actuation modes demonstrate the possibility of achieving biomimetic motions, similar to that of animals and insects.Figure 4 shows the complete system setup of the prototype whereby the air compressor was connected to an Arduino Mega processor board and subsequently to the actuators.Different square wave cyclic signals can be programmed into the system to control the input pressure for customized control of motion.
that pointed to opposite directions (Figure 2E).For input pressure large enough to overcome static friction, one lateral thruster was sufficient to achieve rotation, which reduced the number of pneumatic connection to 8 for 2 degrees of freedom (DOF) movement.
The flexion and extension of the limbs were attained through channeling the pressurized airflow into either of the two top inlets (Video S1).The greater the air pressure input, the larger the bending displacement of the limb was.Using all three air propelled limbs resulted in the crawling locomotion of the air-driven robot (Video S2).The input pressure needed to be controlled at around 3 bars to perform this crawling motion, where each gait cycle sequence started off with the extension of its frontal limb (Figure 3A), followed by the flexion of its right rear limb (Figure 3B) and lastly the flexion of the left rear limb (Figure 3C).The second movement locomotion demonstrated was the hopping of the air-driven robot (Video S3), which had greater velocity compared to crawling.To achieve this, the air pressure of 4 bars and above was used to generate more acceleration through the back-facing outlet of the frontal limb.These air-propelled actuation modes demonstrate the possibility of achieving biomimetic motions, similar to that of animals and insects.Figure 4 shows the complete system setup of the prototype whereby the air compressor was connected to an Arduino Mega processor board and subsequently to the actuators.Different square wave cyclic signals can be programmed into the system to control the input pressure for customized control of motion.that pointed to opposite directions (Figure 2E).For input pressure large enough to overcome static friction, one lateral thruster was sufficient to achieve rotation, which reduced the number of pneumatic connection to 8 for 2 degrees of freedom (DOF) movement.
The flexion and extension of the limbs were attained through channeling the pressurized airflow into either of the two top inlets (Video S1).The greater the air pressure input, the larger the bending displacement of the limb was.Using all three air propelled limbs resulted in the crawling locomotion of the air-driven robot (Video S2).The input pressure needed to be controlled at around 3 bars to perform this crawling motion, where each gait cycle sequence started off with the extension of its frontal limb (Figure 3A), followed by the flexion of its right rear limb (Figure 3B) and lastly the flexion of the left rear limb (Figure 3C).The second movement locomotion demonstrated was the hopping of the air-driven robot (Video S3), which had greater velocity compared to crawling.To achieve this, the air pressure of 4 bars and above was used to generate more acceleration through the back-facing outlet of the frontal limb.These air-propelled actuation modes demonstrate the possibility of achieving biomimetic motions, similar to that of animals and insects.Figure 4 shows the complete system setup of the prototype whereby the air compressor was connected to an Arduino Mega processor board and subsequently to the actuators.Different square wave cyclic signals can be programmed into the system to control the input pressure for customized control of motion.

Finite Element Modeling of Limb Bending
To model the bending of a curved flexible beam due to varying air pressure input, a Finite Element Modeling (FEM) approach is proposed in this paper (Figure 5).To the authors' best knowledge, little or no prior modeling work has been performed on the bending of curved actuator beams created by air propulsion.
where W is the strain energy function, C10 and C01 are the material parameters, and I1 and I2 are the strain invariants.The values of the parameters were C10 = 1.653MPa and C01 = 1.621MPa, as obtained from our previous work [24].Computation simulation was then performed with various experimental forces to obtain the bending displacement of the curved beam.Finally, the relationship between the bending displacement and the respective input pressure was established, allowing for better understanding and control of the robotic limb.

Mechanical Experimental Setup and Evaluation
Initial measurements of actuating force to various input pressures were carried out (Figure 6A) using a load sensor.Pneumatic limbs with square outlets of length 2 mm and 3 mm were fabricated.The tip of a Digital Force Gauge DS2-50N (Imada, Northbrook, IL, USA) was placed perpendicular to the surface of a pneumatic limb at 2 mm from the distal end, and pressurized air ranging from 0

Finite Element Modeling of Limb Bending
To model the bending of a curved flexible beam due to varying air pressure input, a Finite Element Modeling (FEM) approach is proposed in this paper (Figure 5).To the authors' best knowledge, little or no prior modeling work has been performed on the bending of curved actuator beams created by air propulsion.

Finite Element Modeling of Limb Bending
To model the bending of a curved flexible beam due to varying air pressure input, a Finite Element Modeling (FEM) approach is proposed in this paper (Figure 5).To the authors' best knowledge, little or no prior modeling work has been performed on the bending of curved actuator beams created by air propulsion.
where W is the strain energy function, C10 and C01 are the material parameters, and I1 and I2 are the strain invariants.The values of the parameters were C10 = 1.653MPa and C01 = 1.621MPa, as obtained from our previous work [24].Computation simulation was then performed with various experimental forces to obtain the bending displacement of the curved beam.Finally, the relationship between the bending displacement and the respective input pressure was established, allowing for better understanding and control of the robotic limb.

Mechanical Experimental Setup and Evaluation
Initial measurements of actuating force to various input pressures were carried out (Figure 6A) using a load sensor.Pneumatic limbs with square outlets of length 2 mm and 3 mm were fabricated.The tip of a Digital Force Gauge DS2-50N (Imada, Northbrook, IL, USA) was placed perpendicular to the surface of a pneumatic limb at 2 mm from the distal end, and pressurized air ranging from 0 The experimental actuating force to input pressure was first obtained from the robotic limb under various pressures.A model of the robotic limb was then import into COMSOL Multiphysics ® software for finite element simulation.The mechanical behavior of the NinjaFlex ® material was represented by the 2-constant Mooney-Rivlin model [22,23]: where W is the strain energy function, C 10 and C 01 are the material parameters, and I 1 and I 2 are the strain invariants.The values of the parameters were C 10 = 1.653MPa and C 01 = 1.621MPa, as obtained from our previous work [24].Computation simulation was then performed with various experimental forces to obtain the bending displacement of the curved beam.Finally, the relationship between the bending displacement and the respective input pressure was established, allowing for better understanding and control of the robotic limb.

Mechanical Experimental Setup and Evaluation
Initial measurements of actuating force to various input pressures were carried out (Figure 6A) using a load sensor.Pneumatic limbs with square outlets of length 2 mm and 3 mm were fabricated.
The tip of a Digital Force Gauge DS2-50N (Imada, Northbrook, IL, USA) was placed perpendicular to the surface of a pneumatic limb at 2 mm from the distal end, and pressurized air ranging from 0 to 5 bars was used.For the experimental evaluation of the proposed FEM approach, the horizontal displacement of the actuator limb was measured at various input pressures (Figure 6B).Care was taken to ensure that the displacement of the limb has reached equilibrium with constant airflow, before measurements were recorded.Ten readings of each data point were taken.
to 5 bars was used.For the experimental evaluation of the proposed FEM approach, the horizontal displacement of the actuator limb was measured at various input pressures (Figure 6B).Care was taken to ensure that the displacement of the limb has reached equilibrium with constant airflow, before measurements were recorded.Ten readings of each data point were taken.

Experimental
The results for the experimental force-pressure curve are presented in Figure 7.The outlet width of 3 mm could achieve greater actuating force than that of 2 mm.However, further increase in width above 3 mm were not tested due to the geometric constraints of the actuator width.This was because to maintain the external width of the actuator as small as possible, any increment in the outlet width would result in the surrounding wall thickness dropping below 1 mm and becoming porous.A small actuator width allows the robot size to be kept small and reduce the amount of input air pressure needed to actuate it.

Simulation Results
The finite element analysis simulation of the robotic limb model to obtain the theoretical displacement from the input force can be found in Figure 8.This approach allowed us to collate the

Experimental
The results for the experimental force-pressure curve are presented in Figure 7.The outlet width of 3 mm could achieve greater actuating force than that of 2 mm.However, further increase in width above 3 mm were not tested due to the geometric constraints of the actuator width.This was because to maintain the external width of the actuator as small as possible, any increment in the outlet width would result in the surrounding wall thickness dropping below 1 mm and becoming porous.A small actuator width allows the robot size to be kept small and reduce the amount of input air pressure needed to actuate it.
Robotics 2017, 6, 34 5 of 10 to 5 bars was used.For the experimental evaluation of the proposed FEM approach, the horizontal displacement of the actuator limb was measured at various input pressures (Figure 6B).Care was taken to ensure that the displacement of the limb has reached equilibrium with constant airflow, before measurements were recorded.Ten readings of each data point were taken.

Experimental
The results for the experimental force-pressure curve are presented in Figure 7.The outlet width of 3 mm could achieve greater actuating force than that of 2 mm.However, further increase in width above 3 mm were not tested due to the geometric constraints of the actuator width.This was because to maintain the external width of the actuator as small as possible, any increment in the outlet width would result in the surrounding wall thickness dropping below 1 mm and becoming porous.A small actuator width allows the robot size to be kept small and reduce the amount of input air pressure needed to actuate it.

Simulation Results
The finite element analysis simulation of the robotic limb model to obtain the theoretical displacement from the input force can be found in Figure 8.This approach allowed us to collate the

Simulation Results
The finite element analysis simulation of the robotic limb model to obtain the theoretical displacement from the input force can be found in Figure 8.This approach allowed us to collate the predicted displacement results and compile them against their respective input pressures.The final predictive quadratic polynomials for 2 mm and 3 mm outlet widths are presented as: respectively, where s is the displacement (mm) and p is the input pressure (bars).The predictive equations were plotted out and compared against experimental readings (Figure 9).The simulation results can be observed to be within one standard deviation of the experimental data.An increasing discrepancy between theoretical and experimental results can be observed as pressure increases due to increasing head loss of airflow through the channel.
predicted displacement results and compile them against their respective input pressures.The final predictive quadratic polynomials for 2 mm and 3 mm outlet widths are presented as: respectively, where s is the displacement (mm) and p is the input pressure (bars).The predictive equations were plotted out and compared against experimental readings (Figure 9).The simulation results can be observed to be within one standard deviation of the experimental data.An increasing discrepancy between theoretical and experimental results can be observed as pressure increases due to increasing head loss of airflow through the channel.
respectively, where s is the displacement (mm) and p is the input pressure (bars).The predictive equations were plotted out and compared against experimental readings (Figure 9).The simulation results can be observed to be within one standard deviation of the experimental data.An increasing discrepancy between theoretical and experimental results can be observed as pressure increases due to increasing head loss of airflow through the channel.

Application of Air-Driven Robot
In a more application-based approach, we used the air-driven robot to perform simple manipulation tasks.The first task was to grip a 15-g plastic cup and lift it off the ground and then lower it back down (Figure 10A, Video S4).For this purpose, only two limbs angled at 120 • were used with an input pressure of 3 bars.It was observed that the highly compliant actuators could conform to the surface curvature of the cup and maintain enough friction to lift the latter off the table.The second task involved picking up a roll of tape and depositing it into a plastic cup (Figure 10C, Video S5).Because the diameter of the roll of tape is less than that of the previous cup, the input pressure had to be increased to 4 bars to achieve greater bending curvature and also to compensate for the head loss due to an additional actuator.Lastly, the robot was made to hop towards a plastic block and kick it with its front limb (Figure 10B, Video S6).

Application of Air-Driven Robot
In a more application-based approach, we used the air-driven robot to perform simple manipulation tasks.The first task was to grip a 15-g plastic cup and lift it off the ground and then lower it back down (Figure 10A, Video S4).For this purpose, only two limbs angled at 120° were used with an input pressure of 3 bars.It was observed that the highly compliant actuators could conform to the surface curvature of the cup and maintain enough friction to lift the latter off the table.The second task involved picking up a roll of tape and depositing it into a plastic cup (Figure 10C, Video S5).Because the diameter of the roll of tape is less than that of the previous cup, the input pressure had to be increased to 4 bars to achieve greater bending curvature and also to compensate for the head loss due to an additional actuator.Lastly, the robot was made to hop towards a plastic block and kick it with its front limb (Figure 10B, Video S6).

Discussion
There are several primary application areas for the air-driven robot.Due to its miniature size compared to other pneumatic-actuated robots, the former can be deployed in search and rescue missions, for example, in earthquake crisis where gaps between rubbles are small [25].They can also be deployed for reconnaissance or surveillance [26,27] on uneven or compliant terrains since legged walking on such surfaces are more efficient than rolling wheels [28,29].With sufficient air supply, hovering capabilities can be integrated into this air-propelled robot, creating a versatile drone that can transverse air, land and sea.Lastly, the use of air-propelled actuation can be utilized for medical devices like assistive exoskeletons [30,31] for rehabilitation.The potential of generating substantial amount of force through a small channel and aperture can streamline the size and weight of such exoskeleton designs.Lastly, the advantages of air-propelled soft limbs as compared to rigid limbs in tripedal robot [32,33] are that the former are more compliant to irregular surfaces, lighter and have more degrees of freedom.
The proposed finite element approach to predict the displacement response of the soft actuator limb to varying air pressures was validated.This approach allows for quick modification, evaluation and optimization of superficial limb design, provided the design of the air channel remains unchanged.The significance of such approach is for better control of the limb movements when designing control algorithms in future.
A limitation of this study is the small amount of output force.The force, although small, is sufficient to create biomimetic locomotion and perform simple tasks, which was the main aim of this paper.Future improvements to increase the output forces to perform more rigorous tasks can be achieved through greater input air pressure and improving the design of the channels and actuators to reduce air flow resistance and head loss.Future works can also include the dynamic behavior modeling of these actuators for better depth of understanding of their speed and performance.

Discussion
There are several primary application areas for the air-driven robot.Due to its miniature size compared to other pneumatic-actuated robots, the former can be deployed in search and rescue missions, for example, in earthquake crisis where gaps between rubbles are small [25].They can also be deployed for reconnaissance or surveillance [26,27] on uneven or compliant terrains since legged walking on such surfaces are more efficient than rolling wheels [28,29].With sufficient air supply, hovering capabilities can be integrated into this air-propelled robot, creating a versatile drone that can transverse air, land and sea.Lastly, the use of air-propelled actuation can be utilized for medical devices like assistive exoskeletons [30,31] for rehabilitation.The potential of generating substantial amount of force through a small channel and aperture can streamline the size and weight of such exoskeleton designs.Lastly, the advantages of air-propelled soft limbs as compared to rigid limbs in tripedal robot [32,33] are that the former are more compliant to irregular surfaces, lighter and have more degrees of freedom.
The proposed finite element approach to predict the displacement response of the soft actuator limb to varying air pressures was validated.This approach allows for quick modification, evaluation and optimization of superficial limb design, provided the design of the air channel remains unchanged.The significance of such approach is for better control of the limb movements when designing control algorithms in future.
A limitation of this study is the small amount of output force.The force, although small, is sufficient to create biomimetic locomotion and perform simple tasks, which was the main aim of this paper.Future improvements to increase the output forces to perform more rigorous tasks can be achieved through greater input air pressure and improving the design of the channels and actuators to reduce air flow resistance and head loss.Future works can also include the dynamic behavior modeling of these actuators for better depth of understanding of their speed and performance.The air-driven robot presents the potential application of air propulsion to achieve locomotion and elastic deformation of soft bodies.These soft air-propelled actuators can be scaled down to smaller sizes compared to conventional pneumatic air bladder actuators, without compromising on the durability and integrity.The robot presented in this paper is fabricated with a commercial 3D printer; it is inexpensive and can be easily modified to suit several applications.However, a major disadvantage of the proposed air propulsion actuation compared to conventional pneumatic approaches includes the requirement of a continuous air supply to maintain final shape.Another limitation would be the decreased actuating force compared to conventional pneumatic actuators.The air-propelled locomotion, which is demonstrated with the air-driven robot, opens up another untapped field of nature-inspired design that can be integrated into a myriad of drone and exoskeleton applications.The evaluation and comparison of the proposed air-propulsion actuator with our previous works in conventional pneumatic bladder actuators [6,36,37] is presented in Table 2.

Conclusions
In conclusion, we have demonstrated the feasibility of using air-propulsion to achieve biomimetic locomotion in soft 3-D printed robots.The tri-pedal robot can crawl, pinch, grasp and kick while powered from a pneumatic source.A finite element approach to model the displacement response of the curved actuator limb to varying input pressure was proposed and evaluated.This paper shows the potential of utilizing air-propulsion for bending and movement in soft robotics applications.

Figure 1 .
Figure 1.Air-driven robot with three flexible limbs and three lateral thrusters: (A) isometric view; and (B) top view.

Figure 1 .
Figure 1.Air-driven robot with three flexible limbs and three lateral thrusters: (A) isometric view; and (B) top view.

Figure 2 .
Figure 2. Design of the air propelled limb and lateral thrusters where the arrows indicate direction of airflow: (A) wireframe model of the limb depicting the two channels running side by side; (B,C) cross sectional view showing airflow in each channel; and (D,E) isometric and plane view of lateral thruster showing the direction of air flow to generate rotation.

Figure 3 .
Figure 3. Biomimetic gait locomotion achieved through air-propulsion: (A) extension of front limb to stride forward; (B) flexion of the back right limb; and (C) flexion of left back limb to complete one gait cycle.

Figure 2 .
Figure 2. Design of the air propelled limb and lateral thrusters where the arrows indicate direction of airflow: (A) wireframe model of the limb depicting the two channels running side by side; (B,C) cross sectional view showing airflow in each channel; and (D,E) isometric and plane view of lateral thruster showing the direction of air flow to generate rotation.

Figure 2 .
Figure 2. Design of the air propelled limb and lateral thrusters where the arrows indicate direction of airflow: (A) wireframe model of the limb depicting the two channels running side by side; (B,C) cross sectional view showing airflow in each channel; and (D,E) isometric and plane view of lateral thruster showing the direction of air flow to generate rotation.

Figure 3 .
Figure 3. Biomimetic gait locomotion achieved through air-propulsion: (A) extension of front limb to stride forward; (B) flexion of the back right limb; and (C) flexion of left back limb to complete one gait cycle.

Figure 3 .
Figure 3. Biomimetic gait locomotion achieved through air-propulsion: (A) extension of front limb to stride forward; (B) flexion of the back right limb; and (C) flexion of left back limb to complete one gait cycle.

Figure 4 .
Figure 4. Overall system architecture for the experimental setup.

Figure 5 .
Figure 5. Finite Element Modeling (FEM) approach for bending of air-propelled curved beams.The experimental actuating force to input pressure was first obtained from the robotic limb under various pressures.A model of the robotic limb was then import into COMSOL Multiphysics ® software for finite element simulation.The mechanical behavior of the NinjaFlex ® material was represented by the 2-constant Mooney-Rivlin model[22,23]:

Figure 4 .
Figure 4. Overall system architecture for the experimental setup.

Figure 5 .
Figure 5. Finite Element Modeling (FEM) approach for bending of air-propelled curved beams.The experimental actuating force to input pressure was first obtained from the robotic limb under various pressures.A model of the robotic limb was then import into COMSOL Multiphysics ® software for finite element simulation.The mechanical behavior of the NinjaFlex ® material was represented by the 2-constant Mooney-Rivlin model[22,23]:

Figure 5 .
Figure 5. Finite Element Modeling (FEM) approach for bending of air-propelled curved beams.

Figure 6 .
Figure 6.Experimental characterization of pneumatic actuator: (A) measurement of actuating force via load sensor; and (B) measured horizontal displacement during bending.

Figure 7 .
Figure 7. Measured actuating force versus input pressure for square outlets of sides 2 mm and 3 mm.

Figure 6 .
Figure 6.Experimental characterization of pneumatic actuator: (A) measurement of actuating force via load sensor; and (B) measured horizontal displacement during bending.

Figure 6 .
Figure 6.Experimental characterization of pneumatic actuator: (A) measurement of actuating force via load sensor; and (B) measured horizontal displacement during bending.

Figure 7 .
Figure 7. Measured actuating force versus input pressure for square outlets of sides 2 mm and 3 mm.

Figure 7 .
Figure 7. Measured actuating force versus input pressure for square outlets of sides 2 mm and 3 mm.

Figure 8 .
Figure 8. Finite element simulation of limb bending via COMSOL Multiphysics ® .The color intensity denotes the relative displacement of the body from its initial resting state.

Figure 9 .
Figure 9. Theoretical and experimental displacement against input pressure for different outlet widths.Error bars are indicated for experimental data.

Figure 8 .
Figure 8. Finite element simulation of limb bending via COMSOL Multiphysics ® .The color intensity the relative displacement of the body from its initial resting state.

Figure 8 .
Figure 8. Finite element simulation of limb bending via COMSOL Multiphysics ® .The color intensity denotes the relative displacement of the body from its initial resting state.

Figure 9 .
Figure 9. Theoretical and experimental displacement against input pressure for different outlet widths.Error bars are indicated for experimental data.

Figure 9 .
Figure 9. Theoretical and experimental displacement against input pressure for different outlet widths.Error bars are indicated for experimental data.

Figure 10 .
Figure 10.Possible robotic motions: (A) grapping of plastic cup to lift it; (B) kicking of obstacles; and (C) picking of objects to place into a cup.

Figure 10 .
Figure 10.Possible robotic motions: (A) grapping of plastic cup to lift it; (B) kicking of obstacles; and (C) picking of objects to place into a cup.

Table 2 .
Qualitative Comparison of proposed actuation method with conventional pneumatic bladder actuators.