Modeling Of Pneumatic Artificial Muscle Research Articles

Adaptive Set-Membership Filter Based Discrete Sliding Mode Control for Pneumatic Artificial Muscle Systems With Hardware Experiments

Pneumatic artificial muscle (PAM), featuring good flexibility and safety, has been widely used in rehabilitation and bionic robots. However, the complex hysteretic nonlinearities and uncertainties of the PAM cause great difficulties and challenges to the accurate modeling and controller design, especially when confronted with unknown external disturbances in applications. This paper proposes a robust control strategy with disturbance compensation for the hysteresis compensation and trajectory tracking of PAMs. Considering the high hysteretic nonlinearity of the PAM, a modified Prandtl-Ishlinskii model is used as a feedforward hysteresis compensator. For the linearized system, adaptive set-membership filtering (ASMF) is used to estimate the nonlinear terms and external disturbances of the overall system. A sliding mode controller (SMC) with disturbance compensation is designed and cascaded to the feedforward hysteresis compensator in series. The stability of the closed-loop system is theoretically proved. The proposed method guarantees that the tracking error of the PAM system is bounded. Finally, the effectiveness and robustness of the proposed controller are verified via a series of experiments on an in-house built testbench for PAMs. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —With the increasing demand on human-robot interaction, the safety and compliance of robots have become one key requirement. PAM is a compliant actuator, exhibiting good flexibility, safety, and clean energy. PAM is widely used in rehabilitation robots, whereas its strong hysteresis nonlinearity and sensitivity to external disturbances affect its motion accuracy. This paper proposes an ASMF-based discrete SMC, which uses an inverse hysteresis model to compensate for the strong hysteresis of the PAM and uses ASMF to estimate the lumped disturbance of the system. Compared with the other filters, ASMF is unique in that its estimation error is bounded, which is very useful in the stability proof of the overall system. The effectiveness of the proposed controller is experimentally verified. Experimental results show that PAM’s hysteresis can be efficiently compensated, and the influence of external disturbances can be attenuated by the proposed controller, resulting in improved motion accuracy and robustness. In future work, efforts will be directed towards the modeling and control of PAMs in multi-DOF robots.

A Review of Design and Modeling of Pneumatic Artificial Muscle

Soft robots, which are often considered safer than rigid robots when interacting with humans due to the reduced risk of injury, have found utility in various medical and industrial fields. Pneumatic artificial muscles (PAMs), one of the most widely used soft actuators, have proven their efficiency in numerous applications, including prosthetic and rehabilitation robots. PAMs are lightweight, responsive, precise, and capable of delivering a high force-to-weight ratio. Their structure comprises a flexible, inflatable membrane reinforced with fibrous twine and fitted with gas-sealing fittings. For the optimal design and integration of these into control systems, it is crucial to develop mathematical models that accurately represent their functioning mechanisms. This paper introduces a general concept of PAM's construction, its various types, and operational mechanisms, along with its key benefits and drawbacks, and also reviews the most common modeling techniques for PAM representation. Most models are grounded in PAM architecture, aiming to calculate the actuator's force across its full axis by correlating pressure, length, and other parameters that influence actuator strength.

A Method for Precise Tracking Control of Pneumatic Artificial-Muscle-Driven Exoskeletal Robot

Exoskeletal robots are of critical importance in the domain of mechanical boosting. The pneumatic artificial muscle (PAM) is commonly used as a flexible actuator in exoskeletal robots designed for upper limbs due to its high power-to-weight ratio, conformability, and safety. This study establishes a new model based on the existing model to improve its control precision by implementing elastic and frictional forces and empirical coefficients, battling against the time-variant hysteresis that PAM’s output force exhibits. In the meantime, a BP neural network is employed in reverse modeling, followed by the adoption of the least-square-based particle swarm optimization algorithm in order to determine the optimized parameter values. PAM provides the Upper Limb Exoskeletal Robot with appropriate auxiliary power, which can be adjusted to accommodate variations in posture change during the lifting process. PAM is also capable of handling variable loads based on the principle of torque balance, constructing a control system according to the inverse dynamics of exoskeletal robots accompanied by an inverse model of PAM’s output force, and finally, rendering tracking control of the elbow angle during the auxiliary process possible. Finally, the tracking error results are calculated and shown; the maximum angular error in the tracking process is 0.0175 rad, MAE value is 0.0038 rad, RMSE value is 0.0048 rad, and IEAT value is 4.6426 rad. This control method is able to improve the precision of tracking control of the elbow angle of the upper limb–exoskeleton coupled system during the process of lifting goods.

Development of an innovative quasi-zero stiffness oscillation model using pneumatic artificial muscle

The paper proposes an innovative nonlinear oscillation model having potential benefits in engineering application such as vibration isolation, vibration absorber and so forth. This model composes four offset slider-crank mechanism and four cam mechanism, whose main feature is to remain the quasi-zero stiffness value within the working region. Furthermore, instead of using conventional elastic elements such as coil spring, rubber air spring, etc. Another potential elastic element which is pneumatic artificial muscle (PAM) will be introduced in this work. Indeed, the PAM can work as a spring for supporting the load simultaneously it may also work as an actuator for creating active force. This means that the proposed model can be changed easily between two working modes such as passive and active one. First of all, the restoring model of a commercial PAM will be analyzed and identified experimentally. Based on these results, an offset slider-crank mechanism is then designed, next designing the cam mechanism will be presented. The constraint of this design is that vertical restoring force of the proposed oscillation model is always constant in working region, attaining the quasi-zero stiffness. The result is to obtain a set of equations describing the profile of the cam. From these equations, a 3D model of the cam mechanism will be built. Finally, a prototype of the proposed model will be fabricated and realized experimentally. The experimental result confirmed the agreement between the measured and simulated data, meaning that the proposed model can offer a constant force-displacement or quasi-zero stiffness curves in working region. This study will offer a useful insight into the dynamic analysis of this oscillation model.

High-Precision Displacement and Force Hybrid Modeling of Pneumatic Artificial Muscle Using 3D PI-NARMAX Model

Pneumatic artificial muscle (PAM) is attractive in rehabilitation and biomimetic robots due to its flexibility. However, there exists a strong hysteretic nonlinearity in PAMs and strong coupling between the output displacement and the output force. At present, most commonly used hysteresis models can be treated as two-dimensional models, which only consider the nonlinearity between the input and the output displacement of the PAM without considering the coupling of the output force. As a result, high-precision modeling and estimation of the PAM’s behavior is difficult, especially when the external load of the system varies significantly. In this paper, the influence of the output force on the displacement is experimentally investigated. A three-dimensional model based on the modified Prandtl–Ishlinskii (MPI) model and the Nonlinear AutoRegressive Moving Average with eXogenous inputs (NARMAX) model is proposed to describe the relationship and couplings among the input, the output displacement, and the output force of the PAM. Experiments are conducted to verify the modeling accuracy of the proposed model when the external load of the PAM varies across a wide range. The experimental results show that the proposed model captures well the hysteresis and couplings of the PAM and can precisely predict the PAM’s behavior.

Kinematic and quasi-static analysis model of a novel variable stiffness pneumatic artificial muscle

A novel variable stiffness axial expansion pneumatic artificial muscle based on hexagonal origami is proposed. Based on the presented assumptions, a kinematic analysis model of the pneumatic artificial muscles is presented, and the changes in crease angles, air cavity volume and geometric configurations of the pneumatic artificial muscles during the actuation process are obtained. The equivalent elastic modulus of the hyperelastic material is obtained by fitting the stress-strain curve. The stress state of the crease is simplified as the pure bending model of a straight beam, and the rotational stiffness of the crease is formulated. Based on the energy method, a quasi-static characteristic analysis model of the pneumatic artificial muscles is developed. The pressure-displacement curve under the unloading state and the output force-displacement curve under the loading state are calculated. The variable stiffness characteristics of the pneumatic artificial muscles are evaluated. Compared with the experimental and numerical simulation results, the analysis models are verified. The work will provide analysis models for the mechanical design and force-displacement control of this type of pneumatic artificial muscles.

Bionics Design of Artificial Leg and Experimental Modeling Research of Pneumatic Artificial Muscles

In the research and development of intelligent prosthesis, some of performance test experiments are required. In order to provide an ideal experimental platform for the performance test of intelligent prosthesis, a heterogeneous biped walking robot model is proposed. Artificial leg is an important part of heterogeneous biped walking robot, and its main function is to simulate the disabled a healthy normal gait, which provides intelligent bionic legs gait to follow the target trajectory. The pneumatic artificial muscles (PAM) have good application in the artificial leg. The bionic design of artificial leg mainly includes the structure of hip joint, knee joint, and ankle joint, adopting the four-bar mechanism as the mechanical structure of the knee joint, and PAM are used as the driving source of the knee joint. Secondly, the PAM performance test platform is built to establish the relationship among output force, shrinkage rate, and input pressure under the measured isobaric conditions, and the mathematical model of PAM is established. Finally, the virtual prototype technology is used to build a joint simulation platform, and PID control algorithm is used for verification simulation. The results show that the artificial leg can follow the target trajectory.

Design and modeling of a high-load soft robotic gripper inspired by biological winding**The authors have confirmed that any identifiable participants in this study have given their consent for publication.

The improvement of the load capacity of soft robotic grippers has always been a challenge. The load improvement methods of existing soft robotic grippers mainly include the development of soft actuators with high output force and the creation of closed gripping structures. Inspired by winding behaviors of animals and plants, we propose a high-load soft robotic gripper driven by pneumatic artificial muscles (PAMs) that combines the advantages of a high force soft actuator and a closed gripping structure. Most existing model formulations focus on characterizing the end force generated to the length contraction and applied pressure of PAMs. However, the focus of this work is to build the force model of PAMs in winding shape to analyze the tightening force of the high-load soft gripper, and the model is validated by a tightening force test. An experimental work is carried out to characterize the load capacity and multi-object gripping capacity of the high-load soft gripper. We experimentally prove that it can lift heavy objects that weigh up to 35.5 kg, which is more than 47 times its weight. This work contributes to the load improvement of soft robotic grippers, and the mathematical modeling of engineering systems with winding structures. The developed high-load soft gripper is expected to enter the practical application field from the laboratory.

Analysis on the Impact Factors for the Pulling Force of the McKibben Pneumatic Artificial Muscle by a FEM Model

Modelling the behaviour of Pneumatic Artificial Muscle (PAM) has proven difficult due to its highly complicated structure, nonlinear nature of rubbery material, and air compressibility. To overcome these limitations, a FEM (Finite Element Method) model using Abaqus and CATIA is derived for the quantitative analysis on the impact of different factors on the pulling force of PAM. In the Abaqus a two parameter Mooney–Rivlin model is utilized to consider the hyper-elastic nature of flexible material. Then both Abaqus and CATIA are used in the parametric design of a 3-Dimensional model of PAM. Furthermore, the FEM model is employed to predict the static force exerted by PAM and the results show that the model is promising. The FEM model produces closer results to the test data for the typical PAM. Nonlinear behaviour of PAM is found to be obvious with an increase in both the contraction and the air pressure, different from the linear curves obtained by the fundamental geometrical model. Nonlinear changes in the PAM force are also observed in the numerical study on the effect of structural factors including initial braid angle, initial diameter, initial wall thickness, and flexible material. Besides, these phenomena can be explained by a connection between mechanical and morphological behaviour of PAMs with the FEM model. Generally, this modelling approach is more accurate compared to the fundamental theoretical model and more cost competitive compared to the empirical methods.

Inverse Modeling of Nonlinear Artificial Muscle Using Polynomial Parameterization and Particle Swarm Optimization

The properties of pneumatic artificial muscle (PAM) with excellent power‐to‐weight ratio and natural compliance made it useful for healthcare engineering applications. However, it has undesirable hysteresis effect in controlling a robotic manipulator. This behavior is quasistatic and quasirate dependent which changed with excitation frequency and external force. Apart from this, it also inherits frictional presliding behavior with nonlocal memory effect. These nonlinearities need to be compensated to achieve optimal performance of the control system. Even though an inverse modeling of PAM has limited application, it is important on certain control system implementation that requires the solution to the inverse problem. In this paper, the inverse modeling of PAM in the form of activation pressure was proposed. This activation pressure model was derived according to static pressure and extracted hysteresis components from pressure/length hysteresis. The derivation of the static pressure model follows the phenomenological‐based model of third‐order polynomial. It is capable of characterizing the nonlinear region of PAM at low and high pressure. The derivation of extracted hysteresis model follows the mechanism of dynamic friction. In this principle, the activation pressure model was dependent on regression coefficient of the static pressure model and dynamic friction coefficients of the extracted hysteresis model. The regression constants of these coefficients were characterized from the hysteresis dataset by using model parameter identification and the particle swarm optimization (PSO) method. The result from model simulation shows the root mean square error (RMSE) value of less than 10% error was evaluated at various excitation frequencies and external forces. This inverse modeling of PAM implemented a simple approach, but it should be useful in control design applications such as rehabilitation robotics, biomedical system, and humanoid robots.

Modeling and Controller Design for Pneumatic Artificial Muscle for Ankle-Foot Orthotic Device

In the present era Electric motors are most commonly used actuators for various robotic and bio-robotic applications. However, the functioning of electric motor is not similar to human skeletal muscles. Also, the electric motors are prone to harm human beings in case of failure. Hence, the present work has focused on exploring a bio-inspired actuator, which functions similar to human skeletal muscles and is safe for human beings. The literature review has revealed that such an actuator is pneumatic artificial muscle (PAM). In the present work the researchers have focused on developing an efficient model and control strategy for PAM in order to use it for bio robotic applications. An experimental setup has been prepared to analyze the behavior of PAM for different speeds of operation and different loading conditions during inflation/ deflation. Based on the experimental datasets an experimental model of PAM and Proportional Pressure Regulator (PPR) has been developed using polynomial curve fitting tool of MATLAB. Then a switched mode feedback PID control strategy has been developed for PAM which takes care for the hysteresis behavior of PAM. The control strategy has been simulated to achieve the trajectory angle tracking of ankle joint during the complete gait cycle. The simulation of the proposed control strategy with the developed model has shown that the proposed approach works fairly well and the error in the ankle joint movement could be limited in the range of -0.8° to 0.6° for the complete gait cycle. The result obtained in the present study is similar to the results as reported in the literature. However, this could be achieved with less system complexity using simpler modeling technique and “switched mode feedback PID controller”, which has not been reported by any researcher till date.

COMPARATIVE SURVEY OF VARIOUS STATIC AND DYNAMIC MODELS OF PNEUMATIC ARTIFICIAL MUSCLES

A lesser known type of pneumatic actuators is pneumatic artificial muscle (PAM) although these pneumatic actuators play an important role in industrial, medical and other applications. In this study a PAM model based on the assumption Euler’s law is developed, some static force models (geometric model-based static force model, static force model using maximum force of PAM and static force model using a polynomial function) are compared to Sárosi’s force model and two dynamic models based on Sárosi’s static force model and Hill’s muscle model are presented.

Electric-Pneumatic Actuator: A New Muscle for Locomotion

A better understanding of how actuator design supports locomotor function may help develop novel and more functional powered assistive devices or robotic legged systems. Legged robots comprise passive parts (e.g., segments, joints and connections) which are moved in a coordinated manner by actuators. In this study, we propose a novel concept of a hybrid electric-pneumatic actuator (EPA) as an enhanced variable impedance actuator (VIA). EPA is consisted of a pneumatic artificial muscle (PAM) and an electric motor (EM). In contrast to other VIAs, the pneumatic artificial muscle (PAM) within the EPA provides not only adaptable compliance, but also an additional powerful actuator with muscle-like properties, which can be arranged in different combinations (e.g., in series or parallel) to the EM. The novel hybrid actuator shares the advantages of both integrated actuator types combining precise control of EM with compliant energy storage of PAM, which are required for efficient and adjustable locomotion. Experimental and simulation results based on the new dynamic model of PAM support the hypothesis that combination of the two actuators can improve efficiency (energy and peak power) and performance, while does not increase control complexity and weight, considerably. Finally, the experiments on EPA adapted bipedal robot (knee joint of the BioBiped3 robot) show improved efficiency of the actuator at different frequencies.

Dynamic contraction behaviour of pneumatic artificial muscle

The development of a dynamic model for the Pneumatic Artificial Muscle (PAM) is an imperative undertaking for understanding and analyzing the behaviour of the PAM as a function of time. This paper proposes a Newtonian based dynamic PAM model that includes the modeling of the muscle geometry, force, inertia, fluid dynamic, static and dynamic friction, heat transfer and valve flow while ignoring the effect of bladder elasticity. This modeling contribution allows the designer to predict, analyze and optimize PAM performance prior to its development. Thus advancing successful implementations of PAM based powered exoskeletons and medical systems. To date, most muscle dynamic properties are determined experimentally, furthermore, no analytical models that can accurately predict the muscle’s dynamic behaviour are found in the literature. Most developed analytical models adequately predict the muscle force in static cases but neglect the behaviour of the system in the transient response. This could be attributed to the highly challenging task of deriving such a dynamic model given the number of system elements that need to be identified and the system’s highly non-linear properties. The proposed dynamic model in this paper is successfully simulated through MATLAB programing and validated the pressure, contraction distance and muscle temperature with experimental testing that is conducted with in-house built prototype PAM’s.

空気圧人工筋駆動マニピュレータのモデル化と物体把持制御

Safety is essential as artificial hands have contact with people. We consider a pneumatic drive manipulator that can give flexibility to the structure itself. While pneumatic drive has the advantage of high compliance, it also has disadvantages of low control accuracy and large error. It makes it possible to hold the object in a balanced manner or to handle it manually unconsciously when these features work well. So, we first modeled static characteristic model of pneumatic artificial muscles, and next defined the driving model of the manipulator, and finally considered the potential due to the joint stiffness stored in the manipulator. In this way, we have constructed the equation of motion of manipulators considering flexibility. The effectiveness of modeling is verified by comparing experimental and simulation results. In addition, we confirmed that the manipulator grasps using the flexibility by performing object grasping control.

Experimental Validation for Fuzzy Control of Servo Pneumatic Artificial Muscle Driven by Metal Hydride

This paper presents the servo control problem of pneumatic artificial muscle (PAM) powered by hydrogen-based metal hydride (MH) for mechanical servo actuation. Under various operations of a servo PAM actuator driven by hydrogen-based MH, the desired task of actuator is changed following those various operations. A fuzzy adaptive proportional-integral-derivative (PID) controller is proposed to improve the dynamic performance requirements in both transient and steady-state responses. The fuzzy logic part of the proposed controller is employed to be better than a conventional PID for automatic online tuning of the parameters of PID gain under different operating conditions. The nonlinear mathematical model of PAM actuated by hydrogen-based MH is determined as the desired characteristics of closed-loop control for a fuzzy rule base. Position control is examined to illustrate the performance of the proposed controller. The results show that the proposed technique is more suitable and effective in the case of servo actuation.

Modeling of pneumatic artificial muscle using a hybrid artificial neural network approach

Pneumatic Artificial Muscle (PAM) actuator has been widely used in medical and rehabilitation robots, owing to its high power-to-weight ratio and inherent safety characteristics. However, the PAM exhibits highly non-linear and time variant behavior, due to compressibility of air, use of elastic-viscous material as core tube and pantographic motion of the PAM outer sheath. It is difficult to obtain a precise model using analytical modeling methods. This paper proposes a new Artificial Neural Network (ANN) based modeling approach for modeling PAM actuator. To obtain higher precision ANN model, three different approaches, namely, Back Propagation (BP) algorithm, Genetic Algorithm (GA) approach and hybrid approach combing BP algorithm with Modified Genetic Algorithm (MGA) are developed to optimize ANN parameters. Results show that the ANN model using the GA approach outperforms the BP algorithm, and the hybrid approach shows the best performance among the three approaches.

Control of pneumatic artificial muscle system through experimental modelling

This paper deals with position control of a single degree of freedom (sdof) manipulator actuated by Pneumatic Artificial Muscle (PAM) actuator. Though the compliance characteristics of these actuators are desirable, their inherent non-linearities due to compressibility of air and non-linear load–contraction characteristics make them difficult to model and design of controller becomes very complex. To overcome this, a novel method is hereby proposed to establish an accurate empirical model for the system. The quasi-static characteristics of the PAM are first modelled followed by the dynamic characteristics through spectral analysis. For cost competitiveness, the present work incorporates inexpensive on–off switching valves operated using a novel model based proportional pressure regulator developed using a modified PWM algorithm. Finally, a conventional PID position controller is extended using the empirical PAM model and an inner pressure regulation loop to achieve trajectory tracking of a sdof manipulator. Results for pressure regulation and position control confirm the effectiveness of the adopted approach in achieving performance comparable to the state-of-the-art results at a reduced control complexity and total set-up cost.

Mesterséges pneumatikus izomelemek modellezése és paramétereinek szimulációja MATLAB környezetben

Pneumatic artificial muscles (PAMs) are becoming more commonly used as actuators in modern robotics. The most made and common type of these artificial muscles in use is the McKibben artificial muscle that was developed in 1950's. The braided muscle is composed of gas-tight elastic bladder, surrounded by braided sleeves. Typical materials used for the membrane constructions are latex and silicone rubber, while nylon is normally used in the fibres. This paper presents the geometric model of PAM and different MATLAB models for pneumatic artificial muscles. The aim of our models is to relate the pressure and length of the pneumatic artificial muscles to the force it exerts along its entire exists.

Mathematical Model of Pneumatic Artificial Muscle Reinforced by Straight Fibers

This article describes a mathematical model of a pneumatic artificial muscle reinforced by straight fibers. The pneumatic artificial muscle is lightweight and high power. In addition, it is possible for it to emit exhaust into the atmosphere because the transmission medium of its energy is air, and it needs neither a tank nor maintenance like hydraulic equipment. In addition, safety to a person and the environment is high because the base of the actuator is a soft polymeric material even if damage to the artificial muscle is caused. On the other hand, because the device is composed of a thin film cylinder, and is easily influenced by outside power for the conversion of the volume change in rubber into physical contraction axially, and its passive character is strong, precise positional control is difficult. However, the living thing that has a verbose degree of freedom enables minute motion and walking, etc. by skillfully adjusting to avoid impedance, because it understands its own muscular characteristic beforehand. Similarly, it is thought that the precise positional control is possible by understanding the characteristics of an artificial muscle beforehand. In this research, it is assumed that the expansion shape of the pneumatic artificial muscle that we developed from the pressure distribution is equivalent to the centenary curve, and its model is based on dynamic balance. The result shows the effectiveness of control of an artificial muscle that uses highly accurate calculations and models.