Pneumatic Muscle Actuators based on McKibben .... C , the tube after the input valve is modelled ... together with the gas pipe before the valve are modelled.
Proceedings of the 2002 IEEE International Conference on Robotics & Automation Washington, DC • May 2002
Enhanced Dynamic Performance in pneumatic Muscle Actuators S. Davis, J. Canderle, P.Artrit, N. Tsagarakis and Darwin G. Caldwell Dept. of Electronic Engineering, University of Salford Manchester M5 4WT, UK Abstract
actuators, ie combining controlled motion, high power to weight and volume ratios, with portability and safety for humans operating close to or with the robot. These restrictions have prompted work on a variety of actuation systems with potential in generic and niche applications including: Shape Memory Alloys, Electro-Rheological Fluids, magneto-strictive actuators, ultrasonic motors, polymeric actuators, and pneumatic based systems such as the Flexator/ROVAC and pleated pneumatic actuators [2-5]. Among the most promising of these new actuators is the pneumatic Muscle Actuators (pMAs) developed at Salford and derived from the McKibben muscle, pioneered in the 1960’s [6] for rehabilitation applications. At the time the power/weight performance of the system and the inherent compliance were seen as positive features but control was still a problem and development was discontinued. It was resurrected briefly by Bridgestone in the 1980’s [7] and although work was again discontinued the potential of pneumatic actuation for robotic applications was recognised and several new pneumatic based designs have since been developed [8-11]. Addressing the modelling issues Hanaford et al [9] and Caldwell et al [11] showed that increasingly accurate models of the forces could be developed and Caldwell et al showed that when operated with an adaptive controller the muscles can rapidly and effectively adapt to structural, operational and environmental changes [8]. But despite showing that the controllability issues could be addressed with the new pMAs, new issues arose primarily due to the relatively limited bandwidth and but to a lesser extent the compliance and the quantity and efficiency of air usage. This paper shows how modifications to the physical structure of the pMA and consideration of the effects of efficient air flow can have benefits in terms of increased bandwidth, increased system stiffness and reduced air consumption. These performance enhancements also have benefits in terms of power and volume to weight ratios. Initially, the paper provides an introduction to the pMAs and outlines their characteristics. Section 3 studies the theoretical features that limit the performance and develops design concepts that will give performance enhancements for both isometric and isotonic conditions. Section 4 shows implementation of these improvements (isometric
Pneumatic Muscle Actuators based on McKibben muscles have performance characteristics that may be of considerable significance in robotics due to their power/weight ratio and use as user friendly soft drives. However, the dynamic response (bandwidth) has been inferior to electric systems, with a secondary concern over system stiffness. In this paper, the bandwidth limit is addressed from two perspectives; air flow effects and the physical structure of the actuator. It is shown that; i). By reducing the dead volume within the muscle structure (by the addition of a variety of filler materials) the bandwidth can be increased by up to 400%, with similar increases in system stiffness. At the same time the air volume used to power the actuator can be reduced by up to 80-90%. The methods of achieving these improvements are fully assessed. ii). By ensuring effective air flow rates, it is shown that bandwidth limits can be increased by several 100% and potentially increases of 1000s% are possible.
1.
INTRODUCTION
Actuators are responsible for transferring energy into mechanical motion that permits and determines the exact nature of any interaction with the environment. For organic systems this has lead to the evolution of muscle, which forms a unique soft, compliant actuator that provides power for all animals of all sizes [1]. In engineering, electrical drives form the primary robotic power source with some limited use of hydraulics and pneumatics. Although these systems have been well proven and successful in conventional robotics the need to operate in new arenas places constraints on these designs. Recent developments in robotics have suggested that core technologies for the next generation of mechatronic systems will require a fundamental paradigm change, with an evolution from principles based on a bearing-gearsmotors schema to a softer biologically inspired mechanism of muscle-joint-tendons [2-3]. Among the most fundamental features of this change will be the need for actuation systems which can emulate the performance of natural muscle in forming a safe and natural interaction medium, while still possessing the beneficial attributes of conventional engineering 0-7803-7272-7/02/$17.00 © 2002 IEEE
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performance improvements of up to 400%). Section 5 shows the performance enhancement in an ankle joint for a bipedal robot, with final conclusions and future work.
2.
ACTUATION SYSTEM
The pMA is a two-layered cylinder in which there is an inner containment liner (an elastomeric material), an outer flexible double helix layer of braided material such as nylon, Kevlar, polyester etc and endcaps that seal the open ends of the muscle. The detailed construction, operation, and mathematical analysis can be found in [8,11]. This basic structure of the muscles gives the actuator a number of desirable characteristics: i). Muscles are available in a range of lengths and diameters with increasing diameter producing increased contractile force. ii). Actuators have exceptionally high power and force to weight/volume ratios. iii). Displacement (contraction) depends on the loading and construction but is typically 30% of the dilated length – this is comparable with natural muscle [1]. iv). The pMAs are highly flexible, soft in contact and have excellent safety potential. This gives a soft actuator option which is again comparable with natural muscle. v). System controllers have achieved an accuracy better than 1% of displacement. Bandwidths for antagonistic muscle pairs of up to 5Hz can be achieved. Force control using antagonistic pairs of muscles is also possible [1]. vi). The contractile force for a given cross- sectional area of actuator can be over 300N/ cm2 for the pMA compared to 20-40N/cm2 for natural muscle [8,11]. vii). pMAs can operate safely in aquatic or other liquid environments and are safe in explosive/gaseous states. viii). The actuators accommodates lateral and rotational misalignments making rapid construction feasible. Control of the actuator requires regulation of the air flow. In this paper the muscles are energised by 8 port Matrix (758 series) valves operating in a PWM structure. The valves are pulsed at 120Hz.
flow ρ (current) will depend on the circuit components. Therefore P −P (1) ρ= s RT + Rs
Figure 1: Pneumatic circuit and its electrical equivalent. Where P is the pressure in the actuator measured by a pressure sensor at the inlet. Considering a constant volume for the actuator it can be written:
ρ = CA ⋅
dP dt
(2)
The assumption of the constant volume is possible for isometric testing since the muscle is securely attached at both ends and therefore actuator dimensional changes are negligible. Combining equation (1) and (2) describes the flow during the “charging” of the actuator.
ρ+
1 PS ⋅ ∫ ρ ⋅ dt = ( RT + RS ) ⋅ C A RT + RS
(3)
Therefore, the gas flow during “charging” is:
PS ⋅ e − t /( RT + RS )⋅C A RT + RS
ρ=
(4)
Similarly, considering the circuit, figure 1, as a low pass pneumatic filter the cut-off frequency is:
fc =
1 2 ⋅ π ⋅ ( RT + RS ) ⋅ C A
(5)
The capacitance of the actuator is determined using the equation of the ideal gas [12]. P ⋅V = n ⋅ R ⋅T (6) Where R is the gas constant R = 8 .314 N ⋅ m / mol ⋅ K , T is the absolute temperature and n is the number of moles. Differentiating the above equation with respect to the time and assuming that the volume V is constant gives:
3. AIR IN-FLOW EFFECTS ON THE ACTUATOR PERFORMANCE As with all pneumatic actuators, pMAs are powered by the inflow of the fluid (air) with the pneumatic energy being converted to mechanical motion. The technique and efficiency of the conversion process is the defining feature of the actuator used. This is completely analogous with electrical drives as modelled in figure 1. The actuator volume corresponds to a capacitance C A , the tube after the input valve is modelled as a linear resistor RT while the pressure source resistance together with the gas pipe before the valve are modelled by the resistor RS . As in an electrical circuit the mass
ρ=
dn V dP = ⋅ dt R ⋅ T dt
(7)
Equations (7) and (2) suggest that the actuator capacitance relates with the actuator volume as follows
CA =
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V R⋅T
(8)
therefore if the volume is reduced the capacitance decreases resulting in an increased cut-off frequency.
3.1
flow restriction of the valve ports this presents no significant flow reduction. The valve-muscle pipes are each less than 15cm with a 2mm inner diameter. The muscle inlet port is of diameter 6mm. This is the “standard” supply set-up used for all subsequent tests. The air flow for the tests was regulated by increasing the number of open valves ports 1 to 7. This increases the flow rate (defined in the valve specification) from 1.6l/s to 11l/s in regular steps. The performance of the muscles was measured under both isotonic and isometric conditions. The pressure at the inlet was measured using a Honeywell Differential gauge sensor 0-2MPa.
Enhancing System Bandwidth
From above, there are clearly a number of approaches to increasing the actuator bandwidth, involving either reducing the supply air flow resistance (increasing the flow rate) or reducing the muscle capacitance. In the remainder of this paper the effects of delivering these changes in the design of the actuators and the supply chain will be explored.
3.1.1
Increasing Flow Rate
3.2.1
For pMA type systems it is clear that increasing the air flow potential has important performance implications and there are a number of factors that can be used to develop this side of the operation; i). The muscle diameter and the inlet port size. To minimise air flow resistance the inlet port should be as wide as possible. The diameter of the muscle forms the ultimate air flow restriction and cannot be altered without changing the muscle. ie a new actuator. ii). The diameter of the supply pipes. These should be as large as possible to reduce RT . Ideally, this should be comparable with the width of the muscle end cap. Unfortunately supply pipe rigidity means this is only feasible for very small diameter muscles. The supply pipe should also be as short as possible to minimise resistance, transmission time delay and ‘storage’ volume of the pipe. iii). Restrictions in connectors. Pipe connectors form a potential source of flow disruption and resistance and their use should be minimised or removed. iv). The supply pressure. The master cylinder pressure acts in a manner analogous to the supply voltage. Higher supply pressures therefore tend to enhance the flow rate. v). Restriction of air flow through the valve manifold and orifice forms a final flow restriction. Although all the previous parameters effect the dynamic, the most critical features in the current system is the valving since the controlled orifice has a diameter of 1mm as opposed to a minimum pipe diameter of 4mm or above.
3.2
Isometric operation
In its fully extended condition both ends of the muscle were clamped to a rigid steel structure with the end remote from the inlet nozzle fastened to a load cell (Tedea Huntleigh 500kg), figure 2. The air flow was increased from 1.6l/s to 11l/s as outlined and the resultant dynamic force response was measured, figure 3.
Figure 2 Setup to identify the dynamic model. From these results, as predicted, the response increases as the flow rate increases. The overall increase in bandwidth approaches 400% and shows that flow rate specification and optimisation is critical in describing the performance of any pMA type system. As expected the response is a curve, as the number of ports increases so RT reduces and from (5) we see that the input resistance RS becomes the limit to the cut off frequency. If this resistance were reduced it is expected that further increases would be observed.
Flow Rate Effects on Dynamics
Since the Matrix valves controlling the muscles are in 8 port block with identical (and specified) flow characteristics it is possible to accurately equate the flow rate and the dynamic response. Each of the valve ports can be opened/closed independently. The minimum orifice diameter within the valves is 1mm. To characterise the effects of increased air flow on pMA performance a large (1.05m fully extended, diameter 21mm) muscle was used. This muscle size helps to reduce measurement errors common in smaller pMAs. The supply pipe from the source to the valves was a 6mm inner diameter PVC pipe of length 2m. Given the later
8
Bandwidth (Hz)
7 6 5 4 3 2 1 0 0
1
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5
6
7
Number of parallel valves
Figure 3. Effect of Flow Rate on Bandwidth during Isometric Testing.
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8
3.2.2
Isotonic testing
the force would be maintained while giving a faster dynamic, ie muscle capacitance is reduced. Consideration of the exact nature of any filler suggests that it should fill the maximum amount of space without restricting the air flow, while being light so as to minimise any increase in actuator mass. In addition it should be incompressible. Several options were tested.
Using the “standard” configuration isotonic tests were conducted with a loading of 200N. As before the active ports were increased from 1 to 7 and the dynamic response (shortening rate) recorded, figure 4. As before, the bandwidth of the system has increased significantly, approaching 425%. As with the isotonic tests (and for the same reason) the increase in bandwidth is non-linear, however, further extrapolation is again reasonable.
4.1
Solid Granular Filler The first filler tested was a granular component, oval in shape with length 5mm and diameter 2mm. In the tests, on the 1.05m muscle outlined previously, the actuator was fully stretched and filler was added with the fill level being monitored. The isometric test format in section 3.2 was repeated and the response measured, figure 6, as the percentage fill volume was increased. It can be seen that as the percentage filler increases the bandwidth increases peaking at approximately 50% increase for the 55% fill level. Above 55% fill the bandwidth decreased sharply. This trend is highly non-linear and difficult to predict but it is believed that the profile is influenced by the granular structure which makes air flow to the extremes of the actuator difficult. In fact above 55% fill the restriction is such that it is greater than the improvement produced by reducing the dead volume and this causes the fall in performance.
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Bandwidth (Hz)
2
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1
0.5
0 0
1
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3
4
5
6
7
8
Number of parallel valves
Figure 4. Effect of Flow Rate Increase on Bandwidth during Isotonic Testing. At this time no tests have been conducted to determine the ultimate theoretical flow rate limit. This will be effected by many secondary effects making the final limit difficult to predict. However, it is reasonable to predict that bandwidths substantially (several 100s%) above those previously measured are achievable.
% increase in bandwidth
60.00
4. MODIFICATIONS TO IMPROVE DYNAMICS The previous section has shown that optimising the air supply chain enhances the dynamics but this has yet to consider performance improvement due to muscle structure modification. From (5), the bandwidth (cut-off frequency) can be increased by reducing resistance as shown above or by reducing capacitance ie the volume of the actuator. This generally means that a smaller less powerful muscle has a higher bandwidth. The task is therefore to reduce the internal volume increasing the bandwidth without loosing contractile force.
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Figure 6. Granular Filler Effect on Dynamic Response 4.2
Solid Filler From the experiments with the granular filler it was clear that the grain structure prevents the free flow of air within the muscle and there is a critical point at which the performance drops rapidly. To remove this air flow problem the tests were repeated with a solid filler. The actuator was filled with a sealed hollow tube (to maximise volume and minimise weight) of diameter 5 mm less than the pressurised diameter of the muscle. The volume of the filler was increased and the dynamic response monitored as in the previous isometric and isotonic tests, figure 7. From these results it was observed that the dynamic response of the muscle increased by up to 250% in isometric tests with 75% filler. Above this level there was once again a rapid decrease in performance, which is again believed to be due to restrictions in air flow. Up to the ‘knee’ the profile is basically an exponential rise as might be expected.
Figure 5. Radial force acting on the sides of the muscle. Figure 5 shows that the driving pressure within the muscles acts radially on the actuator side walls and this is converted into longitudinal motion by the braided shell structure. The pressure acting on these sidewalls and the area of the side walls is the driving mechanism and not the (total) internal volume. Therefore if this dead space is reduced while maintaining pressure on the walls
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have less stiffness than electric or hydraulic systems. In some applications it is suggested that this makes pMAs less acceptable. Tests were conducted to determine if the addition of a filler and in particular the liquid filler caused a change in the system stiffness.
% increase in bandwidth
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Stiffness (N/m)
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Percentage of muscle volume filled
Figure 7. Solid Filler Effect on Dynamic Response Liquid Filler: Although the solid filler solved many of the flow difficulties, the air flow was still restricted as reflected in the ‘knee’ at 75% fill. To attempt to remove this restriction a liquid filler (water) was tested. This material has the benefit that when pressurised the fluid flows and fully fills the muscle. In essence the actuator is now acting as a hydraulic system driven by low pressure pneumatics. As in the previous tests the liquid (filler) volume of the actuator was increased and the isometric dynamic response was recorded, figure 8. With a fill volume of 80% a bandwidth increase approaching 400% was produced. As with the solid filler the response is an exponential increase. This increase in bandwidth and its relations to filler volume is comparable (up to the ‘knee’ for both the liquid and solid filler tests. This was not the case for the granular filler and is further evidence that the grain structure prevented the free flow of air through the actuator. It is expected that if the volume filled by the liquid could be further increased the bandwidth improvement would be greater. This will require further consideration of the pipe fill structure.
2500
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Percentage of muscle volume filled
Figure 9. Effects of Filler on Actuator Stiffness The muscle was filled with a known volume of liquid filler at an air pressure of 200kPa, and a loading of 200N was applied. The extension of the muscle was measured and the spring constant calculated, figure 9. The test was repeated for a series of volumes of filler and at an operating pressure of 200kPa. From figure 9, there is a significant increase in stiffness from 1100N/m at 0% filler to almost 5000N/m with a fill volume of 95%. 4.5
REDUCTION IN VOLUME OF AIR USED Since the new actuator structure contains a filler reducing the internal dead volume, it follows that the air volume used in any test can be reduced in line with the volume of the actuator/supply pipes occupied by the filler. In some instances 80-90% of the air volume has been filled with a comparable reduction in air volume used and a significant energy saving. Although this is a trivial result this air saving can have important benefits in terms of the overall use of the actuators, and their ability to operate for extended periods or autonomously.
Predicted
400
% increase in bandwith
3000
2000
4.3
Experimental
3500
350 300 250 200
5.
150 100
The results presented above showed the effect of flow dynamics and filler on the response of a single muscle, however, in robotics or any mechatronic system the pMAs must be used as antagonistic pairs with one muscle acting as a flexor and the other an extensor as for natural muscle. To demonstrate the benefits of the actuator enhancements on a real system, tests were conducted on an ankle joint of a humanoid robot. This ankle joint, figure 10, has two dof (dorsi/plantar flexion and eversion/inversion). During the testing the motion in the sagittal plane (dorsi/platar flexion) is maintained fixed while the controlled and monitored action is observed in the frontal plane. The muscle pairs used in these tests are 30cm in length when fully stretched and with a maximum diameter of 40mm. For base testing the ankle was driven by a
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TESTING ON AN ANTAGONISTIC PAIR
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Percentage of muscle volume filled
Figure 8. Liquid Filler Effect on Dynamic Response. The relationship between the bandwidth improvement and the filler volume is given by % increase in bw = ( Fillvol/(Actvol –Fillvol )) *100 Fillvol – Filler volume, Act vol – Actuator Volume and is plotted in figure 8 for comparison. 4.4
Effects of Filler on Actuator Stiffness Although pMAs due to their braided structure tend to be stiffer than conventional pneumatic systems they still
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sinusoid cycle of ±20°. The input frequency was varied from 0.1Hz to 10Hz and the response monitored, figure 11. The muscles are then filled with 200ml of water and the air flow rate doubled from 1.5 to 3l/s. The effects of these changes on the bandwidth were recorded table 1.
pipes, minimal pipe connectors and large orifice valves. Ultimately the limit will occur were the supply system offers negligible resistance in comparison to the resistance in the pMA itself. Although this limit has not been approached in this work, it has been shown that substantial increases are very possible and there is good reason to predict dynamic performance approaching electric and hydraulic limits can be achieved. In addition, by considering the structure of the actuator and particularly how the internal dead space can be minimised bandwidth increases of up to 400% have been achieved. The work has shown that different filler materials can produce these improvements and currently liquid fillers appear to form a particularly effective material (the muscle is in essence a combined hydraulic/pneumatic actuator) with added benefits of increased stiffness and reduced air usage giving greater efficiency. These benefits can be applied in both single and more usefully antagonistic pair configurations. Future work will consolidate and seek to enhance the performance further, looking at new filler options.
Figure 10. Ankle Structure. 20
15
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7.
5
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-10
-15 0
0.2
0.4
0.6
0.8
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1.2
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Figure 11. Typical Antagonistic Muscle Response Flow Rate Fill-Non Fill 1.5l/s No Filler 1.5l/s Filler 3l/s No Filler 3l/s Filler
Bandwidth 0.6Hz 0.9Hz 1.2Hz 1.5Hz
Table 1. Bandwidth Enhancement From table 1, there are clearly significant improvements when adding the filler and/or increased air flow. Although the performance is not optimised it is clear that the performance enhancement seen with a single muscle can be replicated for a muscle pair with excellent potential for the use of these drives.
6.
REFERENCES
[1] D.G.Caldwell, “Biomimetic Actuators: Polymeric Pseudo Muscular Actuators and pneumatic Muscle Actuators”, Mechatronics; an Internal Journal, Vol. 10, pp499, 530, 2000. [2] H. Inoue, “ Whither Robotics: Key Issues, Approaches and Applications”, IROS’96, pp. 9-14, Osaka, Japan, Nov. 1996. [3] D. G.Caldwell, N. Tsagarakis, P. Artrit and G.A.MedranoCerda, “Bio-mimetic Principles in Actuator Design for a Humanoid Robot”, European Journal of Mechanical and Environmental Engineering, Vol. June 1999. [4]. JJ.Grodski and G.B.Immega,”Myoelectric control on a ROMAC protoarm”, Int. Sym. Teleoperation & Control, 297308, 1988. [5] F. Daerden, Lefeber D. and Kool P., “Using Free-radical Expansion Pneumatic Artificial Muscles to Control a 1 dof Robot Arm”, CLAWAR’98, pp.209-214, Brussels, Nov. 1998. [6] R.A. Schulte, The Characteristics of the McKibben Artificial Muscle", In the Application of External Power in Prosthetics and Orthetics, Publ. 874, Nas-RC, 94-115, 1962. [7] K.Inoue, “Rubbertuator and Applications for Robots”, 4th Int. Symp. On Robotics Research, pp.57-64, S.Cruz, USA, 1987. [8] D.G.Caldwell, G.A.Medrano-Cerda, and M.J. Goodwin, "Control of Pneumatic Muscle Actuators", IEEE Control Systems Journal, Vol.15, no.1, pp.40-48,Feb. 1995. [9] P. Chou and B. Hannaford, "Measurement and Modeling of McKibben Pneumatic Artificial Muscles", IEEE TRANS On Robotics and Automation Vol 12, No 1,Feb.1996. [10] B. Tondu and P. Lopez, “Theory of an Artificial Pneumatic Muscle and application to the modelling of McKibben Artificial Muscle”, C.R.A.S., French National Academy of science, 320, pp.105-114, 1996 .[11] N. Tsagarakis and D. G. Caldwell “Improved Modelling and Assessment of pneumatic Muscle Actuators”, ICRA 2000, San Francisco, USA May 2000. [12] M.M. Abbot and H.C Ness, “Theory and Problems of Thermodynamics”, McGraw-Hill, 1972.
CONCLUSIONS
Pneumatic Muscle Actuators based on McKibben muscles have been known for some time and have performance characteristics that may be of considerable significance in robotics. However, the dynamic response has been inferior to electric systems, with a secondary concern regarding the system stiffness. This paper has shown that the major constraining factors on the dynamics of pMA systems is the supply pipe and valve resistance (energy delivery system) which should be as low as possible. This requires large bore
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