Design and Dynamic Model of a Frog-inspired Swimming Robot Powered by Pneumatic Muscles
© The Author(s) 2017
Received: 17 January 2017
Accepted: 24 July 2017
Published: 4 August 2017
Pneumatic muscles with similar characteristics to biological muscles have been widely used in robots, and thus are promising drivers for frog inspired robots. However, the application and nonlinearity of the pneumatic system limit the advance. On the basis of the swimming mechanism of the frog, a frog-inspired robot based on pneumatic muscles is developed. To realize the independent tasks by the robot, a pneumatic system with internal chambers, micro air pump, and valves is implemented. The micro pump is used to maintain the pressure difference between the source and exhaust chambers. The pneumatic muscles are controlled by high-speed switch valves which can reduce the robot cost, volume, and mass. A dynamic model of the pneumatic system is established for the simulation to estimate the system, including the chamber, muscle, and pneumatic circuit models. The robot design is verified by the robot swimming experiments and the dynamic model is verified through the experiments and simulations of the pneumatic system. The simulation results are compared to analyze the functions of the source pressure, internal volume of the muscle, and circuit flow rate which is proved the main factor that limits the response of muscle pressure. The proposed research provides the application of the pneumatic muscles in the frog inspired robot and the pneumatic model to study muscle controller.
The increasing demand for underwater exploration and development, water detection, and other works in the scientific and military fields  has led to the rapid development of bionic underwater robots . These robots mimic animal locomotion mechanisms, such as biological motion and musculoskeletal characteristics, which have been the focus of several studies [3, 4]. With regard to underwater swimming methods, most research has focused on the waving and oscillating propulsion of fishes, jet propulsion in squids, multi-legged crawling propulsion, hydrofoil flapping propulsion in turtles, and swimming motions of frogs [5–10].
Frogs brilliantly possess land jumping and underwater swimming abilities , and thus greatly inspired relevant robot designs in bionic research. The amphibious robot can serve in an extended wide terrain to complete tasks. Therefore, frog inspired robot is a promising topic to mimic its swimming and jumping movements which are accomplished by the same hind leg. However, current research focuses on the jumping prototype and mechanism of swimming, while the development of frog-inspired swimming prototype is less studied.
Swimming mechanisms have been widely investigated through the analysis of motion characteristics , propulsive force , and flow field structures . Using experimental observations, Pandey et al. established a CAD model of a bionic frog swimming robot to mimic biological frog motions .
Frog swimming is intermittent and shows explosive movements. Thus, the driver must have high output power and fast response. Pneumatic artificial muscles have high-power mass ratio and flexible characteristics, and are similar with biological muscles in terms of driving the skeletal system . In the present study, the frog-inspired robot is driven by pneumatic muscles that simulate the performance of biological frog muscles. The similarities between the pneumatic and biological muscles must be determined and analyzed to understand the relationship between the amphibious movements and musculoskeletal system of frogs.
Traditional drivers, such as motors, run through complex mechanisms . Meanwhile pneumatic muscles have been widely used because of its simple assembly  and are mainly controlled by tracking control methods [19–21]. Several studies have performed on pneumatic muscles, mainly focusing on the modeling and control of pneumatic valves [22–24]. The precise pressure proportional valve is typically used to achieve output accuracy, but the cost is expensive and the flow rate of the pressure proportional valve is relatively small. Further, such setup is not suited for situations demanding large flow inputs. In this paper, pneumatic muscles are controlled by high-speed switch valves, which have high flow rate and fast response, thereby simplifying the design of the frog-inspired robot. In addition, high-speed switch valves are light weight, occupy small volume, and incur low cost, and is thus preferable in the robot system.
To mimic frog swimming performance, a frog inspired swimming robot is developed with pneumatic muscles and high-speed switch valves to study pneumatic characteristics during leg extension.
2 Design of Frog-inspired Robot
2.1 Modeling of the Frog-inspired Robot
2.2 Structure of the Frog-inspired Robot
2.2.1 Robot System
A micro air pump is placed in the rear trunk. Meanwhile, given the size of the air pump, we make it pass through the baffle plate connected to the cooling fin of the pump. The source chamber is connected to the outlet of the pump and filled with high-pressure compressed air. The high-speed switch valves are mounted in the middle of the baffle plate on the bottom face. The electrical unit is located in the front head of the exhaust chamber, which is also connected to the inlet of the pump. Therefore, the switch valve controls the flow from the source chamber to the muscle for pressurizing and from the muscle to the exhaust chamber for depressurizing.
2.2.2 Design of the Hind Legs
Each joint has two muscles mounted in an antagonistic way to control the angle position and joint stiffness. For the knee and ankle joints, we selected the pneumatic muscle of DMSP-20-150N-RM-CM, whose length is 150 mm and has a maximum contraction rate of 25% and maximum contractile force of 1500 N. We selected those with lengths of 180 mm for the hip joints.
2.2.3 Design of Pneumatic Circuit
The three revolute joints of each hind leg use six pneumatic muscles in total, and each pneumatic muscle is controlled by two high-speed switch valves. Thus, the entire hind limb requires 12 pneumatic high-speed switch valves. We consider the hip joint as an example to explain the working principle of the pneumatic circuit. The body and the thigh crank are connected with a joint shaft. Each end of the crank is hinged to the muscles, and the other ends are connected to the body frame. During muscle contraction and stretching, the crank (fixed with the thigh frame) rotates relative to the body. To reach the initial position, the charging valve 1 and discharging valve 2 are open, and the discharging valve 1 and charging valve 2 are closed. The recovery muscle then starts to contract, and the driving muscle stretches until the joint rotates clockwise to the preset position (Figure 6). During the propulsive phase, the hip joint must rotate counterclockwise quickly, and thus the charging valve 1 and discharging valve 2 are close, and charging valve 1 and the discharging valve 2 are open. The recovery muscle of the hip joint then starts to stretch and the driving muscle contracts. The hip joint rotates counterclockwise quickly to a specific position.
3 Model of the Pneumatic System
The dynamic characteristics of the pneumatic system must be analyzed to determine the function of the musculoskeletal system of the frog-inspired robot and lay the foundation for its control system design. The pneumatic muscles used in the robot have apparent nonlinearity and hysteresis characteristics. The previous modeling of the pressure dynamic process is based on the ideal conditions, which can lead to different response results. The dynamic models of the source chamber, muscle volume, exhaust chamber, and switch valves are established to simulate the pressure process of the pneumatic system.
3.1 Dynamic Model of the Source Chamber and Exhaust Chamber
According to thermodynamics, dU s = C v M sdT s, dW s = P sdV s and idM = (C v + R)T sdM, where C v is the constant volume specific heat of air, R denotes the gas constant of air, and dT s is the temperature differential in the source chamber.
3.2 Dynamic Model of the Pneumatic Muscle
3.3 Dynamic Model of the Pneumatic System
The saturation term is added in the simulation process because of the calculated maximum flow rate in the main pipe. The muscle length is derived from the joint angle. With muscle length and initial pressure from the source chamber, the pressurizing processes in the chambers and muscles can be simulated, and the rationality of the established model can be verified by comparing the results to lay the foundation for future designs of robot control systems.
4 Simulations and Experiments
Parameters of the frog-inspired robot
Body length l 0/m
Body width w 0/m
Thigh length l 1/m
Crus length l 2/m
Palm length l 3/m
Palm area S/m2
Total mass m/kg
Displacement V d/L
The swimming cycle is divided into the propulsive and recovery phases according to body velocity. The leg motions are powerful and rapid in the propulsive phase, while the legs recover slowly during the recovery phase. Therefore, the experiments and simulations on the hind leg extensions were conducted to test the muscle capacity to drive the system. The pressures in the pneumatic muscles were controlled by the high-speed switch valves with open loop control.
4.1 Swimming Experiments
Each joint had a delay of about 0.1 s, because of the influence of the delay in the pneumatic system and mechanical clearance in the joints. The joint data would be used in the subsequent simulations to compute the pressure dynamic process according to previously established pneumatic model.
4.2 Simulation of the Pneumatic System
According to Eq. (8), the aeration volumes of each joint can be obtained by integrating the flow rate during muscle pressurizing. The aeration volumes at standard state were computed in the simulation. The aeration volume at the hip muscle is 0.455 L and that at the knee and ankle muscle is 0.401 L. The aeration volumes are the key factors that verify the design of the pneumatic system.
4.3 Analysis on the Pressurizing Process
The response speed of the pneumatic muscle reflects the performance of the driving capacity and is a key factor to simulate the musculoskeletal system [29, 30]. The response speed is mainly restricted by the pressurizing process. The simulations with different source pressures, muscle volumes, and flow saturations in the pneumatic circuit were calculated to analyze the factors of muscle performance. Therefore, the pressure response in the pneumatic muscle can be obtained.
The flow rate limitation in the pneumatic circuits is the main factor that controls the pressure response in the muscle. Therefore, in the robot design, extending the main pipe diameter and number of main pipes is an effective way to improve the pressurizing speed. The results of the experiments and simulations verified the pneumatic model of the frog-inspired robot.
A frog-inspired robot is designed to mimic the frog swimming based on its three DOFs in the leg and the pneumatic muscles serving as the joint driver. The prototype can perform untethered swimming which are supported by the integrated pneumatic, control, and communication systems in the body.
The pneumatic system is modeled based on flow rate characteristics during the pressurizing and depressurizing of the muscles to analyze the nonlinearity of the driver. The pneumatic model is proved reasonable by the simulations, and the findings is the base for the controller design in the near future.
The experiments and simulation of the robot indicate that the robots driven by pneumatic muscles are feasible and the flow rate is the main factor for the quick response of the pneumatic system.
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