Proceedingsof the 1997EEJ5 International Conferenceon Robotics and Automation Albuquerque, New Mexico- April 1997
Investigation of Bipedal Robot Locomotion using Pneumatic Muscle Actuators Darwin G.Caldwel1, G.A.Medrano-Cerda, and C.J.Bowler Dept. of Electronic Eng. University of Salford, Salford, Lancs., M5 4WT, UK.
[email protected]
Abstract Bipedal locomotion and particularly the human gait is a highly automated and complex process involving large numbers of actuators. unfortunately actuator technology is an area of robotics with many conflicting requirements such as: high power density, high power to weight ratio, rapid response, accurate repeatable control, cleanliness, high efficiency, and low cost, which make selection complex. Pneumatic Muscle Actuators (based ain the McKibben Muscle) which can provide positioin and force control better than 1% have been appliied to upper limbs with some success and with contractile forces in excess of 1OOON (in units weighing less than 50g) there is considerable potential for use in bipedal locomotion. This paper will explore the design of a bipedal robot to take advantage of the potential of these actuators. Muscle co-ordination and control sequences will be considered for striding and standing activities and it will be shown that in terms of the energy requirements PMAs are very capable of providing a reliable bipedal drive source with linear actuation, low mass, fast response, compliant energy storage and simple construction. 1.
INTRODUCTION Bipedal locomotion and particularly the human gait is a highly automated and complex process involving, large numbers of actuators El]. Research in this area therefore presents substantial challenges to scientists in areas such as applied mathematics, biology, physiology and engineering. At present it would be unrealistic to attempt a practical realisation of a full organic biped, however, to grasp the essence of bipedal locomotion there is no need to consider dynamical systems of such complexity. In fact in the past 20 :years numerous researchers have developed mechanisms which are capable of producing simple walking patterns. Particularly interesting is the work of Inaba who has developed a 0.25m high biped with two
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arms, vision and gripper hands [2]. The robotic joints are driven by small dc servomotors providing for statically balanced walking, standing up, sitting down, swinging, rolling over on the ground and carrying small light loads. Unfortunately increasing the size of Inaba's robots is not a simple problem. To achieve this goal, robots with efficient actuation systems and energy saving features need to be developed. As observed by Rad et a1 [3], the selection of the drive for legged robots is not a trivial procedure. Small dc motors impose restrictions in terms of the available torques and power. Usually speed reduction assemblies (gears, pulleys-beltskables) are used to match the high torque-low velocity requirements of the robot to the low torque-high velocity characteristics of the motor. The consequences of this are efficiency losses and the introduction of additional dynamics, which may be non-linear (eg backlash). To reduce energy consumption Alexander [4] suggested the use of compliant elements, e.g. pogo stick-like springs and retum springs for swing leg reversal. In fact, Raibert [ 5 ] used the pogo stick principle by incorporating an air spring in his hydraulically powered monoped and biped robots. More recently [3], Rad , considered using mechanical springs for an electrically powered monoped, and Nakano et al. [6], developed a biped with flexible legs. Further energy savings can be achieved by incorporating "passive dynamics" in the robot design (i.e. gravity and inertia alone can generate a walking cycle). McGeer built a gravity powered three legged mechanism capable of walking down inclines ~71.
From studies of the development of bipedal actions it is clear that most bipeds have tended to use electric actuation (ac or dc) with occasional use of hydraulic actuation in the form of hydraulic motors or exceptionally pneumatic devices [2-71. As in other areas of robotics the development of actuators for bipeds is a critical factor in the development of the technology especially where the biped must be free to move autonomously without tethering. Actuators as used in today's mechanical systems have several
often conflicting requirements: high power density, high power to weight ratio, rapid response, accurate repeatable control, cleanliness, high efficiency, low cost and so on. Robotic systems accentuate these requirements with light weight, high power and fast, accurate response becoming paramount. Traditionally, hydraulic and electrical systems have been the preferred drive mechanism, but these have well documented limitations especially where compact high power weight outputs are required for applications such as dexterous manipulation and multi-degree of freedom arms. These restrictions have prompted work on a variety of newer actuation systems with potential for use in generalised as well as specific areas. These newer technologies include: Shape Memory Alloys, Electro-Rheological Fluids, magneto-strictive actuators, ultrasonic motors, polymeric actuators, and pneumatic based systems [8]. Pneumatic systems in particular satisfy many of the prime robotic requirements: cheap, reliable, quick action, safe, high powerlweight ratio, however, in their most common form, as a cylinder, they suffer from two major disadvantages: poor positionallvelocity control, and high compliance which means that load variations adversely affect position. Alternative forms of pneumatic actuator have sought to use the natural advantages of pneumatics while addressing the problems. Systems developed include: the Flexator, ROVAC, Rubbertuator, McKibben muscle and graphite-lined cylinders [9]. Previous work has indicated that Pneumatic Muscle Actuators (based on the McKibben Muscle) weighing less than 50g can when operated at pressures of up to SOOkPa, produce contractile forces in excess of lOOON with force and position control better than 1%. These actuators have been applied to upper limb motions. The aim of this research was to simply model the gross actions of the human muscles as demonstrated in the contractile behaviour of the PMA and determine if this type of actuation system has the potential to drive a bipedal system. This work will initially show further development of the system model and energylpower potential, before describing the construction of an anthropomorphic scale robot energised by 4 antagonistic pairs of muscles actuating the hip and knee. The ability of these actuator to provide power in striding and standing activities will be explored and -co-ordination actions needed to produce these effects will be considered. Finally the potential for the future developed of a new series of bipeds having linear actuation, low mass, fast response, compliant energy storage and simple construction will be discussed.
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ACTUATOR DESIGN [S-101
Pneumatic muscle actuators (PMA) are constructed as a two-layered cylinder, figure 1. The inner layer is made from rubber tubing, with two aluminium plugs (one with an air inletlexhaust pipe) forming the termination connectors to seal the ends of the tube. This acts as a pressurised containment unit. Around the rubber tubing there is a flexible sheathing formed from high strength interwoven (but not bonded) nylon fibres. The flexibility of this structure means that it can be stretched or compressed without damage, but at the same time this shell prevents the delicate rubber liner from over-inflating and rupturing. To prevent energy losses due to the initial expansion of the rubber liner, the rubber layer has a diameter greater than the at rest diameter of the flexible wall. The muscles are available in a number of sizes providing variable force potential and actuator displacement ranges which can be used for a variety of robotic applications. Rubber Seal Rubber Seal
/
Rubber laan LVr
\ .mn
MyIOU
Figure 1. Pneumatic Muscle Actuator Design
Figure 2. Trapezoidal Nature of Actuator 3.
MATHEMATICAL MODELS
Models have been derived from both system equation evaluation and MATLAB simulation. System Theoretical Model [lo-111 The factors critical in the determination of the driving force in any pneumatic system are the pressure difference and the area over which a distortion pressure is applied. With conventional cylinders only the piston face plate is free to move and only this area is critical. In the braided muscle the flexibility of the structure means the whole shell/liner interface forms the transfer medium for the actuation force. The braided structure of the external nylon shell means that the muscle may be considered as a series of 2 dimensional trapezoids. In this design, as the actuator stretches or compresses the interweave angle will change and
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indeed the whole surface area of the muscle varies. If the cylindrical muscle is 'opened', figure 2, the 2-dimensional nature is easily observed. If I is the length of one side of the trapezoid, the overall length of the muscle Lmus andl the diameter DmUs are: L,,,
= 2*A*l
*cosamus
=
h *cos amus
{ 1)
and Dmus = f *sin amUS
C2)
where A is the number of trapezoids in the x plane, h is helical fibre length (h= 2AI) and amUS is the interweave angle, f is the diametric distance parameter and equals 2BUn , and B is the number of trapezoids in the y plane (around the muscle body).From this, the surface area, Sa, at any interweave angle and the volume (which is inveirsely proportional to intemal pressure and therefore driving force) can be determined; Sa=%*Dmus*Lmus=n*(f *sin amus)*(h *cos
amus)
(3)
and
where K = (n/4)*f2*h. From this analysis the minimum pressure can be found to occur at an interweave angle of approx. 54.7O. At this minimum intemal pressure the actuator is in its most stable condition. Any changes from this state (either from elongation or compression) will cause an increase in pressure and induce a force to retum to the minimum energy state. An alternative approach to the force problem and the energy generated is to consider the work performed by the system. The input work (Win) is in the form of pneumatic energy and this is given by: dWin=P'dV (5) where P' is the is pressure difference between atmosphere and the supply pressure in the actuator and dV is the volume change. The output work (Wout) is produced by the shortening (or extension when starting from a compressed state) of the actuator with changes in volume. dWout = - FdLmUs {6} where F is the actuator output force and dL,, is the linear displacement. If the system is 'lossless' then energy conservation determines that the input work equals the output work and using the concept of virtual work gives:
F=-
verifying the above analysis. This basic theory although providing for the main forces associated with pneumatic muscle action does not account for all the factors involved in the use of these devices. Other factors that need to be considered include: i) End plate effects/shell distortion effects. The forces generated by the endplates effects, Fep ,will be
P'h2(3cos2 an,,) 4n2n
where n is the wrap number = f/ (nD,,, ). From this it will be seen that under ideal conditions the actuator force will be again zero at 54.7"
80 1
where Aepl is the area of the end-plate at the air inlet pipe and Aep2 is the area of the end-plate remote from the inlet. This force is negative as the end-plates always cause elongation and the convention with this analysis is that contractile forces are positive. ii) Fibre shell/liner friction During the contraction or elongation of the muscle the inner rubber and the shell and the fibres of the shell make contact. This introduces a loss which can be observed in the hysteresis of the actuator performance profiles. Chou [12] has estimated that this friction can be approximated by a constant loss term of +2.5N, positive for shortening and negative for lengthening. Ffr = f 2 S N (9) Additional losses are attributed to line leakage, frictional effects, rubber elasticity, expansion energy for the liner, valve losses and dead spaces.
MATLAB Model Estimation [S-IO] Although single muscle operation is a possible option for control, a dual muscle system was preferred as this allows both position control and compliance regulation through the opposal actions of the muscle pair. This in many ways replicates the action of human muscle and provides a more realistic feedback sensation. Experimental tests were carried out to obtain inputoutput data records. These records were used to estimate the parameters of a linear discrete model using off-line linear least squares methods. The model with two inputs and single output is given by: A(z-l) y(k) = z"
C(z-') uo(k) + z"
D(z-l) ul(k) + d + n(k) { 10)
where y denotes the position sensor reading (volts), uo and u1 represent the duty cycles for each muscle, n denotes unmeasurable noise and d is a constant which may be used to model effects of non-zero means in the data. The inputs were generated by adding pseudo-random variations of a specified amplitude to a fixed duty cycle. The fixed duty cycle was chosen to correspond to the mid-point of the available range [9, I 13. The off-line analysis, using MATLAB, indicated that a model with 5 parameters and a time delay of 3 units was adequate. The chosen model structure is given by:
Muscle sizes used range from 50cm in length to ~ ( 2 - 1= ) 1 + a1 2-1
+ a2 2-2 + a3 i3,
C ( i ' ) =CO,
For on-line identification the model parameters are estimated using recursive least squares with a variable forgetting factor 181.
This model has been used for adaptive control of a dexterous manipulator [8-1211. 4.
BIPEDAL MOTION - SYSTEM DESIGN
The biped constructed to test the actuation potential of the Pneumatic Muscles was designed to be anthropomorphic in scale although the complexity of the design was kept simple, figure 3. The mechanism consists of two jointed legs having free motion at the hips and knees with an inverted pendulum spinal column to assist with balance along the sagittal plane. At the hips the robot stands 1. lm high. The limbs are constructed from steel and aluminium and the total mass of the system including the pneumatic actuators (each of which weighs 50g) is less than 3kg. The actuation is provided by 4 antagonistic pairs of pneumatic muscles, 4 are connected between the pelvic girdle and the upper thigh to drive the 1% and Provide hip stabilisation during leg extensions and 4 to extendcontract the lower high.
Figure 3. Biped Construction with Muscle Attachment Points
8@~1@1p4Ba7 diam&x3pf app@ximat@APOmm for all
muscles.. The length of the muscles is dependent on the position on the biped. The artificial muscles have actions which cause thigh flexion-extension and calf flexionlextension. The quadriceps equivalent muscles (Knee extensors) are connected from a mounting point on the upper thigh directly to the front of the shin. During initial testing it was observed that the knee point leverage was vital to the motion of the lower leg especially when attempting to stand. With no knee the biped could only poorly extend the knee and standing was not possible at all. The knee was formed from a hinged steel bar which could adopt a variable position dependent on the position of the lower limb. The distance from the 'knee' to the centre of rotation was IOcm. The quadriceps have two major function in this bipedal design. The first is to straighten the lower leg providing a kick type motion. This is generally gravity assisted and does not require a large muscle. The second action was to provide the drive when lifting the robot from a seated position to vertical prior to walking. This was found to be a high stress operation and in fact this operation required more energy input than any other movement undertaken by this robot. For this reason the quadriceps form the largest muscles in the biped. The muscles also provide knee stabilisation during the walking phase. The knee flexor muscles were attached to the rear section of the frame from the area of the upper thigh to the calf on the lower leg. These muscles were used to bend the knee during a walking phase, single leg support and in performing a kicking action. The major output from these muscles is during the lift phase of the walk were the shin section is raised. As this has a relatively low mass smaller muscles could be used. In fact the knee flexor muscles are the least powerful in this system . The Hip flexor muscles are attached from the hip girdle to the lower thigh. These muscles are used to move the mass of the whole of the leg. Since the hip girdle is free to move, the hips must be locked before trying to move the leg. If this does not happen the hips will tip (upper body bends towards the floor) forward since the loading provided by the upper body (spine) is much less than the leg. Should the robot be required to lean forward clearly this can easily be achieved by energising the muscle without locking the hip. To prevent the hip girdle from moving forward it is locked in place by the Hip extensor muscles (hamstrings). These muscles are connected from the rear of the hip girdle to the rear of the lower thigh. They perform two primary actions. First they lock the
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5.2 Stride Phase
pelvis providing a base for motion of the opposite thigh/leg, ancl secondly they return the thigh to its normal position during a stride. The second motion is heavily gravilty assisted. The muscles are energised by 8 port Matrix valva operating in ii pulse width modulation structure. The Matrix valves have a pulsing frequency of up to 200Hz although 40Hz pulses were found to be adequate for this operation providing rapid yet smooth motion. It has previously been shown, [9], that controlled motion of PMAs using these valves and an adaptive controller can give position control of better than I % withi a bandwidth for antagonistic pairs of muscles of up to 5HZ. The inputs to the valves are generated from a PC (486/66) using an interrupt driven timer for each muscle. This was adequate for the testing of the pneumatic muscles as dynamic walking and balancing were not requirements of the present design.
From the upright position the robot was required to execute a stride. The actuator control stages in taking a stride are shown in table 1, where Y - muscle energised, N equals muscle not energised, R = right leg muscles, and L = left leg muscles. For small strides (
