A Review on the Development of Pneumatic Artiﬁcial Muscle Actuators: Force Model and Application

: Pneumatic artiﬁcial muscles (PAMs) are soft and ﬂexible linear pneumatic actuators which produce human muscle like actuation. Due to these properties, the muscle actuators have an adaptable compliance for various robotic platforms as well as medical applications. While a variety of possible actuation schemes are present, there is still a need for the development of a soft actuator that is very light-weight, compact, and ﬂexible with high power-to-weight ratio. To achieve this, the development of the PAM actuators has become an interesting topic for many researchers. In this review, the development of the different kinds of PAM available to date are presented along with manufacturing process and the operating principle. The various force models for artiﬁcial muscle presented in the literature are broadly reviewed with the constraints. Furthermore, the applications of PAM are included and classiﬁed based on the ﬁelds of biorobotics, medicine, and industry, along with advanced medical instrumentation. Finally, the needful improvements in terms of the dynamics of the muscle are discussed for the precise control of the PAMs as per the requirements for the applications. This review will be helpful for researchers working in the ﬁeld of robotics and for designers to develop new type of artiﬁcial muscle depending on the applications.


Introduction
The development of robotic systems is becoming increasingly prevalent today, with possible applications including personal or mobile robots working alongside humans, as well as exoskeletons worn to restore or improve human abilities.Due to their flexibility and soft nature, Pneumatic artificial muscles (PAMs) have evolved as the possible actuation strategy among the other available actuators in the market over the last 30 years [1].The field of artificial muscle actuator is highly interdisciplinary and attracts many researchers from the fields of mechanical engineering, material science, electrical engineering, biology, and physics.PAMs are simple mechanical actuators that consist of an elastomeric bladder within a braided mesh sleeve with two end-fittings to seal both the ends of the muscle.Upon pressurization of the bladder by air, the actuator either contracts or extends axially, with the direction of motion dependent on the orientation of the braided sleeve fibers.The contractile PAMs are able to produce higher forces than extensile PAMs and are less prone to buckling; hence, the contractile PAMs are more commonly utilized, and are also known as the contractile actuator.
There are different types of conventional actuating mechanisms such as: electric motors, hydraulic actuators, pneumatic pistons, and shape memory alloys (SMA), along with the flexible actuators used in various applications.However, the use of artificial muscles is more beneficial in comparison to the other actuation mechanism due to their following advantages [2-7]: • PAMs are lightweight and produce a strong force, which provides high power-toweight ratio for the applications.
• PAMs provide flexibility and compliance for the applications in a pressurized or unpressurized condition.• PAMs deliver a safe and compatible interaction with the human environment only by controlling the volume flow rate of operating air into the muscle.• Simple PAMs can be fabricated from inexpensive materials, which reduce the overall manufacturing cost.• PAMs provide the linear contractile motion with a monotonically decreasing loadcontraction relation like the skeletal muscle, which can control joint compliance.

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PAMs exhibit the nature of essential compliance for installation for providing required power, and the values of speed along with force are in the range of what is needed.

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Because of the direct connection, replacement of a defective PAM with a new one can be done easily and swiftly by uncoupling the muscle along with pneumatic tubing.• Due to the intrinsic and adjustable compliance, PAMs can be made to have a soft touch and, consequently, are well-suited for safe human-robot interaction.
Due to these benefits, a number of groups have investigated the design geometries and fabrication methods of different types of artificial muscle actuators.The physics behind the operation of PAMs is the same as that of human muscle as it converts the pneumatic power to pulling force.The compressibility of the air plays a significant role in the artificial muscles for the unpredictable impact.Various types of conventional PAMs, as shown in Figure 1, have been developed depending on the different operating principles, applications, and design concepts [6].These can be classified in the literature into four major types, such as braided muscles, pleated muscles, netted muscles, and embedded muscles.For various medical applications, high torques are required at low to moderate speeds.Therefore, the proper selection of the actuator is the crucial part to avoid undesired phenomena like backlash, friction, and extra inertia to the structure.It may lead to a more complicated design with heavy construction, which is not acceptable by the user.Hence, there is a need to make it lightweight and compact to actuate the body's compliant joints in a real environment.In response to this, Kalita [7] presented theoretical and experimental studies to evaluate the safe operating range of PAM for different conditions with the nonlinear characteristics present in the muscle actuator.For the actuation of these devices, electrical motors like DC motors, AC motors, stepper motors, and linear motors are commonly used, through which high acceleration and positional accuracy can be achieved.However, for human-robot interaction, the high rigidity of the joints in these robots will be very dangerous for the operator due to a large amount of weight of the electric motors.The power-to-weight ratios for the electric actuators are in the order of magnitude of 100 W/kg with higher peak values and the range of the output torques within 1-10 Nm per kilogram [8][9][10].To achieve high torques at a low speed, some gearing attachment or high-performance motors has to be developed.Raab and Isermann [9] mentioned that hydraulic actuators with a power-to-weight ratio of 2000 W/kg can achieve high torques at low speeds.Though there is a chance of leakage in the energy source due to high operating pressure, it can be directly connected to the robot joints.With the use of the servo-valve control, this kind of actuation can acquire the necessary compliance characteristics.
Pneumatic cylinders are the most commonly used pneumatic actuators with power-toweight ratios of 400 W/kg, which can be operated with moderate speeds [9].The inherent compliance characteristics are present in the pneumatic actuators due to the compressibility of the air pressure; therefore, PAM has been used as an alternative pneumatic actuator in the medical applications to achieve better power-to-weight ratio than the pneumatic cylinder.The muscle actuator is operated with the help of the pressurized air through a core deformable membrane, and the required motion can be obtained.Due to the use of the viscoelastic materials in most of the available PAM, it is lightweight in nature, and the deformation is based on the material elongation.The power-to-weight ratio of these kinds of actuators is normally higher than 1 kW/kg [11].Other new particular actuators like shape memory alloys (SMA) and polymeric actuators have been used in various applications, but these actuators are very much specific-application-oriented, and their speeds of operation are also very low [10,12].Table 1 presents a comparison of the maximum strain (stroke divided by resting length), actuation stress (force divided by cross-sectional area), and specific work (work divided by mass) of several types of actuators, which is inspired by the work of Woods [13].PAMs combine large usable strains with significant actuation stresses to yield a higher ratio of work to mass (i.e., specific action) than several other actuation technologies such as electromechanical actuators, solenoids, and piezoelectric or magnetostrictive materials.Hence, due to the advantages of PAM over the other actuators, these muscle actuators are the most suitable for various industrial [6] and medical [14,15] applications.In addition to these performance advantages, PAMs boast a variety of structural advantages as well.PAMs are very durable and have long fatigue life, having demonstrated only small wear and tear signs after 120 million actuation cycles [16].The PAM actuators significantly gained importance in the field of biomedical as well as industrial applications including micro/nano scales in recent years due to the above-mentioned advantages of the PAM over the other available actuators.However, the effectiveness and safety of the applications depend on the nature of PAMs based on the material properties, dimensions, and operating conditions.To understand these properties of the PAMs, a comprehensive systematic review is demanded on the available PAM actuators based on the design types and applications along with the force models utilized by the muscle actuators.The scope of this state of the art is to address the following research questions about the PAM actuators: (1) What are the basic operating principles of PAM actuators?(2) How are the PAMs advantageous over the other actuators?(3) What types of PAMs are available in the market or developed by research?(4) How have the muscles been modeled for understanding the muscle force?(5) What should be the design criteria for efficient PAMs? (6) What are the different applications found in the fields of biorobotics, medicine, and industry?(7) What are the possible developments required in the PAM actuators for future prospects?
Therefore, to address these impending questions, a systematic review is presented in this work to provide a brief idea on the interesting and trending topic of PAM actuators.In the next section, the basic concept and operating principle of the PAM actuators are discussed followed by the different kinds of muscle actuators available in the literature as well as in the market.Thereafter, the muscle force models developed by many researchers and designers are investigated along with the different kinds of applications based on the fields included.Finally, a discussion on the design criteria, research gap, and challenges along with possible directions for improvement in the development of muscle actuators are presented.

Concept and Operation
Pneumatic Artificial Muscle (PAM) is a contractile and linear motion actuator operated by the air pressure.The main two parts of most of these kinds of actuators are the flexible core and the reinforced closed membrane like shell and diaphragm.Both ends of these muscle actuators are closed with the end fitting (closures, clamps).The core membrane is bulged outward or squeezed due to the supply of the air pressure and through which the mechanical power is transmitted to a load.The core contracts axially apply a pulling force on its load due to the radial expansion or contraction.Therefore, the force (tension, load) and the motion achieved by the PAM actuator are linear and unidirectional.To understand the basic concept and working principle of muscle actuators, an antagonistic arrangement has been developed with the help of a chain-sprocket mechanism and it can be used for testing a wide range of muscle available in the market before use in the actual applications [17].This contractile operation, which extends upon inflation, differentiates these actuators from the bellows.The PAMs are known with various names in the literature as: Pneumatic Muscle Actuator [11], Fluid Actuator [18], Fluid-Driven Tension Actuator [19], Axially Contractible Actuator [20,21], and Tension Actuator [22,23].
The basic energy source to a PAM is primarily air either forced into it or extracted from it.This creates a pressure difference between the air inside the muscle and its surroundings, through which the PAM can be actuated to obtain the required motion.More energy can be transferred by overpressure as compared to underpressure.Most of the PAMs operate at overpressure with ambient pressure around 100 kPa, though there is possibility to design an underpressure operating muscle [24,25].Hence, by supplying compressed air into the muscle, the required motion can be obtained to move a load and vice versa by discharging the air pressure.
The basic operations of the PAM can be considered with two examples: (1) under a constant load and with varying gauge pressure, and (2) with a constant gauge pressure and a varying load.Figure 2a, for the first operation, shows a PAM that is fixed at one end with a constant mass (M) hanging from the other side.The pressure difference across the membrane, i.e., its gauge pressure, can be increased from an initial value of zero.At zero gauge pressure, the volume of the membrane is considered to be minimum V min and its length maximum l min .Now, the actuator is pressurized to a gauge pressure P 1 , which makes the muscle bulge and, at the same time, it develops a pulling force.This force will lift the mass (M) until the equilibrium point where the generated force will equal to the mass weight Mg.In this condition, the volume of the PAM is increased to V 1 and its length is contracted to l 1 .Further increasing the pressure to P 2 , this process will continue until it reaches the maximum allowable gauge pressure P max .From this kind of operation of the PAM, two basic actuator behavior rules can be noticed, where a PAM shortens by increasing its enclosed volume and it will contract against a constant load if the pneumatic pressure is increased.The second type operation of PAM under constant gauge pressure is shown in Figure 2b with an example.Here, the gauge pressure is kept at a constant value P with a decrease in the load where the muscle will inflate and shorten.If the load is completely removed, as shown in Figure 2b, the swelling goes to its full extent with the maximum volume of the PAM, V max .In this situation, the length of the muscle will reach the minimum value l min and the pulling force will drop to zero.PAM will not be able to contract beyond this point and behaves as a bellows at a shorter length, which generates a pushing instead of pulling force.This means that a PAM will shorten at a constant pressure if its load is decreased and its contraction has an upper limit at which it develops no force along with its enclosed volume is maximal.From these two examples of PAM operations, it can be concluded that PAM has an equilibrium length for each pair of pressure and load.This characteristic is in total contrast to the operation of a pneumatic cylinder where the developed actuation force only depends on the pressure and the piston surface area so that, at constant pressure, it will be consistent regardless of the displacement [4].In the next section, the design of four classifications of PAMs are explained along with some advanced pneumatic muscle actuators.

Classification of Pneumatic Artificial Muscle
According to Marcinčin and Palko [24], in 1930, various muscle-like actuators had been developed by a Russian inventor named S. Garasiev.These actuators can be classified based on the design and operation characteristics, such as: (1) pneumatic or hydraulic operation, (2) overpressure or underpressure operation, (3) braided/netted or embedded membrane, and (4) stretching membrane or rearranging membrane.Though the hydraulic operation is considered only for completeness sake, the main feature of the artificial muscles is their inflation and deformation.Due to this feature, the flexibility is needed in the muscles for which the material strength along with the pressure difference should be limited.This makes the PAM an attractive and advantageous actuator over the other hydraulic actuator.The third characteristic mentions the tension carrying element of the muscle, which is a structure either embracing the membrane or embedded in the membrane.The last characteristic describes how the membrane inflates where it can be able to expand radially; either the membrane material has to stretch, or the radial section has to change by rearranging the membrane's surface.In the case of pure rearranging, the total membrane surface is constant regardless of contraction and volume.This allows for greater tension to be developed as no energy is put into stretching membrane material.Based on these characteristics, further, this review will focus on four types of PAM, namely, the braided muscles, which are the most frequently used, the pleated PAM, the netted muscle, and the embedded muscle, which was developed as an improvement with regard to the drawbacks of the braided design.

Braided Muscle
Braided muscles are composed of a gas-tight elastic tube or bladder surrounded by a braided netting (weave, braid, sleeve), as shown in Figure 3.The braid fibers run helically about the long axis of the muscle at an angle (pitch angle, braid angle, weave angle).The tube is pressurized laterally against the sleeve and the internal pressure inside the tube is restricted by braid fiber tension due to fiber curvature.The fiber tension is incorporated at the endpoints of the braid to balance the external load.Hence, the pressing contact between tube and sleeve is necessary to lift the load, and braided muscles cannot operate at underpressure.The most common braided muscles are the McKibben muscle [2, 3,26,27], where both its inner tube and braid connected to fittings at both ends.Another this type of muscle is known as sleeved bladder muscle [28], which has only the braid connected to end fittings and in which the inner tube is an unattached bladder.The McKibben muscle, as shown in Figure 4, was derived from a patented design by Morin [25], who embedded the fibers into a rubber diaphragm.According to Baldwin [29], it was first introduced by the physician, Joseph L. McKibben, in the 1950s to actuate an orthotic device for polio patients due to the similarity in length-load curves between this artificial muscle and skeletal muscle [30,31].The general behavior of these muscles with regard to shape, contraction, and tension when inflated will depend on the geometry of the bladder and surrounded braid at unpressurized condition along with the materials used.Usually, these braided muscles have a cylindrical shape because of a cylindrical bladder and a constant pitch angle throughout the braid.The sleeved bladder muscles, patent by Beullens [28], are different from the McKibben type in the design of the inner bladder, where it is not connected to the sleeve, which means that there is no passive spring force is added to muscle tension.The main advantage of this type of PAM is its extreme ease of assembly.

Pleated Muscle
Pleated muscle actuator was developed by Daerden and Lefeber [32,33], which is shown in Figure 5a.There is no material strain and friction involved in this type of muscle when it is inflated.This is due to the muscle membrane, which consists of the number of pleats in the axial direction and inflates by unfolding the pleats.Furthermore, membrane stresses in the parallel direction (perpendicular to the axis) are kept negligibly small and decrease with increasing the number of folds.Basically, there is no required external energy to inflate the membrane and, due to the absence of friction, no hysteresis is observed.The characteristics of this type of muscle depend on the ratio of full length to minimum diameter, strain behavior of the membrane's material, contraction rate, and applied pressure.A modified version of the pleated muscle actuator by Terryn et al. [34] is shown in Figure 5b, where the membrane is constructed out of a self-healing polymer.

Netted Muscle
The main difference between braided and netted muscles is the density of the grid surrounding the membrane, where a mesh with relatively large holes with a braid is tightly woven.Due to this, the membrane is of the stretching kind where the muscle can withstand only low pressures.Therefore, this type of muscle actuator will usually have a diaphragm of the rearranging kind.Figure 6a shows the Yarlott muscle by J. M. Yarlott [18], which includes an elastomeric bladder of a prolate spheroidal shape netted by a series of cords or strands.This actuator takes the spheroid bladder shape in its inflated state, and when elongated, the axial strands straighten out and push the bladder into a shape characterized by a series of ridges and valleys.Figure 6b shows another type of netted muscle, the Robotic Muscle Actuator (ROMAC), which was designed by G. Immega and M. Kukolj in 1986 [20].ROMAC consists of an articulating polylobe bladder harnessed by a wire netting and closed at either end by fittings [35], where the bladder is made of a sheath that is characterized by its high tensile stiffness, flexibility, and fluid-tightness.The netting or harness is comprised of non-stretchable flexible tension links joining at nodes to form four-sided diamond-shaped apertures in the network.Figure 6c shows the Kukolj muscle by M. Kukolj [21], which is a modification of the standard McKibben muscle.The main difference between the muscles is the sleeve, where the McKibben muscles have a tightly woven braid, and the Kukolj design uses an open-meshed net.In a nonleaded condition, there is a gap between the net and the membrane, which only disappears at a suitably high extending load.

Embedded Muscle
In embedded muscles, the load-carrying structure of the actuators is embedded in its membrane.The Morin muscle by A. H. Morin [25], consists of a rubber tube embedded by threads of a high tensile stiffness.The threads can be arranged along the actuator's long axis or in a double helix about that axis, and the fiber material may be used like cotton, rayon, asbestos, or steel.Depending on the working of operating pressure, three designs of Morin muscle have been shown in Figure 7a, namely, an overpressure design as shown in a longitudinal cross-section, an underpressure design, and a concentric membranes design.The Baldwin muscle by H. A. Baldwin [29], based on the design of Morin muscle [25], consists of an elastomeric membrane, a very thin surgical rubber that is embedded by glass filaments in the axial direction.The Under Pressure Artificial Muscle (UPAM) developed by K. Nazarczuk in 1964 at the Warsaw Polytechnic [24], exhibits similar design as the Morin muscle [25].As gas is sucked out of the membrane it collapses in a non-axisymmetric way, i.e., it is squeezed and flattened in the middle.
The Paynter Knitted Muscle developed by H. M. Paynter [23] has a spherical bladder of elastomeric material that is reinforced by a knitted structure of strong, tough, and flexible fibers.When fully inflated, the muscle takes on the shape of the original bladder and knitting sphere.Figure 7b shows the Paynter Hyperboloid Muscle, which is an alternative design described by H. M. Paynter [19].The elastomeric membrane of the muscle is made with the neoprene rubber or polyurethane, which takes the shape of a hyperboloid of revolution in its fully elongated state.The membrane is embedded by a sleeve of inextensible, flexible threads of metal wires, cord, polyester fibers, or para-aramid fibers attached to the end fittings.Figure 7c shows the Kleinwachter torsion device by Kleinwachter and Geerk [36], where the inflatable membrane technique can be used in designing a torsional device, which refers to a torsion muscle.The device has a toroid diaphragm embedded with stiffening filaments and attached at its outer edge to a ringshaped structure along with its inner edge to a shaft.Along with these classifications of the traditional PAMs, there are more advanced pneumatic muscles designed and developed in the literature [37][38][39][40][41][42][43][44][45][46][47].An artificial muscle tube has been developed by Nakamura et al. [38], as shown in Figure 8a, in which high-intensity glass fiber had been built into a natural latex rubber tube (Straight fibre type).Kalita and Dwivedy [39,40] fabricated an affordable PAM actuator as compared to the McKibben type using natural silk fibers (Pat and Muga Silk) reinforcement with silicon rubber, which can be easily modified depending on the requirement of the applications.Veale et al. [41] developed the Planar Fluidic Muscles, known as Peano muscles or pouch motors, as shown in Figure 8b, which have the potential to provide the high force and compliance of McKibben muscles with the low threshold pressure of pleated PAMs. Figure 8c shows a Soft Robotic Muscle (SRM) actuator fabricated by Oguntosin and Akindele [42] with the help of silicone rubber using a molding process.Greer et al. [45] designed the series Pneumatic Artificial Muscle (sPAM), as shown in Figure 8d, which is made from a thin rectangular sheet of polyethylene tube that is sealed (heat bonded) on one end so that it inflates.Wirekoh and Park [43] designed the Flat Pneumatic Artificial Muscle (FPAM), as shown in Figure 8e, which is made of a silicon substrate that contains embedded Kevlar fibers.[41]; (c) SRM [42]; (d) sPAM [37]; (e) FPAM [43]; (f) sFPAM [44]; (g) HCRPAM [45]; (h) rPAM [46]; (i) High-displacement PAM [47].
Further, a modification has been done to the FPAM by integrating with force and position sensors, which resulted in a sensorized, Flat, Pneumatic Artificial Muscle (sFPAM) by Wirekoh et al. [44], as shown in Figure 8f.Han et al. [37] developed a High-Contraction Ratio Pneumatic Artificial Muscle (HCRPAM), as shown in Figure 8g, which consists of three parts viz., an elliptical tube that generates the expansion force, a diamond-shaped band that converts the expansion force of the elliptical tube into the output contraction force, and a two-stage spline that maintains the straight elongation of the elliptical tube.Figure 8h shows the reverse Pneumatic Artificial Muscle (rPAM) by Skorina et al. [46], which consists of silicone rubber that is radially constrained by symmetrical double-helix threading.Yang et al. [47] designed a high-displacement pneumatic artificial muscle, as shown in Figure 8i, which is made of textiles or plastics that can include integrated electronics to sense its pressure and displacement.Depending on the various design of PAMs, the force models considered in the literature have been discussed in the next section to better understand the dynamics and control of the PAM.

Force Model of Pneumatic Artificial Muscle
There are many studies available regarding the mathematical modeling of PAMs.The basic component of the modeling is the relation between the pressure and the length of the PAM actuator to the exerted force along its entire axis.The muscle force is primarily considered a function of operating pressure, material properties, and dimensions of the muscle, which play an important role in the PAM's dynamical behavior.Therefore, the mathematical modeling of PAM is very important in understanding the relationship between the factors for various applications and controlling the overall functioning of the muscle.However, PAM exhibits strong nonlinear force-length characteristics, making it challenging to model and control, as well as to obtain the demanded performance features [33,48].Kelasidi et al. [49] explained the most common and important mathematical modeling of PAM found in the literature.

Geometrical Model
There are two geometric models of PAM, which are the most common and widely used, namely, the Chou and Hannaford model [2] and the Tondu and Lopez model [3].The Chou and Hannaford model [2] is the simplest geometrical model for a static performance of the PAM.With this approach, the PAM has been modeled as a cylinder, as shown in Figure 9, with a length L, thread length b, diameter D, and number of thread turns n.The angle θ is defined as the angle of the threads with the longitudinal axis.Utilizing the energy conservation principle, the simple geometric force of PAM F g is calculated as follows, multiplying the gauge pressure P with the change in volume with respect to length [50].Another widely used geometrical model of PAM is the Tondu and Lopez model [3], which is based on the virtual work theorem.The expression for the contraction force generated by the muscle which is a function of the control pressure and the contraction ratio is written as follows [3,51,52]: sin 2 θ 0 and r 0 is the nominal inner radius, l is the length of the muscle, l 0 is the initial nominal length, P is the pressure and θ 0 is the initial angle between the membrane fibres and the muscle axis.A disadvantage of the model is its design, which is based on the hypothesis of a continuously cylindrical shaped muscle.In contrast, it takes a conic shape at both ends when it contracts.Consequently, the more the muscle contracts, the more its active part decreases.This phenomenon results in the actual maximum contraction theoretically being smaller than that expected from Equation (2) [53].Hence, to improve Equation (2), Tondu and Lopez [3] considered an empirical factor k in addition to account for the end deformation of the PAM as follows: where 0 ≤ ≤ max , and max = ( 1 k )(1 − β α ).By inserting the parameter k within the considered static model , the value of the maximum force given at zero contraction is not get affected.This is in concordance with the conducted experiment since the PAM has a cylindrical shape only when its contraction ratio is zero.

Biomimetic/Biomechanical Model
There is a method of PAM modeling which is popularly known as biomimetic or biomechanical model due to similarities with the biological muscle and try to model in the literature [27].Basically, PAM is a composite of a rubber mold with embedded structural fibers, which creates a force in the longitudinal direction extending the circumferential direction in pressurized condition.A phenomenological approach is considered by Serres et al. [54,55] to understand the dynamics of PAMs by modeling it with three elements: a spring element, a damping element, and a contractile element in parallel, as shown in Figure 10.X is the displacement of PAM, M is the mass of moving parts, C is the damping coefficient, F c f is the contractile force coefficient, K is the spring coefficient of PAM, and F is the external load.Further, by taking the Laplace transform and setting the initial conditions to zero, the transfer function of the phenomenological model of PAM is derived as follows [54], where X d is the desired displacement of the PAM and τ = ( C K ).

Empirical Model
PAM with different lengths and diameters can be modeled with the help of simplified empirical models.In this approach, The stretched length is zero when the air pressure inside PAM only the atmospheric pressure, and this length increases when the air pressure also increases [56].The natural mechanical operation of the PAM and the mechanical spring exhibit similar behavior when a tensile force is being applied to them, as shown in Figure 11.Usually, the stiffness of the spring is fixed and depends on the material properties and geometry of the spring, whereas the stiffness of PAM is variable and also depends on the above properties in addition to the air pressure inside the muscle.Based on the experimental observation by Wickramatunge and Leephakpreeda [57,58], the pulling force acting on PAM can be modeled as similar to the force acting on a mechanical spring where the stiffness parameter of PAM can also be specified as K.The stiffness parameter K is the function of the operating gauge pressure P and the stretched length of the PAM L s .The elastic force generated by PAM, F elastic is given below.
The stiffness K explicitly has been considered as a second order polynomial of P and L s which is represented as follows: where the constant parameters q 1 , q 2 , q 3 and q 4 can be found from experimental data by applying the method of least squares.Further, higher degree polynomials can be applied to obtain the desired precision requirement.In another experimental work by Li et al. [59], the force-contraction quasi-static characterization of the PAM is considered along with a linear least squares fit at each operating pressure.The muscle force F mus is estimated to vary as a linear function of the contraction and operating pressure P as follows.
where α 1 , α 2 , α 3 , β 1 , and β 2 are the experimental constant parameters which are obtained from the least squares fit.Using this muscle force equation, Kalita and Dwivedy [60] evaluated the safe operating range along with the critical values of the different parameters present in the McKibben type muscle actuator using parametric instability regions and validated by performing experiments.
Along with these, various other novel methods have been proposed in the literature for the analysis of PAM to establish accurate empirical models.A PAM motion caused by a nonlinear force that mainly depends on parameters like pressure and deformation is obtained analytically by applying the optimal parameter identification method.This method has finally been proved and tested on an experimental rig by Sárosi et al. [61] and Palomares et al. [62].Cullinan et al. [63] and Cveticanin et al. [64] have investigated the steady state position of the mass of the system and the force influenced by the pressure of the PAM mathematically and experimentally.Colbrunn et al. [65] studied the static and dynamic mathematical model for the braided pneumatic actuator.Tóthová et al. [66] used two PAMs for antagonistic motion connected through the chain gear and investigated based on modified Hill's basic model.Hildebrandt et al. [67] presented a nonlinear cascaded control strategy to move a trolley actuated through pneumatic muscle actuators to follow a reference path.Carneiro et al. [68] used two servo valves for pneumatic force actuation.Tothova et al. [69] discussed the analytical model of muscle force based on the measured values.
In cases of higher positioning requirements and motion in two opposite directions needs, two PAMs in an antagonistic connection are highly preferred, just like in real muscles in the living bodies [61,[70][71][72][73]. Šitum and Trslić [73] discussed a nonlinear mathematical model for a PAM pair in an antagonistic arrangement based on an original and unique ball-on-beam system.Liu et al. [74] and Xie et al. [75] used advanced techniques like the modified Prandtl-Ishlinskii (MPI) model to control the inherent hysteresis nonlinearity for the accuracy of trajectory tracking control of PAM.Other advanced force models for the PAM have been mentioned, which are discussed in the literature such as the approximate deducted model using the maximum force of PAM [76], the polynomial function model [77], and the exponential function model [78].
Ashwin and Ghosal [5] presented a discussion on some more different empirical models from the literature and the key equations for the muscle force those are discussed in Table 2.In Table 2, l 0 , r 0 , and t 0 represent length, outer radius, and thickness of the bladder before deformation, respectively, and, after deformation, these change to l, r, and t, respectively.The initial inner radius of the bladder represents by r i = r 0 − t 0 , whereas the initial and final winding angles of the braid are denoted as θ 0 and θ, respectively.The symbols N, m, and b represent the number of turns of the braid along the length, number of strands of braid, as well as the length of a single braid strand, respectively.P is the input pressure, F represents the muscle force, and the strain in the bladder along the axial direction is = (l 0 − l l 0 ).All other unknown parameters used in the equations are considered to be constant in general.

Author
Muscle Force Equation

Nonlinear Model
A highly nonlinear nature is present in the PAM due to the air compressibility, valve actuation, viscoelastic material properties, and load contraction characteristics due to flexible structure.The other factors like the irregular shape of the rubber bladder geometry [91], elastic energy [83,87,92,93] present in the bladder and braid, and threshold pressure [94] also contribute to the nonlinear characteristics of the PAM.Therefore, to include these nonlinearities, some specific models have been presented in the literature.Kalita and Dwivedy [95][96][97][98] investigated the responses and behaviors of the nonlinear PAMs by adding a cubic nonlinearity αx 3 to the muscle force Equation (7) for the consideration of nonlinearities present in the muscle actuator.The nonlinear dynamics of a system attached with a PAM is studied under simultaneous resonance condition [95] and principal parametric resonance condition [96].The fluctuation of operating pressure in the muscle is considered to be a periodically time varying pressure P = P 0 + P m sinωt, where P 0 and P m represents the dynamic pressure and static pressure inside the muscle, respectively [95,96].The governing equation of motion for the system results in a forced and parametrically excited system with cubic nonlinearity due to the nonlinear muscle force as shown below.
The nonlinear dynamics present in the PAMs have been studied by considering a constant pressure inside the muscle, which resulted in harmonically excited system in [97] and a system under hard excitation in [98].In the experimental work [97], the nonlinear parameters in the muscle force are obtained by performing experiments for the system under simple resonance condition with the help of a developed antagonistic experimental setup.The chaotic behaviors present in the muscle actuator are investigated with the system under hard excitation where the forcing amplitude is higher than the coefficient of the linear term and subjected to super-and sub-harmonic resonance conditions [98].As the superposition rule is not applicable to nonlinear systems, the responses obtained in one resonance condition may not be useful for other resonance conditions.Hence, dynamic modeling and analysis are very much essential, particularly for the systems attached with PAM due to their high nonlinear nature.
Determining accurate values for constants in nonlinear models often requires precise experimentation.Therefore, by considering the material properties precisely along with an extensive computation, the nonlinear material modeling may provide better accuracy.A nonlinear Mooney-Rivlin material [99,100] is considered for the elastic properties of the bladder, and the stress components from strain energy density functions are used in the force balance equations.Considering this material, Kothera et al. [93] derived the following muscle force expression by using an energy balance method where E b is Young's modulus and λ 1 , λ 2 , and λ 3 are the stretch ratios of the braided Mooney-Rivlin material [99,100].Later, this model is used by Woods et al. [101] for generating large trailing edge flap in a helicopter with the help of PAM.Wang et al. [87] described a static model of PAM by using Mooney-Rivlin material where Hoop force F s and axial force F θ acting on bladder during inflation are found analytically in terms of λ 1 and P. Thus, from the static force balance equations from braid, the muscle force can be obtained as follows.
Some other nonlinear materials, such as neo-Hookean material [102], are also considered for the bladder of PAM in the work of Trivedi et al. [83], in which the modeling and the axial muscle force expression can be written as follows.
In the work of Ball and Garcia [91], the authors considered the thin wall approach in modeling of PAM and the force expression is given as follows: where, F stands Here, P 0 is the acting pressure at the outer radius by the bladder on the sleeve and σ 1 and σ 2 are the material constants and stretch ratios.In the case of the thick-walled bladder as well as prestrained bladders, the thin wall tube model is applied successively as if the thick cylinder is an array of concentric nested thin tubes.The computational method calculates the pressure P 0 of the innermost layer and works sequentially outward.Depending on the various design and force models considered for PAMs, a number of applications can be found for the muscle actuators, which are presented in the next section.

Applications of Pneumatic Artificial Muscle
The first commercially available Pneumatic Artificial Muscle (PAM), which was manufactured and marketed by Bridgestone Corp. of Tokyo, Japan, known as the Rubbertuators [103] in the late 1980s, was used in various application for some time.Nowadays, Shadow Group of Companies from the U.K. [104] and Festo AG & Co. from Germany [105] are manufacturing various kinds of PAM for industrial robotics and medical applications [106].The PAMs are very much suitable for multiple applications like exoskeletons along with rehabilitation assistance [6,107,108], grasping and handling delicate objects with complex geometry [109][110][111], a robotic mechanism where multiple sophisticated movements are required [112][113][114][115][116], and industrial and service robotics [6,[117][118][119].PAMs are mainly used as robotic actuators in applications where compliance and low powerto-weight ratio are essential.Winters [120] mentions sleeved bladder muscles as having potential to be a suitable power system in prosthetics.
Caldwell et al. [11] used 18 small McKibben muscles that were 90 mm long, 10 mm diameter, and 5.5 gm to power a dexterous, four-fingered manipulator.Each finger of the manipulator was powered by four muscles and the thumb by six muscles.In another work of Caldwell et al. [48], the authors reported about the McKibben muscle to power the elbow and wrist of an anthropomorphic arm along with full humanoid robot [121].The Shadow Group of Companies used 28 PAMs with 14 on each leg for designing the Shadow Biped Walker [104].Hannaford et al. [122] manufactured an anthropomorphic arm with the help of fifteen McKibben Muscles, called the Anthroform Biorobotic Arm and which is controlled by simulated spinal neural networks.Grodski and Immega [123] used ROMAC muscles to control a single degree of freedom (DOF) teleoperated arm with the help of myoelectric signals acquired from the biceps and triceps of the operator.Inoue [103] researched the Soft Arm powered by Rubbertuators, and it was developed by Bridgestone Corp. of Tokyo, Japan The robot has a shoulder, an upper arm, a lower arm and wrist, four to five DOFs, and a useful payload of a maximum of 3 kg.Depending on the various properties of the muscle actuators, the applications of PAM can be found in the most three significant areas in the literature [6], namely, (a) Biorobotic, (b) Medical, and (c) Industrial applications.In the following subsections, the uses of PAM in these three applications are explained, starting with the various biorobotic applications using PAMs in the next subsection.

Biorobotic Applications
PAMs have been used in various biorobotic applications or biomimetic robots that imitate the morphology and physiology of humans and animals.As shown in Figure 12a, Kawamura et al. [124] designed a humanoid robot, Intelligent Soft Arm Control or ISAC, which consist of two six DOF arms and multiple PAMs that antagonistically actuated each joint of the arms.A six-legged insect-like robot, Airbug was developed by Berns et al. [125] using fluidic muscles in the antagonistic arrangement.Jaryani [126] presented a dynamic formulation of a series of antagonistic artificial-muscle-driven devices for generating locomotion and computed muscle-force control for the planar locomotion of a snake robot.Daerden et al. [127] designed a hopping robot composed of a lower and upper leg, hip, and a body that slides along a guide shaft with pleated PAMs for the knee joint movement.Witte et al. [128] developed the four-legged prototype Pneumatically Actuated dyNamically sTable quadrupEd Robot (PANTER) using PAM, which has four active DOFs.Ajax, a cockroach-inspired robot with legs, as shown in Figure 12b, was designed by Kingsley et al. [129], which is controlled with the help of several PAMs.The biped robot, Lucy, a two-dimensional walking robot, was constructed by Verrelst et al. [130] using 12 pleated PAMs for six DOFs in two articulated legs each, as shown in Figure 12c.Tsujita et al. [131] developed a three-legged robot with antagonistic pairs of PAMs, which is controlled by a nonlinear oscillator network.Niiyama et al. [132] designed a bipedal jumping and landing robot, as shown in Figure 12d, called Mowgli, which consists of six PAMs.Niiyama and Kuniyoshi [133] developed a bipedal robot with an Artificial Musculoskeletal System based on PAMs.Tsujita et al. [134] constructed and controlled a quadruped robot with PAMs in antagonistic pairs to drive the musculoskeletal system.A fully PAM-actuated humanoid muscle robot torso, as shown in Figure 12e, the Zwei-Arm-Roboter, was developed by Boblan and Schulz [135] in human-like proportions and functionality.As shown in Figure 12f, a Pneumatic Athlete Robot was presented by Niiyama et al. [136] with a musculoskeletal system driven by PAMs and applied human muscle activation patterns for dynamic bipedal running.Andrikopoulos and Manesis [137] discussed the development and control of a vertical climbing robot, which is actuated with the help of four PAMs.Fukuoka et al. [138] developed a quadruped robot with realistic legs driven by PAMs for achieving a running gait and designing a controller for the same.Shadow Robot Co., London.UK presented the Shadow Robot Leg, which is a human-sized PAM-actuated robotic leg developed for investigation of myoelectric control of powered prosthetic legs [104].Festo AG & Co., Esslingen, Germany constructed two robots with the help of PAM, namely, Airic's robotic arm and Aqua ray robot [105].Airic's robotic arm, as shown in Figure 12g, depicts through artificial bones and muscles where the bone structure is moved via 30 PAMs, using very small valves based on piezo technology.In Figure 12h, the Aqua ray robot is a remotely controlled fish where three antagonistic pairs of PAMs move the two wings and the tail with the help of artificial tendons.In the next subsection, the uses of PAMs in various medical applications are discussed.

Medical Applications
Due to the presence of characteristics like high power-to-weight ratio, soft and flexible movement, stable motion speed, and adaptable compliance in the PAM, it has been widely used in many medical applications.Along with these characteristics, PAM possesses similar properties with those of human muscle and safe human-robot interaction, which is essential for the therapeutic devices, rehabilitation, surgical equipment, and neurological injuries [6,14,15].Prior and White [139] discussed the performance of a PAM-actuated wheelchair-mounted robot arm.Misuraca and Mavroidis [140] described the design and control of a Human Muscle Enhancer (HME) system, which is used for augmentation of the muscle capabilities of subjects requiring partial lower limb weight-bearing gait support.Tsagarakis and Caldwell [141] studied the utilization and control of a pair of PAMs in antagonistic arrangement during the construction of dexterous prosthetic hands, which is used for strength augmentation.Figure 13a shows a PAM-actuated prosthetic forearm, which has been developed by Wongsiri and Laksanacharoen [142,143] with flexor and extensor groups of muscles.An armor-type muscle suit actuated through PAM has been developed by Kobayashi and Hiramatsu [144] which provides the muscular support to paralyzed patients without attaching any metal frame.Herr and Kornbluh [145] designed a powered ankle-foot orthosis, as shown in Figure 13b, with the use of PAM for leg rehabilitation to provide single joint support to the plantar flexion in different phases of gait.RUPERT [146,147], a therapeutic device, as shown in Figure 13c, has five DOFs, is powered by four PAMs, and which can be able to provide supplementing therapy in addition to the clinic treatment of patients suffering from upper extremity impairment.Vimieiro et al. [148] developed an exoskeleton system consisting of a hip orthosis equipped with PAMs to assist the lower limb movements.Ferris et al. [149][150][151] developed a powered ankle-foot orthosis, as shown in Figure 13d, that utilized PAMs for assisting patients during gait rehabilitation after injury.Gupta and O'Malley [152] designed a five DOFs PAM-actuated haptic arm exoskeleton for training and rehabilitation in virtual environments.As shown in Figure 13e, a novel motorized orthosis actuated through PAM was presented by Knestel et al. [153] for intensive home-based gait training in patients with neurological disorders.Deaconescu and Deaconescu designed a PAM-actuated isokinetic equipment, as shown in Figure 13f, for recovery exercises of the hip and knee joints [154] and a robotized arm for persons with locomotive disabilities [155].Figure 13g shows a hip exoskeleton for gait support, designed by Nascimento et al. [156] with pelvic braces and thigh supports.These are actuated with pneumatic artificial muscle connected to the hip joint of the user.Kao et al. [157,158] developed an ankle-foot orthosis (AFO) for in-lab studies at the University of Michigan using two PAMs and analyzed the ankle d/p motion.Like AFO, a pair of powered anklefoot orthosis (PAFOs), as shown in Figure 13h, has been designed with pneumatic muscles for ankle d/p assistance by Norris et al. [159].
Lewis and Ferris [160] designed an exoskeleton which comprises a pelvic part and thigh cuffs being attached to the hip joint for f/e motions.It is actuated by a pair of pneumatic muscles placed on the lateral side, which provides passive a/a.A pneumatic actuated knee exoskeleton has been proposed by Kim et al. [161] with two PAMs that mimic the functions of rectus and biceps femoris muscles.Leclair et al. [162] developed an ankle-foot exoskeleton powered by a PAM to obtain the passive ankle d/p motion.Kim et al. [163] designed another AFO to provide ankle plantarflexion motion for elderly people, which comprises of a basic single DOF exoskeleton and an artificial pneumatic actuator.Malcolm et al. [164,165] developed an AFO with pneumatic muscles to study the effects of an active AFO for human movements.Dragone et al. [166] developed a novel mechanism actuated by the artificial muscles for the optimal regulation of the compliance of the biorobotic joint an Exoskeleton Rehabilitation Robot.This mechanism is characterized by a soft and hybrid actuation exploiting the storage/release of the elastic energy by bistable Von Mises elastic trusses.Chi et al. [167] presented a design of a rehabilitation robotic device driven by PAMs that can be equipped on the upper limb for stroke patients under an accurate control.An intelligent controller, adaptive sliding controller adding compensator (ASC + C) was proposed by Nguyen et al. [168] to operate a PAM-actuated robotic arm for assisting in the rehabilitation exercise of the elbow joint function.Dao and Yamamoto [169] developed a highly compliant lower-limb rehabilitation orthosis system, AIRGAIT, powered by muscle actuators for guiding the subjects' lower limb to a designate trajectory, with an estimation of disability and adaption of the compliance accordingly.A novel design with single-PAM for a one degree-of-freedom (1-DOF) robotic lower-limb system was developed by Tsai and Chiang [170] with the advantage of a mechanism for developing a multi-axial therapy robotic system.This system uses the stretching/contraction characteristics of a single-PAM and the torsion spring designed by the mechanism to realize joint position control.Chu et al. developed a multi-functional robotic arm actuated through PAMs with a multi-degree of freedom for performing upper limb rehabilitation exercise tasks.In addition to these applications, many applications of PAMs in medical instrumentation can be found [59,85,115,116,[171][172][173].Li et al. [59] developed a compact and lightweight forceps' manipulator for laparoscopic surgery with PAMs, as shown in Figure 14a, which allows for the perception of manipulation force without the usage of the force sensor.Ashwin and Ghosal [115,116] designed an endoscopic attachment which can be used to independently position an endoscopic catheter tip at a desired location with the help of three miniaturized pneumatic artificial muscles (MPAMs).Each MPAM used in the device is of 1.2 mm diameter and 45 mm length and applied a pressure of 137-827 kPa to one or more muscles.Due to the small size, these MPAMs are mainly found in the various medical applications like wearable hand exoskeletons in Figure 14b [171], cardiac compression devices [172], and tool manipulation in surgical devices, as shown in Figure 14c,d [85,173].The uses of PAMs in various industrial applications are discussed in the next subsection.

Industrial Applications
Due to the presence of characteristics in the PAM, such as generating high torques at low and moderate speeds, essential compliance for installation, less mechanical wear, and working as the actuator of portable machinery due to their lightweight properties, it is attractive for many industrial applications.The PAMs are a suitable solution for the actuation of industrial machinery and particularly industrial robots due to their safe human-robot interaction and shock resistance ability.Pomiers [174] developed a modular robot with a single DOF pneumatic element and a 3-DOFs robot arm using rubber PAMs.Presented in Figure 15a is a Robot Arm System designed by Kawashima et al. [175] actuated through rubber PAM, which has six DOFs.Damme et al. [176,177] presented a 2-DOFs planar robotic manipulator, as shown in Figure 15b, which is powered by pleated PAM for assisting in handling heavy loads.Caldwell et al. [178] proposed a prototype design of a teleoperation rig for retrieval of radioactive material, which is a combination of the traditional man-handled manipulation pole and PAMs.PAMs have been used for the identification of the modal parameters of bridges by Deckers et al. [179].Wedler and Denkena [180] developed a parallel-kinematic hexapod tool, which is driven by six PAMs in antagonistic arrangements with pressure and position sensors, as shown in Figure 15c.Radojicic et al. [181] developed a prototype of a hybrid robot, as shown in Figure 15d, which included two bellows and one PAM actuated module for safe human-robot interaction.Yerkes and Wereley [182] described a PAM-activated trailing edge flap for flight control, as shown in Figure 15e.In another work, Wereley et al. [183] presented the applications of PAM for the the actuation schemes of a morphing cell for a wing section and trailing edge flaps for wings or rotorcraft blades.
Lin et al. [184] designed a soft robot actuated by single McKibben muscle actuator for enhancement in the crawling capability inside a pipe for the purpose of pipe inspection and maintenance.Stoll et al. [185] presented a compliant pneumatic rotary drive unit with three or more working chambers actuated through PAMs for using in human-robot collaborations.Robinson et al. [186] developed a robotic arm actuated through artificial muscles for lifting weight in different industrial as well as medical scenarios with the exploration of control algorithm for smoothly and accurately track the desired motions of a manipulator.Brown et al. [187] developed the AGAS system, an autonomously controlled deployable airdrop system that consisted of a round parachute and controlled by four PAMs.Pohl [188] developed the FM Motion Seat, as shown in Figure 15f, a driving and flight simulator based on a hexapod structure with six spatially oriented PAMs that moved the seat in all the six axes and acted as a passive suspension.As shown in Figure 15g, Engineered Arts Limited from Cornwall, U [189] developed the RoboThespian, a PAMactuated humanoid robot, which is created for education, communication, interaction, and entertainment.Jake Loniak from The Art Center, Pasadena, CA, USA [190] designed the Deus Ex Machina project, as shown in Figure 15h, which is an electric, single passenger, vertically parking, and wearable motorcycle.With seven artificial vertebrae behind the helmet, for supporting the rider's head, the control of the Deus Ex Machina is achieved by 36 PAMs and 2 linear actuators combined with the rider's body.In the next section, a discussion has been included by summarizing this review and making a conclusion on the development of the PAMs for future prospects.[176]; (c) parallel-kinematic hexapod tool [180]; (d) hybrid robot [181] (e) PAM-activated trailing edge flap [182]; (f) Crawling soft robot [184]; (g) Compliant pneumatic rotary drive unit [185]; (h) Heavy-lift robotic manipulator [186].

Discussion and Conclusions
Over the years, many researchers and designers have been attracted to the use of PAM in industrial and medical applications due to their advantages, such as high force-to-mass ratio, soft and flexible structure, and easy installation with safer human interactions.PAMs are suitable for the execution of positive load feedback, where smooth, accurate, and fast responses are essential.It also produces a significant force when fully stretched and can be used in applications like exoskeletons and rehabilitation devices due to the lightweight nature of this actuator, where the weight of the equipment is a restriction.Basically, these muscle actuators consist of a thin rubber tube (bladder) that is covered or embedded with a braided mesh shell.Both ends of the muscle are closed where one end is used as an air inlet, and another is connected to the load.When the compressed air is supplied to the muscle through the inlet port, the internal bladder tends to increase its volume against the braided mesh shell.However, the non-extensibility of the braided mesh threads causes the actuator to shorten and produce pulling forces if it is connected with the load.Based on the primary working principle of PAM and advantages over other actuators, this work presents a detailed review on the development of different traditional muscle actuators along with recently developed advanced muscle actuators.This review further includes the derived muscle force models for understanding of the different parameters present in the muscle dynamics along with the nonlinear effect on the systems.The applications of PAMs in the fields like biorobotics, medicine, and industry have been investigated along with modern applications in the field of medical instrumentation.
Many types of PAMs have appeared in the literature, which are different in their mechanical construction and the mathematical model describing the principal operation.Understanding the hysteresis of PAM in the phenomenological model is still a challenge, so many applications depend only on the empirical formulations.However, due to the presence of high nonlinearities in the PAM, the operation of the PAM mainly depends on the proper mathematical model for dynamic behavior and control of the muscle.Moreover, there is still a lack of achieving an accurate mathematical description of the nonlinear dynamics behind the actuation of PAMs.The nonlinear characteristics present highly in PAMs due to the compressibility of air, basic properties of rubber materials, flexible structure, and valve actuation.The presence of nonlinearities in the muscles makes it difficult to understand the dynamics for modeling and control.Though different models have been presented in the literature to understand the behavior and to control the PAM, but there is limited works on dynamic model for the nonlinear characteristics present in the muscles.Therefore, further investigation with improved model of the PAM can be explored for various practical applications.The presence of high nonlinearity in the muscle dynamics gives rise to the vibration issue with the PAM, and many researchers have been trying to solve the vibration problems associated with the muscle.Efforts have been made to improve their dynamic models and provide a better control strategy to attenuate the vibration of the muscle.The performance factors of the muscle actuators such as power density, force density, low-cost, efficiency, peak strain, cycle life, and bandwidth individually provide better results as compared to those obtained from the biological muscle.Nonetheless, it is necessary to work toward developing a PAM that can match all the performance factors simultaneously.These qualities and drawbacks make the PAM an attractive topic for many researchers and industries to study its behavior under different environments.

Figure 11 .
Figure 11.Comparison of PAM and spring system.