Compliant Actuators - facts | AMARSi Projectamarsi-project.eu/system/files/D21.pdf · Fixed...

EU FP7

AMARSi

Adaptive Modular Architectures for Rich Motor Skills

ICT-248311

D 2.1

Marh 2011 (1 year)

Compliant ActuatorsAuthors: Matteo Laffranchi (IIT),Hide SUMIOKA (UniZu),Alexander

Sproewitz (EPFL),Dongming Gan (IIT),Nikos G. Tsagarakis (IIT)

Due date of deliverable 15st March 2011Actual submission date 6th April 2011Lead Partner IITRevision FinalDissemination level Public

This deliverable focuses on the design of compliant actuators. The state ofthe art of compliant actuation systems is firstly introduced by presenting someimplementations of the different functional principles. A comparison analysisof the features/capabilities of the presented designs motivate the introduction ofthe CompAct compliant actuation module. The CompAct is the main actuationunit developed for the compliant humanoid platform. After the introduction ofthe CompAct unit the design of the lower body of the compliant humanoid ispresented followed by the description of the two compliant quadruped robots cur-renlty under development within the AMARSi project.

2

Contents1 Design principles for compliant actuation systems 2

1.1 Fixed compliance actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Variable compliance actuators . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2.1 The series configuration . . . . . . . . . . . . . . . . . . . . . . . . 71.2.2 The antagonistic configuration . . . . . . . . . . . . . . . . . . . . . 10

2 The compliant humanoid platform 172.1 The mechanical design of the CompAct . . . . . . . . . . . . . . . . . . . . 182.2 Compliant module stiffness model . . . . . . . . . . . . . . . . . . . . . . . 192.3 Dynamics of the CompAct actuator . . . . . . . . . . . . . . . . . . . . . . 202.4 Selection of an appropriate stiffness value based on impact studies . . . . . . 21

2.4.1 Impact model and dynamics analysis . . . . . . . . . . . . . . . . . 222.4.2 Worst configuration analysis . . . . . . . . . . . . . . . . . . . . . . 232.4.3 Integrated dynamic model and the worst configurations of a 4-DOF

humanoid arm/leg robot . . . . . . . . . . . . . . . . . . . . . . . . 242.4.4 Stiffness design for the joints of the 4-DOF arm/leg robot based on the

four worst case configurations . . . . . . . . . . . . . . . . . . . . . 262.5 The design of the AMARSI Compliant Humanoid . . . . . . . . . . . . . . . 27

2.5.1 The Mechanics of the Lower Body . . . . . . . . . . . . . . . . . . . 28

3 The Oncilla robot 323.1 Summary of achievements for the quadruped robot . . . . . . . . . . . . . . 323.2 Functional principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.3 Mechanical implementation and integration into the robotic hardware . . . . 333.4 Actuator dimensioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.5 Joint stiffness range and energy storage capacity . . . . . . . . . . . . . . . . 343.6 Actuation power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.7 Simulation/experimental results demonstrating the performance of the com-

pliant platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4 The quadruped robot Kitty 374.1 Spinal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.1.1 Biological spinal structure . . . . . . . . . . . . . . . . . . . . . . . 374.1.2 Artificial spinal structure . . . . . . . . . . . . . . . . . . . . . . . . 39

4.2 Design of the quadruped robot . . . . . . . . . . . . . . . . . . . . . . . . . 424.2.1 Leg Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.2.2 Actuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.3 Experiments and results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.3.1 Experiments and results based on robot with fully actuated spine . . . 444.3.2 Experiments and results based on robot with partial actuated and pas-

sive spine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

1 Design principles for compliant actuation systems


The creation of mechatronic systems with bio-natural properties from the actuation point ofview has been the inspiration of the robotic community for many years. This replicationthough has failed so far mainly due to the complexity and inherent properties of the organicactuation/transmission system (muscle-tendon-joint-bone) which have prevented its emula-tion from the traditional engineered actuation paradigms. Looking on the diverse range ofactuation techniques it can be seen that the natural world appears to have developed a muchmore ubiquitous design, with the organic muscle providing power for animals ranging fromthe largest whales to microbes with adaptation to cope with environmental extremes. Yet, thepotential benefits, which can be gained in any mechanism with the incorporation of biologicalactuation concepts, are well known, the majority of today’s robots lack these characteris-tics. In these systems, key actuation technologies such as electric, pneumatic and hydraulichave been employed and effectively used in a variety of application domains, traditionallyin the form of a stiff position or torque controlled source units to provide accurate displace-ment/forces for precise trajectory tracking and task execution. Recently, with the introductionof new applications domains such as virtual/tele-presence, robot aided therapy/assistance andpersonal/entertainment robotics it has become increasingly clear that the traditional actuationapproach is not suitable for addressing the high requirements of these new application do-mains. The requirement for closer human-robot interaction have highlighted the need for in-herently safe robotic systems which can match the performance of biological systems in termsof ability to cope with unpredicted interaction with the human and/or environment enablingsafe interaction and efficient task execution. These are key developmental features of all newgeneration systems. In fact, these requirements are directly linked to the actuation system.The lack of such an actuator unit that can mimic some of the properties of the natural mus-cle, e.g. compliance is probably one of the most significant barriers that prevented so far thedevelopment of robotic systems exhibiting bio-natural functional behaviour and performance.The introduction of these new properties within robots has the potential of solving many of theproblems of conventional stiff robots but on the other hand places new challenging demandsas the development of novel actuation prototypes with high integration density and issues asthe control of the resulting actuation systems which inevitably results more complex due tothe introduced compliance - related dynamics.

In the growing fields of wearable robotics, rehabilitation robotics, prosthetics, and walkingrobots, fixed or variable compliance actuators are being designed and implemented becauseof their ability to minimize large forces due to shocks, to safely interact with the user, andtheir ability to store and release energy in passive elastic elements. Hence a device that canprovide compliance is needed to achieve these characteristics. From the engineering perspec-tive, the methods for the implementation of this concept in robots are essentially three: activecontrol, passive compliance and hybrid active/passive solutions. The first approach consists inthe implementation of control strategies e.g. impedance/admittance control which artificiallyreplicate a desired level of compliance. Compliance can be incorporated into the robot bymeans of a passive approach as well: in this case passive elastic elements e.g. springs areembodied into the structure. The first part of this deliverable will report on the design princi-ples adopted in the implementation of compliant actuators. This part is followed by a section

2


which compares the different designs to make the selection of a suitable approach to be usedin the development of the cCub humanoid which will be used within the AMARSi project.

1.1 Fixed compliance actuators

The ability of the stiff actuation units to interact with their surroundings can be increasedby means of the active approach explained previously, however the existence of delays at allstages of the software system make these conventionally stiff actuated systems incapable ofmanaging high-speed contact transients because of their limited bandwidth. To address thelatest a wide range of experimental novel compliant actuation systems have been developedduring the past fifteen years. Fixed compliance actuators represent the first attempts towardsthe development of compliant actuation systems. These actuators incorporate a fixed stiffnesspassive element within their stucture, usually placed between the rigid actuator(s) and theload. Fixed compliance actuators can be implemented following two main approaches, i.e.antaongistic or series design. A conceptual schematic of the latter implementation is shown inFig. 1.1

Figure 1.1: Conceptual schematic of a Series Elastic Actuator

One particular type of system with inherent fixed passive compliance is the Series Elastic Ac-tuator family, [6]. These actuators are made by the series combination ”motor-gearbox-elasticelement-link” and hence employ only one actuator and one elastic element per degree of free-dom. A conceptual schematic of a SEA is presented in Fig. 1.1. In the configurations shownin 1.1, the effort needed to drive the link is delivered by the motor-gearbox group, while θinis the angle of the input pulley of the compliant element and the output angle is θout. Thefixed stiffness implementation has two control variables which are the input-output angularpositions of the compliant element θin and θout, Fig. 1.1. The solution proposed in [6] in-cluded a DC motor coupled to a planetary gearbox and a fixed stiffness torsion spring. Thissolution has been implemented also for the linear case and has been powered by hydraulicactuators as well, [39]. Given the low impedance (attenuated by means of the series com-pliance) and low friction, SEAs can achieve high fidelity force control and are hence suitedfor robots operating in unstructured environment. The delicate and expensive loadcells/torquesensors typical of force/torque controlled robots (see e.g. [23]) may ultimately induce chatterin force control due to their high stiffness. These sensors are replaced with compliant elastic

3


elements (e.g. springs, which are robust, stable and inexpensive) in Series Elastic Actuators.The force/torque delivered by the actuator can be estimated by means of the Hooke’s law, 17,18 and the measurement of the compression of the compliant element:

Fa = klx (1)

in case of linear SEAs, where F is the force applied by the actuator, kl and x are the stiffnessand compression of the linear compliant element, respectively. Similarly as for the lineardesign, in case of rotary implementations:

Ta = ktθS (2)

where T is the torque delivered by the actuator while kt and θS are the stiffness and compres-sion of the rotary compliant element, respectively. From the mechanical perspective linear ortorsion springs can implement the series elasticity (see e.g. the electric or hydraulic SEAs,[39], [6]) however rubber elements held between alternating teeth have been used as well, 1.2,[41]. The compliant element deflection state can be used to obtain precision in the estimation

Figure 1.2: Left, conceptual schematic and right picture of the elastic element which uses rubber balls[41]

of the torque or force in case of rotary or linear SEAs. The estimated effort variable can bethen feed back to implement force/torque control, Fig. 1.3. The signal Fdesired is used asreference for the feedforward and the feedback controllers FF and FB. The force Floadis estimated from the deflection of the spring element and is compared with the reference inorder to return an error Ferror. This latter signal, together with the measured position xloadand the reference Fdesired is used to generate an appropriate control signal for the electricalmotor. The main disadvantage of the preset stiffness of SEAs can be overcome by means ofthe application of admittance/impedance control strategies, [17, 38, 28]. Fixed complianceactuators can be used also in rehabilitation robotics as in [9]. In this work a prosthetic ankledevice has been developed using a SEA which employs also parallel compliance. The seriescompliance is used to protect the motor-gearbox group from shock loads generated during thefoot strike. The parallel elasticity is instead engaged only when the ankle is dorsiflexed, in-creasing the torque control bandwidth in order to allow the prosthesis controller to capture thetorque-velocity behaviour of the human ankle in walking. The same performance improve-ments brought by Series Elastic Actuators (e.g. improved safety in human-robot interaction,

4


Figure 1.3: Force/Torque control of a SEA, [40]

Figure 1.4: (a) Conceptual schematic and (b) model of the ankle prosthesis [9]

ability to absorb the shocks, enhancement of the force/torque control performance) are validalso for fixed stiffness antagonistic setups. In fact, an antagonistic joint is made of two serieselastic actuators placed antagonistically which deliver the agonist/antagonist forces F1, F2 tothe joint as shown in Fig. 1.5. The two spring elements have fixed stiffness k. The stiffness ofthe output pulley can be computed to be, [30]:

∂T

∂θ= 2r2k (3)

where r is the constant radius of the pulley. Equation 12 shows that the equivalent joint stiff-

5


Figure 1.5: Conceptual schematic of the antagonistic actuator setup

Figure 1.6: Legged biologically-inspired compliant robot

ness is constant for a constant stiffness of the spring components. This solution has been usedin legged robots as in [41] where series elastic actuators were used in series with tendons actu-ating each joint, Fig. 1.6. This bio-inspired design however has some problems as calibrationissues due to the pulleys eccentricity as well as too much distal mass, [41].

1.2 Variable compliance actuators

Variable compliance actuators are actuators which are capable of passively regulating theirphysical compliance. Obvious advantages that a variable stiffness implementations offer whencompared with the fixed passive compliance units are the ability to regulate both stiffnessand position and the wide range of stiffness and energy storage capability. The advantagesgained by this capability are clearly shown in mammals: muscles and tendons change theirstiffness as a function of the motion/task they have to perform. Arm muscles assume a stiffconfiguration when the arm has to perform an accurate task, while they are compliant whenthey are performing the ”loading” phase of a throw. Similarly, if we analyze jumping we seethat leg muscles are compliant during the ”loading” phase of the jump or during the landing

6


phase where they absorb the shock [31], while during the ”pushing” phase, they are stiff.There are several reasons for this variation in stiffness but among others the most pressing isthe exploitation of the elastic energy stored within the muscles and tendons [32]. This enablesvariable compliance actuators to achieve performance that is not possible with a conventionalstiff robotic system as Wolf et al showed when comparing a rigid joint and a compliant jointin a SDOF setup during a throw task [33]. There work showed that there is a clear differencebetween the velocities of the links and the throw distances obtained in the two cases. Thismotivates researchers to implement variable compliance into the actuation systems using avariety of different designs, however variable compliance actuators can be categorized intotwo main groups. One is formed by actuators which present variable compliance placed inseries between the actuator and the load while the antagonistically-actuated joints form thesecond group.

1.2.1 The series configuration

The main advantage of this type of approach is that two different actuators are used to set theequilibrium position of the joint and the stiffness independently. Some examples of variablestiffness actuators implemented with the series approach are presented next.

The Actuators with Adjustable Stiffness (AwAS and AwAS-II)

AwAS and AwAS-II are series type of variable stiffness actuators which can change the posi-tion and stiffness independently. In both actuators one big motor changes the position and asmall motor tunes the stiffness. Adjusting the stiffness in both actuators is done through a lever

Figure 1.7: Physical model of AwAS and AwAS-II

mechanism (Fig.1.7). A lever has three principal points; the pivot: the point around which thelever can rotates, the spring point: the point at which springs are located and the force point:

7


the point at which the force is applying to the lever [13]. In AwAS, [10, 14, 11] the force andpivot point are kept fixed and to change the stiffness the spring point is changing.The stiffnessin this case can be defined as:

K = 2Ksr2(2 cos2 φ− 1) (4)

where Ks, r and φ represent stiffness of the springs, the distance between the spring pointand the pivot (which is adjustable) and the angular deflection, respectively. Using this conceptstiffness can be achieved in a good range since it depends on the square of the arm r. Therange of stiffness depends on the stiffness of the springs and length of the lever. However inAwAS-II,[13, 12] force and spring points are kept fixed but instead the pivot point is changing.Using the lever allows adjusting the stiffness energitically efficient since in the lever to changeeach of principal points, the displacement needed to change the stiffness is perpendicular tothe force generated by the springs. Therefore the stiffness motor doesn’t need to directlycounteract against spring’s forces. The stiffness in this case can be defined as:

K = 2Ksα2(L1 + L2)2 cosφ (5)

where L1 represents the distance between the pivot and the springs and L2 is the distancebetween the pivot and the force. α is the ratio (adjustable) which is L1

L2.Using this mechanism

the stiffness can be achieved in the largest possible range from zero to infinite sice it dependson the ratio. The ratio becomes zero when the pivot reaches the spring point and it becomesinfinitive when the pivot reaches the force point. This range does not depend on the stiffnessof the springs and lever’s length. Therefore shorter lever and softer springs can be used in thismechansim which leads to have a lighter and more compact setup compare to the mechansimapplied to AwAS.

The Jack Spring actuator

A linear series-type variable stiffness actuator is the Jack Spring, [15]. In this solution, stiff-ness is varied by changing the number of active coils of the series spring. The adjustment ofthe stiffness is done by rotating the spring about the coil axis. This rotation is transformed ina linear motion of the spring along its axis thanks to the geometry of the shaft on which thespring is mounted. In fact, this shaft is machined with the same coil geometry of the springand the inside/outside motion of the spring (achieved by screwing/unscrewing the spring onits shaft) changes the effective stiffness of the actuator by varying the active spring coils, 1.8,accordingly with the following formula which describes a coil spring stiffness:

K =

(Gd4

8D3na

)(6)

In 17 G is the material shear modulus, d is the wire diameter, D is the coil diameter, andfinally na is the number of active coils. The Jack Spring actuator principle works on this lastparameter to vary the stiffness of the overall actuator. In this concept, one motor is used toadjust the equilibrium position of the actuator and a second motor is used to adjust the stiffness.

8


Figure 1.8: Active and inactive coil region in the Jack Spring Actuator

MACCEPA

Van Ham et al, [16], developed the MACCEPA actuator. Similarly as in the designs presentedpreviously two independent actuators, M and m are used to set the equilibrium position andthe apparent stiffness of the joint, respectively. Fig. 1.9 presents a kinematics scheme of theMACCEPA mechanism, showing three different bodies pivoting around a central axis a. Thepart of length B can rotate about the axis a and has a linear tension spring attached to oneextreme. The other end of the spring is attached to a point b which is fixed on the body shownon the right by means of a cable. When the angle between the lever arm and the right body α is

Figure 1.9: Working principle of the MACCEPA

different from zero the force generated by the elongated spring generates a torque between theleft and the right bodies which tends to align the body shown on the right with the lever armof length B. When the angle α is null, the lever arm is aligned with the spring and no torquewill be generated. The smaller motor m is used to pretension the tension spring at point b bypulling the cable connected to the spring. The length of the tensioned spring when the angleα is null is defined as P . The relationship between the compression angle α and the torque Tcan be calculated to be:

T = kBC sin(α)

(1 +

P − L√B2 + C2 − 2BC cos(α)

)(7)

9


where k is the spring stiffness and L is the natural length of the spring. Equation 18 showsthat the relationship between the compression angle and the delivered torque depends on thespring preload P − L meaning that the overall joint stiffness can be regulated acting on thepreload of the spring using the motor m. The angle ϕ imposed by the main actuator sets theequilibrium position of the joint.

1.2.2 The antagonistic configuration

Antagonistically-actuated joints employ two compliant elements to provide power to the joint.This design is biologically-inspired, since mammalian anatomy follows the same concept,i.e. a joint actuated by two muscles arranged in an antagonistic manner. The muscle-tendoncooperation gives the driven link (arm, leg etc) a controllable and variable compliance. Inaddition to biological muscle this type of antagonistic compliance controlled can be achievedusing both conventional two motor electric drive designs and other more biologically inspiredforms such pneumatic Muscle Actuators (pMA). In the latter case compliance is an inherentcharacteristic of the actuator, while for an electrical design compliant elements (generallysprings) have to be embodied into the system. From the engineering perspective, this conceptcan be implemented using three different layouts which are shown in Fig. 1.10. In literature,these three basic setups are referres as ’simple’, ’Cross coupled’, and ’Bidirectional’, see1.10. A simple antagonistically-actuated joint uses two driving elements. The stiffness of the

Figure 1.10: The Simple, Cross-coupled and Bi-directional antagonist setups

joint and the angular displacement of the driven link are set by means of a combination ofthe actuation inputs q1, q2 (see Fig. 1.11). By co-contraction of these actuators preloadingand, thus, tuning of the stiffness is achieved, while the rotation of the joint is obtained bythe antagonistic motion of the drives. An example of this simple antagonistic layout isrepresented by a joint actuated by pneumatic muscles, Fig. 1.12. In this layout, the nonlinearforce/elongation relationship can be exploited to implement the variability of the joint stiffnesslevel by varying the pneumatic pressure in the bladders. When McKibben artificial muscles areemployed, the following equation can be used to model the relationship between the generatedforce F , the actuator elongation L and the pressure in the tube P .

F = k(L2 − L2

min

)P (8)

where k and Lmin are constant parameters depending on constructive details.

The same ’simple’ antagonistic actuation approach could be implemented using electrical ac-tuation systems. Differently from the system presented previously, where pneumatic muscles

10


Figure 1.11: The Simple, Cross-coupled and Bi-directional antagonist setups

Figure 1.12: Simple antagonistic setup using pneumatic muscles

are employed, in this case compliance is not an inherent property of the actuator and thereforecompliant passive elements (usually springs) have to be incorporated between the actuatorsand the load. This is the case of the actuator presented in [34].

Migliore’s Actuator

This actuator uses two conventional electrical drives connected in an antagonistic manner tothe output joint through nonlinear springs. A positive angle α of the agonist servo motorprovides positive rotation of the angle θ of the output drive, while the antagonist actuator setsan angle β in opposition to the output joint angle, Fig. 1.13. Using linear springs in theconfiguration shown in 1.13, the output joint stiffness will be:

Slinear = R2J(k1 + k2) (9)

11


Figure 1.13: Conceptual schematic of the actuator presented in [34]

Figure 1.14: Mechanism to implement the stiffness nonlinearity, [34]

where RJ is the radius of the output pulley, k1 and k2 are the stiffness of the springs of theagonist and antagonist servos. Equation 20 shows that the output joint stiffness depends onlyon the constructive parameters of the joint and on the springs stiffness (i.e. constant). Thevariation of stiffness of the spring components can be set to be linearly related with the co-contraction by using elastic elements with quadratic force-elongation relationship as follows:

F (x) = a(x− x0)2 + b(x− x0) + c (10)

where F is the force applied by the motors, x is the elongation of the spring component, x0 isthe natural length of the spring and a, b, c are constants. Using such spring components, thestiffness of the output joint, S will be:

S = 2aRSR2J(α+ β) + 2bR2

J (11)

where RS is the radius of the driving pulleys. In this case stiffness can be varied by means ofthe co-contraction of the drives (given by the sum of α and β), with constant offset 2bR2

J . Onthe other hand, the displacement of output joint is achieved by means of the agonistic motionof the motors. Equation 21 is implemented mechanically by means of a quadratic profile ofthe part named ’Frame’ of the nonlinear spring component schematically shown in Fig. 1.14.The assembly shown in Fig. 1.14 replaces the conventional extension springs shown in the

12


antagonistic setup of Fig. 1.13 therefore permitting the regulation of the joint stiffness.

Variable Stiffness Actuator (VSA)

The VSA is a Variable Stiffness Actuator which implements the so-called ’cross-coupled’arrangement, 1.10. Referring to Fig. 1.15 the VSA consists of three pulleys (2, 3, 4) connectedby means of a timing belt (1). Pulleys 2 and 3 are actuated by means of position-controlledbackdrivable DC motors, while the output pulley (4) is connected to the link. The output jointstiffness can be computed to be:

σ = 2KR

(hm,1 − hm,1

hm,1+h2,m − h2,m

h2,m

)− 2KR

(hm,1Lm,1

4h3m,1+h2,mL2,m

4h32,m

)(12)

where K is the linear spring stiffness, R is the radius of the pulleys 2, 3 and 4, hm,1, hm,1and h2,m, h2,m are the natural and active lengths of springs 5 and 7. Lm,1 and L2,m are thelengths of the belt between the pulley pairs 2-4 and 3-4. This means that stiffness can bechanged by acting on the active length of the springs and on the belt length. In detail, bymeans of high/low co-contraction, high/low compression of the springs 2 and 4 (Fig. 1.15)will generate high/low apparent output joint stiffness. In practice, the antagonist motion

Figure 1.15: CAD view and nomenclature of the VSA [19]

of the drives varies changes the apparent angle between the spring axis and the belt and thiscreates the nonlinear stiffness/compression relationship whic permits the stiffness adjustment.Agonist motion of the drives only generate displacements of the output shaft.

Actuator with Mechanically Adjustable Series Compliance (AMASC)

Another antagonistic-based design is the Actuator with Mechanically Adjustable Series Com-pliance (AMASC) presented in [20]. The main advantage proposed by this design is that,similarly as for serial setups and differntly from conventional antagonistic setups, it enablesan independent control of position and stiffness. Figure 1.17 shows a simplified conceptual

13


Figure 1.16: Conceptual schematic showing one of the antagonistic pairs [19]

Figure 1.17: Simplified conceptual schematic of the AMASC [20]

schematic of the AMASC. The rotation of the driving pulley on the left, J1, sets the equi-librium position of the output link J2, while the distance between the two pulleys x3 setsthe pretension of the nonlinear spring elements and is imposed by a second actuator. Thenonlinear function between the elongation x3 and the generated force is in this case quadratic:

Fz(z) = kz2 (13)

where Fz(z) is the generated force and is function of the spring component elongation z. zcan be set by appropriate tuning of the degree of freedom x3. The behaviour of this actuator istherefore similar to that of [34] presented previously: two nonlinear quadratic spring compo-nents arranged antagonistically are employed to create the variability of stiffness of the outputjoint. The nonlinear relationship between elongation and generated force is implemented in theAMASC by means of the series of the springs with a spiral pulley - based mechanism (1.18).The gearing of the spiral pulley-based mechanism varies proportionally with the springs de-flection to create the desired quadratic relationship, 24. The two spring function when placedin direct opposition, the single effective spring force Feff can be computed by substitutingthe (x3 − ∆x) and (x3 + ∆x) for z.

Feff (x3,∆x) = Fz((x3 + ∆x)) − Fz((x3 − ∆x)) (14)

14


Figure 1.18: Overall conceptual schematic of the AMASC [20]

where x3 is the pretension of the two nonlinear springs and ∆x is the deflection from their restposition. By manipulating 24 and 9 the effective force Feff can be computed to be:

Feff = 4Kx3(∆x) (15)

Equation 10 shows that the stiffness of the resulting system can be changed by adjusting thepretension x3.

Variable Stiffness Actuator - II (VSA-II)

The VSA - II, [21], is an antagonistic actuator which uses the bi-directional actuation prin-ciple (refer to Fig. 1.10) and can be represented in the schematic of Fig. 1.19. The VSA-II

Figure 1.19: Conceptual schematic of the VSA-II, [21]

shows several improvements with respect to the previous VSA-I, [19] as for instance a 4-barmechanism which shows higher load capacity and robustness. This mechanism implements avariable transmission system used to obtain a nonlinear relationship between input and output

15


torque/displacements. Using a linear spring on the input, the relationship between deflectionand torque on the output shaft can be made nonlinear, 1.20. The link OA is actuated by a

Figure 1.20: The four bar transmission mechanism of the VSA-II, [21]

motor at O. The torsion spring of stiffness k is linear, however the stiffness at O is nonlinearwith angles β and θ and is described by the following relationship, [21]:

σ(θ) =1

4k

R

L cos θ2√1 −

(RL sin θ

2

)2 − 1

2

+

RL

(R2

L − 1)β sin θ

2[1 −

(RL sin θ

2

)2] 32

(16)

16

2 The compliant humanoid platform


The actuation systems presented previously can be classified in two main categories: fixedand variable compliance actuation systems. However, each of these two groups can be im-plemented following antagonistic or series designs meaning that a total of four families canbe used to classify a compliant actuation system. Obvious advantages that variable stiffnessimplementations offer when compared with the fixed passive compliance units are the abilityto regulate stiffness and position independently and the wide range of stiffness and energystorage capability. This aspect is particularly interesting when low energy consumption levelshave to be reached or when the arm has to be safe and performant at the same time [30]. Thisresult can be explained by a biologically-inspired motivation which means that muscles andtendons change their stiffness as a function of the motion/task they have to perform. Armmuscles assume a stiff configuration when the arm has to perform an accurate task, whilethey are compliant when they are performing the ”loading” phase of a throw. Similarly, ifwe analyze jumping we see that leg muscles are compliant during the ”loading” phase of thejump or during the landing phase where they absorb the shock [31], while during the ”push-ing” phase, they are stiff. There are several reasons for this variation in stiffness but amongthe most pressing is the exploitation of the elastic energy stored within the muscles and ten-dons [32]. This enables compliant actuators to achieve performance that is not possible witha conventional stiff robotic system as Wolf et al showed when comparing a rigid joint anda compliant joint in a SDOF setup during a throw task [33]. These work showed that thereis a clear difference between the velocities of the links and the throw distances obtained inthe two cases. Clearly the introduction of compliance can have very significant effects on theperformance of an actuation system relative to the classical stiff design. On the other hand themechanical complexity, size, weight, cost and integration are still open issues in the variablepassive compliance realizations. As a result their application to multi degree of freedom orsmall scale robotic machines still remains a challenging task. At these matters the fixed com-pliance actuator family clearly demonstrates an advantage when compared with the variablestiffness implementations. The compactness and simplicity of the design can be further in-creased by means of the use of a series approach. In fact, antagonistic designs require at leasttwo actuators and and two compliant elements per degree of freedom, differently from serieselastic actuator which requires one actuator and one compliant joint.

In fixed stiffness designs (as e.g. SEA) the degree of exploitation of the benefits of compliance(especially energy efficiency and performance as the achievement of high mechanical powerpeaks) is limited when compared to variable compliance implementations. However, in caseof fixed compliance actuation human and robot safety requirements can still be guaranteed ifthe joint stiffness is set to an appropriate value. The selection of optimum stiffness values canbe based on the results from analyses of certain critical robot collision scenarios. In addition,its main disadvantage of the preset passive mechanical compliance can be at some degreeminimized by combining the unit with an active stiffness control. This motivates the use of acompact rotary SEA module for the development of the humanoid robot cCub which will beused in this project.

In the next section the design of a new modular and compact rotary series elastic actuator

17


(CompAct) which is used in the cCub humanoid is presented. The actuator shows particu-lar improvements over the existing implementations based on ball-screw/die spring, torsionsprings or extension springs/cable assemblies. The compact design of the actuator is due tothe novel compliant module mechanical implementation. Despite its small size, the actuatorstill retains high level of performance and it is a potential solution for small scale mutli-degreeof freedom systems when compliance is also desired.

2.1 The mechanical design of the CompAct

The mechanical realization of soft actuation unit is based on the concept of the serial elasticactuator, but particular attention has been paid to satisfy the dimensional and weight require-ments of the cCub robot. The high density of the integration is due to the novel mechanicalcompliant module. To minimize dimensions while achieving high levels of rotary stiffness amechanical arrangement, involving a three spoke output component, an input circular pulleyand six linear springs, has been designed and fabricated. The circular component is the inputof the compliant module and is fixed to the output of the reduction drive. The three spokeelement rotates on bearings with respect to the circular base and it is coupled to it by means ofthe six springs which are arranged as shown in Fig. 2.21. The three spoke component finallyforms the output of the compliant module and the mounting base of the output link.

Figure 2.21: The prototype of the CompAct series elastic actuator

The six linear springs when inserted in the arrangement shown in Figure 1 experience a pre-contraction equal to half of the maximum acceptable deflection. Deflections larger than themaximum allowable are not permitted by mean of mechanical pin based locks. Two 12bit

18


absolute position sensors have been integrated within the actuation group measuring respec-tively the mechanical angle of the motor after the reduction drive and the deflection angle ofthe compliant module. The two sensors not only allow the monitoring of the link positionbut also allow the evaluation of the joint torque. Because of the compliance introduced it ispossible to use the sensor measuring the compliant module deflection to estimate the torque.

2.2 Compliant module stiffness model

In this section the stiffness model of the three spoke spring arrangement is presented. Thedeflection of the complaint module results in the generation of torques due to the compressionof the spring elements along their main axis, Figure 2. Considering one of the antagonist linearspring pairs in Figure 3, the axial forces generated by each of the springs when the compliantthree spoke module is deflected from the equilibrium position by an angle of θS is given by:

F1 = KA(xp + x(θS)), F2 = KA(xp − x(θS)) (17)

where xp is the spring pre-contraction and x(θS) = Rsin(θS) is the resulted deflection ofthe two springs along their main axis, KA is the spring axial stiffness and R the length of thespoke arm. The combined axial force applied in any of the three spokes is therefore:

Figure 2.22: Compression of the spring as a result of the module deflection

F = F1 − F2 = 2KARsin(θS) (18)

The corresponding torque generated at the joint because of the axial forces of one antagonisticpair of springs is equal to:

T = FRcos(θS) = 2KAR2sin(θS)cos(θS) (19)

So far we consider that the axial force of the spring is concentrated at one point. Consideringthat the spring has an external radius of rS , it can be seen in Fig. 2.22 that the axial com-pression of the spring is not equal for the whole surface area being in contact with the spoke.

19


Figure 2.23: The three spoke spring coupling arrangement

The areas that are further from the centre of rotation are subject to larger deflections creatinghigher forces. As a result the torque generated by the axial deflection of the antagonistic pairof springs can be computed by

T =1

2rS

∫ R+rS

R−rS2KAR

2sin(θS)cos(θS)dR = 2KA

(R2 +

r2S3

)sin(θS)cos(θS) (20)

Thus, the combined torque at the joint considering the axial forces from all three pairs is

Ttotal = 3T = 6KA

(R2 +

r2S3

)sin(θS)cos(θS) (21)

By directly differentiating the torque equation the rotary stiffness of the three spoke modulewhich is due to the axial deflection of the springs can be obtained as

KS =∂Ttotal∂θS

= 6KA

(R2 +

r2S3

)(2cos(θ2S − 1)

)(22)

Figure 2.24 shows the theoretical stiffness of the module within the range of the deflectionangle, for the first prototype module with the following parameters: KA = 62kN/m,R =20.5mm, rS = 6.3mm

2.3 Dynamics of the CompAct actuator

The actuator consists of three main components, a typical brushless DC motor, a harmonicreduction drive and the rotary compliant module introduced in the previous section. Thesethree components can be represented by the mechanical model shown in Figure 5 below. Themodel is composed of the rotary inertia and viscous damping of the motor JM , DM , the geardrive with the reduction ratio of N , the elastic module with an equivalent spring constant ofKS , 22, the output link inertia and axial damping coefficient JL, DL. In addition, θM , θ0are the motor mechanical angles before and after the reduction drive, θL is the angle of theoutput link and θS is the rotary defection of the elastic module with respect to θ0 such thatθL = θ0 + θS . Finally, τM is the torque provided by the actuator while τ0 is the input torque

20


Figure 2.24: The stiffness profile of the compliant module

Figure 2.25: CompAct SEA mechanical model diagram

of the elastic element and τE is the torque imposed to the system by the load and/or theenvironment. The above system can be described by the following set of dynamic equations:(

JMN2s2 +DMN

2s+KS

)θ0 −KSθL = τ0 (23)(

JLs2 +DLs+KS

)θL −KSθ0 = τE (24)

2.4 Selection of an appropriate stiffness value based on impactstudies

The main issue in safety and performance is the stiffness level selection and location along thekinematic chain of the robot. This section presents a study of choosing the appropriate stiffness

21


levels for the new compliant humanoid robot by analyzing the dynamic system during animpact scenario aiming to ensure that the responded joint torques remain under the maximumtorque capabilities of the actuators. The stiffness selection approach in this study was to findthe worst robot configuration for each joint in the robot, in which if an accidental collisionoccurs at the robot end-effector the joint will experience the highest impact torque. If thegenerated torque is safe for the joints in this worst configuration, it will be safe for all otherconfigurations when the robot joint velocities or the end-effector velocity are within a certainvalue used for the searching of the worst impact configuration.

2.4.1 Impact model and dynamics analysis

The compliant actuator can be simply modeled as in Fig. 2, by introducing a torsion compli-ance between the actuator and the link with equivalent stiffness k. In this way the inertia of theactuator is decoupled from the inertia of the link, leading to a reduced responding torque underimpacts protecting the actuator from potential peak torques dangers. Assuming that there are

Figure 2.26: The compliant joint

m compliant joints in a serial robot, based on the Euler-Lagrange formulation, the dynamicsof the robot can be described by the following equations:

M(q)q̈ + C(q, q̇)q̇ +G(q) = τl (25)

Mm¨theta+

τlλ

= τm (26)

τl = K

(θ

λ− q

)(27)

where q and θ are the vectors of links’ joint angles and motors’ joint angles respectively,M(q) and Mm are the link and motor inertia matrices respectively, C(q, q̇) are the matricesof Coriolis and centrifugal terms, G(q) is the vector of gravitational torques, τl is the vectorof torques acting on the links, τm is the vector of motor torques, λ is the reducer ratio andK is the diagonal matrix of joints’ stiffness coefficients. When the serial robot collides withanother body, the magnitude of impact force can be computed as:

Fc =−(1 + e)vTn

nT [C]n(28)

22


where [C] = J [M(q)]−1JT , [M(q)]−1 is the inverse Cartesian inertia at the end effector, n isthe unit normal vector to the plane of impact of the two bodies. v = vnv is the end-effectorvelocity of the robot when impacting with magnitude v and unit direction nv . 0 < e < 1 isthe restitution coefficient denoting the type of collision (0 for purely plastic collision and 1 forpure elastic one), with e = 1 in this study. Finally, J represents the Jacobian matrix of theserial robot. A general impact occurs in a short period in which the impact force increases firstand then reduces in the restitution. Here Fc is an equivalent force. The impact is consideredto be very fast, thus, configurations of the links are considered to be the same with that beforethe impact. The impact force can be transferred into the generalized torques exerted on thejoints by:

τc = JTnFC (29)

τc is called impact torque in this paper. Thus, the impact force is transferred to the joint torquesin the function of the robot configuration and impact force direction.

2.4.2 Worst configuration analysis

The main weak part of the actuator is the harmonic drive reducer. Thus the aim is to derivethe joint torques on the harmonic drive which will be:

τ = τl + τc (30)

The worst configuration identification for each joint is to find a configuration in which equa-tion 30 returns the highest torque value for the joint. This becomes an optimization problemwhere the goal is to find the worst configuration for each joint (in which 30 is maximized) bysearching the configuration space q(q1, q2, ..., qm), the normal n of the impact force and thevelocity direction nv of the robot tip based on specified 30 as:

max τi(q, nv, n)qimin ≤ qi ≤ qimax i = 1, 2, ...,m

αvjmin ≤ αvj ≤ αvjmax j = 1, or1, 2βjmin ≤ βj ≤ βjmax

(31)

where αvj and βj are angles representing directions of the end-effector velocity and impactforce, for planar robot j = 1, for spatial robot j = 1, 2. Other parameters are known. Thus,m worst configurations can be identified as:

τw1(q1, nv1, n1)τw2(q2, nv2, n2)

...τwm(qm, nvm, nm)

(32)

where τwi stands for the worst configuration qi(qi1, qi2, ..., qim) torque, which is the highestin the whole workspace for joint i with the end-effector velocity in direction nvi and impactforce in direction ni based on the same input parameters. The worst configuration for eachjoint in 32 can be taken as a configuration in which the joint needs to withstand the highest

23


torque in order to resist the external force Fc while trying also to keep the motion of therobot. From the above analysis, it can be seen that only equation 25 is used to get equation31 while equations 26 and 27 which represent the actuator compliant model are not affectingthe worst configuration searching procedure described above. Having identified the worstconfiguration for each joint the actuator compliant joint is then incorporated and simulationstudies (using ADAMS) are performed in the overall system considering both the robot rigidbody and actuator dynamics described by equations 25, 26 and 27.

2.4.3 Integrated dynamic model and the worst configurations of a 4-DOFhumanoid arm/leg robot

In this section the procedures described above are applied for the design of a 4-DOF compliantrobot which can represent the arm or the leg of the compliant humanoid robot. The robotconsists of a 3-DOF joint (shoulder or hip) joint and 1-DOF (elbow or knee) joint as shown in2.27. The three rotational axes(z1, z2, z3) at the shoulder (hip) are intersecting at one point inthe shoulder (hip). The shoulder (hip) is connected with upper arm (leg) followed by anotherrotational joint (z4) which represents the elbow joint, and the forearm (calf) as the end-effector.The wrist (ankle) is not considered in this study. A frame coordinate system o0x0y0z0 is set atthe intersecting point at the shoulder (hip) with z0 collinear with the direction of joint z1 andy0 to the opposite direction of gravity as in 2.27. v is the velocity of the end-effector and F isthe impact force applied at the end-effector. the dynamic equations integrated with the impact

Figure 2.27: Kinematic model of the 4-DOF robot

model in 31 can be specified in terms of the searching parameters and the worst configurationscan be identified by following equations:

max τi(q1, q2, q3, q4, α1, α2, β1, β2)−7π9 ≤ q1 ≤ 7π9−5π9 ≤ q2 ≤ 7π9−π

2 ≤ q3 ≤ π2 i = 1, 2, 3, 4

−π2 ≤ q4 ≤ 5 π

180 ≤ α1, β1 ≤ π

0 ≤ α2, β2 ≤ 2πn.nv < 0

(33)

24


where qi(i = 1, 2, 3, 4) are the joint angles, α1 and α2 represent the direction of end-effectorvelocity, and β1 and β2 describe the direction of the impact force. Here α1 and β1 are theangles between the directions and axis z0, α2 and β2 are the angles between the projectionof the directions on the x0o0y0 plane and axis x0. The direction of the impact force shouldbe within the opposite hemisphere of the velocity, indicating that the impact force should nothave positive element on the end-effector velocity direction and giving a constraint as n.nvbeing negative. The input parameters of the 4-DOF robot are listed in Table 4. The robot

Table 1: Input parameters of the 4-DOF robot

Item Unit Mass [kg] Length [m] Acceleration [rad/s2]Upper limb 2 0.2 N/ALower limb 2 0.2 N/A

Joint 1 N/A N/A 1Joint 2 N/A N/A 2Joint 3 N/A N/A 0.2Joint 4 N/A N/A 1

masses and link lengths and the joint angle ranges are taken from the iCub robot [42]. Onemore important parameter is the magnitude of the end-effector velocity which is set as 1.5 m/sand the joint velocities are obtained by inverse calculating using the robot Jacobian. Thus,basing on equation 33 and the input parameters in 4 with the end-effector velocity as 1.5 m/s,the worst configurations of all four joints can be obtained as

τw1(0.043, 0.58, 0.72,−1.08, 1.97, 0.66, 1.17, 0.65)τw2(1.65,−0.88, 1.17,−1.13, 1.95, 6.05, 2.06, 1.17)τw3(0.72, 2.26, 1.04,−0.34, 2.04, 0.68, 1.37, 1.25)

τw4(0.28,−0.011, 1.39,−0.65, 1.71, 3.37, 2.92, 1.32)

(34)

where the unit of measure of the angles is radians. The worst case configurations are shown inFig. 2.28 in which the red line represents the direction of the impact force and the blue one isthe direction of the end-effector velocity. Thus, in worst configuration for joint 1 in Fig. 2.28,joint 1 needs to support the highest joint torque to support the end-effector velocity of 1.5m/sin the direction shown by the blue line while an impact occurs in the direction of the red line.This is the same for the other three joints in the other figures in Fig. 2.28. Similar to the 2-DOFcase, in the worst configuration searching, another constraint is added as that the maximumjoint angle velocity is no more than 10 rad/s. This is also used to avoid extreme values of jointangle velocities and joint torques in singular configurations when inversely calculating jointangle velocities based on the given end-effector velocity. In Tab. 4, it can be seen that some ofthe obtained joint angle velocities reach 10rad/s, indicating that the obtained configurations inFig. 2.28 reach the maximum joint angle constraint to give the highest values for the motiontorque with high impact torques to be the worst configurations for the joints.

25


Figure 2.28: Worst case configurations of the 4-DOF robot

2.4.4 Stiffness design for the joints of the 4-DOF arm/leg robot based on thefour worst case configurations

Basing on the results obtained previously, a simulation model of the 4-DOF compliant robotis built in the Adams with the system parameters shown in Table 5, in which Ji(i = 1, 2, 3, 4)corresponds to the worst configurations of joint i as in Fig. 2.28. The joint velocities areobtained from the worst configuration searching by inverse kinematics from the end-effectorvelocity, and the input joint torques are the values needed to execute the motion of the robot inthe corresponding worst configurations to give the initial end-effector velocity as 1.5m/s andthe joint angle accelerations in Table 5. In the simulation, the maximum torque the compliant

Table 2: Input parameters of the simulation

q̇1[rad/s] q̇2[rad/s] q̇3[rad/s] q̇4[rad/s] τ1[Nm] τ2[Nm] τ3[Nm] τ4[Nm]J1 10 6.6234 -10 -10 20.6698 -7.7789 4.1519 5.0046J2 10 -4.0564 -10 10 8.5737 20.821 -2.0029 -0.3926J3 10 -10 -10 -10 7.2031 -19.0867 -11.7957 0.2108J4 -10 -10 -0.5938 2.7815 -0.5879 5.9208 -0.1545 10.703

actuator can withstand is 55Nm. The results obtained are shown in Fig. 3.36. The respondedtorques of the four joints are demonstrated together in the four worst configurations. The

Table 3: Stiffness of the 4-DOF robotk1 [Nm/rad] k2 [Nm/rad] k3 [Nm/rad] k4 [Nm/rad]

J1 687 1432 2578 1547J2 3151 286 2005 2864J3 716 544 744 573J4 1890 303 3151 544

final stiffness values as derived from the simulation are listed in Table 6. It can be seen thatjoint 2 requires comparatively smaller stiffness than other joints, which means joint 2 is more

26


Figure 2.29: Simulation results of the 4-DOF arm/leg robot

sensitive to impact forces in these four configuration cases. By comparing the rows in 6, itis obvious that the stiffness of the four joints in the case of joint 3 worst configuration isrelatively lower than other cases. This can also be confirmed by the joint angle velocities inTable 5 as all the four reach the maximum 10 rad/s and this configuration is sensitive to theimpact. In Table 6, the most important values are those underlined, which shows that themaximum stiffness for joint 1 to joint 4 should be 687 Nm/rad, 286 Nm/rad, 744 Nm/rad and544 Nm/rad respectively. By setting the values lower than these numbers, the joint actuatorswill be safe when there is an impact at the tip end with the end-effector velocity as high as 1.5m/s. These underlined values are in the diagonal positions in Table 6, indicating that Ji caseis the worst configuration for corresponding joint i(i = 1, 2, 3, 4).

2.5 The design of the AMARSI Compliant Humanoid

The passive compliant humanoid robot [43], Fig. 2.30 developed within AMARSI is derivedfrom the ”iCub” baby humanoid [42, 44, 45] with similar design specifications with regardsto its dimensions, degrees of freedom (D.O.F), mass and joint range of motion. The size ofthe compliant humanoid will approximate the dimensions of a 4 year old child. Regarding thelower body of robot which is the main focus of this paper, the number of degrees of freedomhas remained unchanged with respect to the original ”iCub”. Each leg consists of 6 D.O.F: 3D.O.F at the hip, 1 D.O.F at the knee level and 2 D.O.F at the ankle. This is a kinematic layoutused in many other bipedal robots. For the waist most humanoids usually have a relativelysimple 2 D.O.F. mechanism. For the compliant humanoid developed within AMARSI a 3D.O.F waist was considered as this implementation offers greater motion flexibility. Thisextra functionality is needed as very young children typically reach for objects from a seated

27


position and flexibility at the waist increases their workspace. Based on above, the waistprovides pitch, roll and yaw motions for the upper body in line with the performance of theoriginal ”iCub” humanoid. In addition, to the above generic specifications and in order tofacilitate the experimental scenarios of the AMARSI project there is a need to incorporatecompliance properties through a synergetic combination of both active and passive complianceprinciples.

Figure 2.30: The mechanical assembly of the lower body of the compliant humanoidF robot

2.5.1 The Mechanics of the Lower Body

The mechanical structure of a leg of the compliant robot and an overview of its kinematics withthe location of the D.O.F is illustrated in 2.32, [45]. From the kinematic perspective the newlower body includes the lower torso (housing the waist module) and the two leg assemblies.The height of the lower body from the foot to the waist is 671mm, with a maximum width anddepth (at the hips) of 176mm and 110mm respectively. The total lower body weight is 17.3kgwith each leg weighing approximately 5.9kg and the waist section including the hip flexionmotors weighing 5.5kg. The components that are subject to a low stress are fabricated inAluminum alloy Al6082 with the medium/highly stressed components (load bearing sectionsof the housing) made of Aluminum alloy 7075 (Ergal) which has an excellent strength to

28


weight ratio. The joint shafts are fabricated from Stainless steel 17-4PH which delivers anexcellent combination of good oxidation and corrosion resistance together with high strength.

The Compliant Leg Module

The compliant leg of the robot has a modular structure allowing for easy assembly and main-tenance. The leg has an anthropomorphic kinematic form composed of the hip, the thigh withthe knee joint, the calf with the ankle joint and the foot, Fig 2.32. All these sections wereradically redesigned in the compliant leg with respect to the original ”iCub” leg assemblyto include the desired passive compliance property provided by the actuation unit presentedpreviously. The hip joint is based on a single side supported cantilever base structure with apitch-roll-yaw arrangement providing a large range of motion. The hip pitch motion is imple-mented using the compliant actuation module previously presented while the yaw/roll motionsuse conventional stiff module (Brushless DC motor combined with a Harmonic gearbox witha peak torque of 40Nm). The hip yaw joint has integrated torque sensing to permit the com-pliance regulation through active control. The hip roll is directly driven by the motor placed

Figure 2.31: Kinematic configuration and the mechanical assembly of the compliant lower body

in the centre of hip joint while torque to the hip pitch is transmitted from the hip flexion motor

29


located in the lower torso (Fig. 2.35) through a cable stage that provides additional secondarygearing (1.5:1) allowing for torques up to 60Nm for the hip pitch motion. The knee joint is

Figure 2.32: KThe ankle and knee compliant actuation modules exposed

directly driven by a compliant actuation group (peak torque up to 40Nm) at the centre of theknee joint, Fig. 2.32. For the purpose of assembly optimization the compliant module for theankle flexion motion has been separated from its motor unit and placed at the ankle side whilethe motor (40Nm) actuating this module is housed inside the calf section, Fig. 2.32 and Fig2.33 . Torque to this joint is transferred through a solid link transmission that also provideadditional variable secondary gearing, Fig. 2.34. This permits peaks torques ranging from45Nm-70Nm depending on the ankle flexion angle with the gear ratio curve tuned to providehigher torques during the initial stage of the push-off gait phase (Dorsiflexion), Fig. 2.34. Thelast D.O.F which produces ankle inversion/eversion uses a stiff actuator (40Nm) located onthe foot plate and directly coupled to the ankle roll joint, Fig 2.33. The sole of the foot isdivided into two parts, Fig. 2.33, forming a single toe that is spring loaded by two torsionalspring elements. The functionality of the two piece foot will be explored for the purpose ofachieving larger strides than those that can be done by humanoids with conventional solid soleplates.

Waist Mechanism

The waist of the compliant was based on the core mechanism used in the original iCub wherethe torque and power of the two actuators used for body pitch and yaw is transferred using acable based differential mechanism, Fig. 2.35. For the waist pitch motion the two high poweractuator assemblies (40Nm each) that drive the pitch and yaw motion apply a synchronousmotion to the two directly coupled differential input wheels. For the roll motion the motorsturn in opposite directions. Yaw is achieved through a pulley shaft directly connected to the

30


Figure 2.33: The mechanical realization of the ’cCub” leg modules.

Figure 2.34: The Ankle flexion variable gear ratio for maximizing joint torques during the push off phase

Figure 2.35: Back and front views of the waist module

upper body frame. The actuator assembly of the yaw pulley (20Nm) is located within the cen-tre element of the differential, Fig. 2.35. The torque is conveyed through a cable transmissionsystem that provides additional gearing (1.5:1) allowing for peak torques of 30Nm for torsoyaw motion.

31

3 The Oncilla robot

3 The Oncilla robot

As part of WP2 (Compliant systems) EPFL-A (Biorobotics Laboratory) is developing a novel,small sized, compliant quadruped cat-robot (oncilla robot). We will use the codename ”on-cilla” robot throughout this document to separate the former cheetah cat robot from the in-development AMARSi oncilla robot. The oncilla animal, also called Tigercat, is a wild catof approximately 2kg weight, originated in South America. The final name of the AMARSicompliant quadruped (cat-) robot has yet to be decided for. This oncilla robot is the successorof cheetah robot. Latter was developed and published at Biorobotics Laboratory [46], andwas the basis for the AMARSi quadruped compliant robot proposal. The AMARSi oncillarobot is a co-development between Biorobotics laboratory (EPFL-A) and its AMARSi partnerResLab at the University of Gentt. EPFL is currently finishing the first design phase of oncillarobot, together with the ordered actuators we expect first test runs in about 12 weeks from now(3rd week of June). To facilitate faster testing we will also assemble a robot version based onRC servo motors. RC servo motors are are easily available (short delivery times), howeverthey are sub-optimal for the final version of oncilla robot. The RC actuated robot version willbe used to test sensors, basic mechanical principles, assembly, novel compliant elements ofoncilla robot, material, and basic locomotion patterns.

3.1 Summary of achievements for the quadruped robot

The three-segmented leg design of the former cheetah robot was fully described (biarticulatecompliant joint mechanism), and based on a single leg SLIP model calculation a specificspring selection was made for the recent version, the oncillar robot. Oncilla robot’s leg designwas extended with a second compliant unit: a ham-string-like tension spring system. Wedecided for three actuators per leg: hip (leg protraction and retraction), knee (leg extension andcontraction), and leg ablation. The first two actuators were carefully selected through reverseestimations of torque and acceleration based on foot locus trajectory assumptions for gaitsup to 3Hz, stand-up procedures of the robot, and reverse estimations and mappings of torqueand speed hardware tests with a swinging lever. We further tested the leg design in simulationusing Webots simulation environment, and a modeled version of the cheetah/oncilla robot. Wefound that leg control strategies purely exploiting the passive compliance of oncilla robot’slegs led to a number of stable trot gaits, up to 3.5Hz (central pattern generator based control,open loop). However stability and speed can be improved by the in-parallel activation of theknee actuator during stance phase (double peak/hump activation). We found trot gait patternsmoving the simulated robot up to 90cm/s forward. We can confirm actual flight-phases for ourmodeled oncilla robot applying above control strategy.

3.2 Functional principle

Oncilla robot inherited cheetah robot’s three-segmented, low-inertia, pantographic legs. Thischoice is bio-inspired and was firstly suggested by [48], and [49, 52]. A two-joint (biarticulate)

32

3 The Oncilla robot

spanning compression spring automatically extends each limb, i.e. is the only mean to erectthe robot (”gravity loaded passive compression spring system”). New for the oncilla robotversion leg design is a second spring (tension-like mechanism) replacing one mid-segmentbar of the pantograph mechanism. The placement of this spring is often used in robotics torepresent the leg’s ham-string , e.g. Puppy Robot by [51] and Reservoir Dog from [53]. Athird compliant element in the leg design will be foot element; however its characteristics arenot fully defined yet. Non-mechanical compliance will be available through the hip joints ofthe quadruped robot. Knee and hip actuator of oncilla robot feature very low gear ratios (lessthan 30:1) and are fully reversible. Together with accurate position sensing (12 bit resolution)and high speed feedback loops (planned for 500Hz-1000Hz) it will be possible to implementa virtual compliant actuator (key word: ”force control”). The knee actuator is decoupled fromthe knee joint by means of a cable mechanism, only tension forces acting at the actuator.Hence we expect to use virtual compliance mainly in oncilla robot’s hip joint.

3.3 Mechanical implementation and integration into the robotichardware

A snapshot from a sketched version of oncilla robot (featuring the larger, brushless motors) isgiven in Fig. 3.36. The expected weight of the robot is about 2.5kg, together with a 3000mAhbattery around 3kg. We designed oncilla robot’s legs to be roughly 50g in weight (excludingthe in-development multi-axes load cell). This will provide us with a very low-inertia leg.Oncilla robot was designed with no extra payload capabilities. Materials used are differenttypes of sheet metal Aluminium (frame, limbs, standard components), glass-fiber reinforcedplastic (FR4 sheet structures), POM (bearing, fixations), brass (bearing, axes), steel (axes,springs, motor parts), ABS plastic (compliance guidance mechanism), and strings for the cablemechanism.

3.4 Actuator dimensioning

Oncilla robot’s brushless motors were selected after an extensive literature review (brushlessversus brushed motors, hydraulic actuation, direct drives, RC servo motors). We then assem-bled a large motor-gearbox combination list (this was work together with AMARSi-partnerResLab, UGentt, Michiel D’Haene). Final motor and gear sizes were then calculated andselected through application scenarios and tests, e.g. foot trajectory assumptions, the robotstanding up, and initial motor-gearbox tests applying a high-speed swinging lever (experimentat ResLab, UGentt). Reverse torque and acceleration profile calculations from above scenar-ios allow calculating expected available torque and speed, energy loss, torque peak, and powerconsumption of the load-gear-motor combination. We used standard mechatronic tools, for-mulas, and assumptions for latter calculations [55]. Load assumptions, available motors, andgear combinations lead to a small set of potential/candidate motors which can drive the loadin terms of torque and speed, and don’t overheat at the same time, and range of gear ratiosfor e.g. an assumed robot trot gait of about 3Hz. Calculations are done both for the hip andthe knee actuator. A third actuator (RC servo motor) is used for leg ablation; this is a new

33

3 The Oncilla robot

Figure 3.36: The figure shows the main components of oncilla robot, including the compliant elements(sketched presentation). Clearly visible are the three-segmented legs (grey, z-shaped), distal black rubberelements depict the feet. The estimated weight of this robot is about 3kg; this includes the weight for thebattery (around 500g).

DOF for the oncilla robot (compared to cheetah robot, e.g. used in Raibert’s quadruped, [47],Raibert’s Bigdog [?], Boston Dynamics LittleDog [50], Semini’s HyQ [54]). We will test itsexact dimensioning with the first prototype.

3.5 Joint stiffness range and energy storage capacity

We have so far fully defined oncilla robot’s biarticulate compliant joint range. The desired ef-fect is a non-linear leg compliance, and less a single-joint compliance. The three-segmentationof the leg design, the placement of the attachment points of the compression spring, the selec-tion of the spring stiffness, and the choice for the pre-stress value of the compression springlead to an digressive (other than linear or progressive) spring-stiffness behavior (Fig. 3.37).Early SLIP-model tests showed that it is advantageous to use pre-stressed springs for therobot’s limbs (Fig. 3.37, starting from 4N).

Energy storage is directly linked to the applying leg force (Fig. 3.37) by the change of the leglength; we expect energy storage values (maximum half the leg length compression) roughlyup to 2 Joule per leg and biarticulate compliant unit. Initial dimensioning of the biarticulate

34

3 The Oncilla robot

Figure 3.37: The plot shows the applying leg force over leg length, the spring behavior of the oncilla leg isnon-linear with digressive characteristics. The configuration plotted uses a 2.3kN/m linear biarticulatedspring. Only the influence of the biarticulte compliance is shown, the ham-string compliant behaviordepends not only on the leg length but also on the angle of attack.

leg spring is based on results from a SLIP model simulation predicting good stability charac-teristics for a single linear, prismatic leg at characteristic hopping speeds. The resulting SLIPmodel stiffness value was mapped onto our non-linear leg characteristics. The latest leg designuses linear springs of roughly 2kN/m.

3.6 Actuation power

Based on the motor-gearbox dimensioning, we have selected and ordered Maxon brushlessmotors and high-duty gearboxes with low gear ratios. The following values do not includeefficiency values for motor and gearbox, but are data sheet numbers recalculated by gear ra-tios. For the hip actuator this leads to a maximum rotor speed (gearbox outgoing rotor) of80rad/s, and a recommended speed of 73rad/sec. Stall torque is 13Nm (the gearbox can toler-ate peak torques of not more than 3Nm), recommended working torque 1Nm. Knee actuatorvalues: max speed 380rad/sec, recommended speed 350rad/sec, stall torque 2.8Nm, and rec-ommended torque 220mNm. However the knee actuator has an additional cable mechanismwhich is effectively gearing down the actuator output. Note that both described compliantunits are working either in parallel (biarticulate compliance) or in series (ham-string compli-ant unit) to the knee motor.

3.7 Simulation/experimental results demonstrating theperformance of the compliant platform

Our oncilla robot is currently still under construction, hence we cannot provide demos withthe hardware platform. However we used the cheetah/oncilla simulation model to extensively

35

3 The Oncilla robot

test the compliant leg design, while applying different leg joint strategies (robot in trot gait,open-loop CPG control, and open control parameter identification using particle swarm op-timization). Our test indicate that the oncilla robot will be able to facilitate the passivelycompliant leg design for a range of trot gaits, i.e. multiple trot gaits with different amplitude,offsets, phase bias etc. We also found valid, fast, and more robust gaits by supporting abovepassive leg compliance with an additional active, in parallel working knee joint control. Latterstrategy leads to stable trot gaits up to 90 cm/s (more than 3 times the oncilla robot’s bodylength), with flight-phases up to 10percent of leg cycle length. We will re-run these experi-ments, which are currently still in simulation, with the real hardware as soon as possible.

36

4 The quadruped robot Kitty


Based on the requirements in the T 2.1 described in the proposal, UniZu has been developingthe quadruped robot called Kitty equipped with a multi-joint spine inspired by the character-istics of biological one. The study of Kitty robot involves the novel design of spine which ishighly-compliant, actuated multi-joint system, evaluation the role of spine in the locomotion,and investigation of rich motor skill to achieve gait transition. Over past decades, it has beenwidely accepted that locomotion is generally perceived as being the function of the legs andthe trunk is considered to be carried along in a more or less passive way [58, 57, 59]. This pop-ular hypothesis appears to have been accepted by most of roboticist as well as biologists and aconsiderable amount of research has been conducted on legged robots with little considerationon its spine. However, Gracovetsky has proposed an alternative hypothesis which emphasizesthe spinal engine, that is, locomotion is first achieved by the motion of the spine; the limbscame after, as an improvement, not as a substitute [60]. This implies that the spine is the keystructure necessary in locomotion and maneuverability as well as in gait transition. Inspiredby this finding from biology, the kitty robot equipped with tendon-driven flexible spine hasbeen developed to test the hypothesis of spinal engine and investigate the rich motor skill toachieve gait transition.

4.1 Spinal Model

4.1.1 Biological spinal structure

As an essential organ of both weight bearing and locomotion, the spine is subject to the conflictof providing maximal stability while maintaining crucial mobility. Morphological adaptationof the spine of mammals with respect to locomotion depends on specific biomechanical de-mands, for instance, the locomotion mode [61]. Therefore, we first described the general char-acteristics of mammalian spine, and then took a cheetah as an example to illustrate its specificspine morphology and its role in locomotion. The spine consists of discrete bony elements,namely vertebrae, ligaments, intervertebral discs and Zygapophyseal joint. The vertebrae arejoined by passive ligaments and kept separated by intervertebral discs. The Zygapophysealjoints are dynamically controlled by muscular activation. Vertebrae (4.38a) are the highlyspecialized bones which collectively make up the spinal column. The bony elements createattachment points for muscles and other bones, allowing for flexible movement in a range ofdirections. The spinal column provides critical support to the animal. Intervertebral discs(4.38(b)) are located between the vertebrae, and firmly joined with the endplates of the ver-tebrae. They are morphologically structured soft tissue cushions serving as the spine’s shockabsorbing system, which protect the vertebrae and other structures (i.e. nerves). The discsallow some vertebral motion: extension and flexion. Individual disc movement is very lim-ited; however considerable motion is possible when several discs combine forces. Ligaments(4.38(c)) are the fibrous, slightly stretchy connective tissues that hold one bone to anotherin the body, forming a joint. Ligaments control the range of motion of a joint, for example,stabilizing the joint so that the bones move in the proper alignment. Mechanically, spinal

37


Figure 4.38: Spine components

ligaments behave as other soft tissues of the body and they are viscoelastic with nonlinearelastic responses [62]. A zygapophysial joint(4.38(d)) is a movable joint between the supe-rior articular process of one vertebra and the inferior articular process of the vertebra directlyabove it as shown in Figure 5. The biomechanical function of each pair of zygapophysialjoints is to guide and limit movement of the spinal motion segment. In the lumbar spine,the zygapophysial joints function to protect the motion segment from anterior shear forces,excessive rotation and flexion [63]. The kinematic analysis of the biological spine has not

Figure 4.39: Ranges of motion throughout the normal spine. From White and Pnjabi Clinical Biome-chanices

Figure 4.40: Instantaneous axes of rotation for the lumbar vertebrae. From White and Pnjabi ClinicalBiomechanics

38


been well known by researchers so far because of its complex biomechanics. However, theranges of motion throughout the normal human’s spine have been measured as shown in Fig.4.39, [65]. The spine can achieve combined flexion/extension, one side lateral bending andone side axial rotation as shown in Fig. 4.40 [65]. The morphology of the spine is differentin mammals with different locomotion mode. In this report, we only took cheetah, a terres-trial quadruped mammal, as an example which is a particular case to make most use of itsspine to achieve maximal stability and maintain crucial mobility. Cheetah’s vertebrae have thefollowing striking features compared to other mammals.

The vertebral bodiesA slight anterior wedge shape and a decrease in sagittal diameter (represented by red line inFig. 4.42 (a)) towards the sacrum as shown in Fig. 4.41 are recognizable in cheetah, in whompredominant sagittal flexion is found in locomotion.

Zygapophyseal joint shapeIt reflects a mammal’s capability to resist torsion, ventral shear and dorsal shear. The cheetah’slumbar vertebra features inclined and plane joint surfaces as shown in Fig. 4.42 (a) which areable to resist torsion and ventral’s shear. However, it is assumed that it counter dorsal shearthrough the tensed spinal musculature.

Figure 4.41: Lumbosacral juncion, from [61]

In addition to the two factors described above, there still exist some features of spine whichmight affect the locomotion, for example, the stiffness and arrangement of the ligaments; thenumber of vertebrae; the stiffness and arrangement of intervertebral discs and so on. However,there are still something remaining unclear in the study of spine, for example, how these spinalmorphological features cooperate to affect locomotion, which plays a more a more importantrole in the locomotion. In order to better explain these questions, a highly-compliant, multi-degree system, artificial spinal structure inspired from biology has been developed by UniZu.

4.1.2 Artificial spinal structure

This spinal structure acts not only as a beam between the forelegs and the hind, but also asan engine to generate movement essential to locomotion. It should be designed in a modulararchitecture. In this case, its morphology can be easily changed by connectors to figure outwhich configuration benefits best under a certain locomotion mode and help biologist to better

39


Figure 4.42: Zygapophyseal joint shape, from [61]

understand the characteristic and role of spine in locomotion.

Fully-actuated spine morphologyAs a first step, we started with a fully actuated artificial spine inspired by biology. Figure 6shows the 3D representation of this spine which consists of cross-shaped rigid vertebrae madeof ABS plastic, silicon blocks and cables driven by motors. The cross-shaped rigid vertebraeare separated by the silicon blocks, which work as intervertebral discs.

Figure 4.43: 3D representation of spinal structure

Each side of artificial vertebrae is connected by a cable through the two holes and the siliconblocks. In the center of the vertebra, there are two faces: a convex and a concave, each ofwhich can match and rotate around the opposite face with the nearby vertebra as shown in4.44. The four driven cables are pulled respectively by the four RC motors, which are able

40


Figure 4.44: 3D representation of the match of vertebrae

Biological spine Artificial spine Function

Vertebra Cross rigid segment 1-Make up the spinal column;2-Create attachment points for muscles and other bones

Intervertebral disk Silicon block 1-Serve as the spine’s shock absorbing system;2-Allow some vertebral motion: extension and flexion

Ligament Fig. 4.45d, e Spring 1-Connect one vertebra to another;2-Control the range of motion of a joint

Muscle Driven-cable 1-Connect one vertebra to another;

Zygapophysial jointBall joint (Fig. 4.44) 1-Guide and limit movement of the spinal motion segment;

2-Protect the motion segment from anterior shearforces excessive rotation and flexion

Table 4: Similarities in morphology between biological spinal structure and the artificial counterpart

to control the stiffness and movement of the spine. In this design, the spine can be bent inall directions within certain predefined angle. Table 4 shows the similarities in morphologybetween biological spinal structure and its artificial counterpart.

Exploration of the spine morphologyThe spine was designed in a modular architecture to investigate the impact of the morpho-logical property of the spine in locomotion. The morphological properties of spinal structureof Kitty robot can be easily changed by the connectors. For example, the artificial vertebraecan be replaced with differently-shaped ones. Or only part of silicon blocks are replaced bysprings, which leads to partial actuated and passive (Fig.4.45(d), Fig. 4.45(e)). As a resultof this configuration, it is more biologically close to animal’s spinal model. If we install tworigid boards to antagonistic sides of the spine, then the DOF of spine will be constrained in theplane perpendicular to those boards. Fig. 4.45 shows an exhibition of developed spinal struc-tures, including rigid spine, passive spine, tendon driven spine, partially actuated and passivespine.

41


Figure 4.45: Exhibition of developed spinal structures. The yellow rectangles highlight the area of thespinal structure with different morphological properties. Red lines emphasize the springs above it.

4.2 Design of the quadruped robot

The developed quadruped robot is shown in Fig. 4.46. It is 23 [cm] long, 29 [cm] wide,20 [cm] high and weighs 1.1[kg]. The robot features a tendon-driven spine consisting ofsilicon blocks and plastic segments without actuation for legs. It was designed in modulararchitecture: in addition to the leg, feet, the morphology and material properties of spinalstructure of Kitty robot can also be easily changed by the connectors.

4.2.1 Leg Design

There are 3 linear springs in each stick-shaped leg to absorb shock from the ground impact.The legs are fixed to the body and able to be easily replaced by other kinds of legs. The bottomof foot is glued with the material which has asymmetry friction feature contributing to controlthe walking direction.

4.2.2 Actuation

Four RC motors (dynamixel RX 28) driving cables through the spine are mounted at the frontand rear parts of body to control the movement of spine. The robot does not have any kind ofactuated joints, for instance, hip or knee joints, and the legs are fixed to the body by screws.The motors are serially connected to a PC by USB2Dynamixel which is used to transforma USB port into a serial port RS485. Position control is taken to generate the movement ofthe spine. However, a goal position should be set within the valid range from -150deg to+150deg. Fig. 4.47 shows the maximal angle the spine can bend in the degree of ±150deg.Due to the error from manufacture and assembly, these angles are not exactly the same, around30 degrees.

4.3 Experiments and results

In order to observe the correlation between the morphological property and the behavior oflocomotion, a series of experiments based on two different kinds of spinal morphology have

42


Figure 4.46: Developed quadruped robot with a tendon-driven spine

Figure 4.47: Maximal bending angle of 4 sides in the spinal structure

been conducted. The first morphology is with fully actuated spine as shown in Fig. 4.45(c),and the second one is with partial actuated and passive one as shown in Fig. 4.45(d). Duringthe experiments, several control parameter sets were tested for 3 trials, and then the best onewas chosen to calculate its average speed, standard speed. The effect of property, structure,and control of the spine on locomotion will be illustrated in the following sections.

43


4.3.1 Experiments and results based on robot with fully actuated spine

Experiment setupThe configuration and feature of this fully actuated spine has already been explicitly describedin 2.2.1. Sine waves with different amplitude, frequency, and phase lag are taken to controlthe spine in the beginning of the study. The definition of the parameters is shown in Table 2.

Type Parameter Illustration

Amplitude

angleUp (aU) The amplitude of the sine waves controlling 4 motors rangesangleDown (aD) from 0 to 150o due to the constraint of the motors.angleRight (aR) If angle≥ 0, then the cable is tightening the spine, otherwise,angleLeft (aL) it is relaxing the spine.

Frequency frequencyUD (fUD) The frequency of up-down movement and right-leftfrequencyRL (fRL) movement

Phase LagphiDown(φD) The phase lag of bottom side, right side and left side withphiRight(φR) respect to up side of the spinephiLeft (φL)

Distance The predefined travel distance of the robot

Table 5: The explanation of control parameters

ResultsMoving forward is a basic criterion for locomotion and an easy start to test its performance.Table 6 shows the parameter set taken for moving forward. The side cables were kept thenatural length without tightening and relaxing. The amplitude of up-down movement was140deg and the frequency of up-down was 2. Phase lag is a key parameter to achieve stableand efficient forward moving. If the phase lag is not properly set, then the power of up anddown motors will be counteracted, leading to energy inefficiency.

Parameter aU aD aR aL fUD fRL φD φR φLValue 140deg 140deg 0deg 0deg 2 0 Pi 0 0

Table 6: Control for walking forward

We observed that the robot is able to walk forward very fast and the fastest speed is up to11cm/s with standard deviation of 0.42 in Tab. 7. The results show that the performance ofwalking forward is stable and reproducible.

Ave Speed (cm/s) 11.06212Std speed 0.42487

Table 7: Reults of the experiments for the forward motion

Figure 11 shows the sequential movements of the spine. The up and down movements areobviously observed. It exhibits periodical movement which contributes to forward moving.

44


Figure 4.48: Sequential pictures of the locomotion under given parameter set. The yellow arrow repre-sents the walking direction.

Since the spine is fully actuated in 4 sides and able to bend in any directions, then it is possibleto achieve turning performance during the locomotion. In order to achieve this, while up-downmovement is still kept, the right-left movements is added to the spine, as shown in Tab. 8. Theonly difference between turning right and left is the flip between φR and φL, which are thephase lag with respect to the up side of the spine.

Params aU aD aR aL fUD fRL φD φR φLTurn right Value 120deg 120deg 120deg 120deg 2 2 pi 0 piTurn left Value 120deg 120deg 120deg 120deg 2 2 pi pi 0

Table 8: Control for turning right and turning left

Table 9 shows that the robot is able to turn right or left easily and stably. However, the speedis not so satisfactory, even if we increase the frequency and amplitude. We contribute the slowspeed to the inappropriate cooperation of 4 motors, which results in more unnecessary torqueto each motor. The optimization of controller is crucial to eliminate this problem. It was alsoobserved that the robot can turn left or right to a maximal angle similar to the other, 49degfor turning right and 46deg for turning left (Table 9). Figure 4.49 shows the trajectories of therobot in the case of turning right and left.

Turning right Turning leftAve Angle (degree) 49.32738 46.2073

Std speed 0.631467 4.311225Ave speed (cm/s) 3.287622 3.443385

Std speed 0.126438 0.227138

Table 9: Results of the experiments

45


Figure 4.49: Trajectories of robot turning right (a) and left (b) under given parameter sets. Red arrowrepresents the walking direction

4.3.2 Experiments and results based on robot with partial actuated andpassive spine

Experiment setupIn order to investigate which morphological feature plays a more important role in locomotion,the second spine morphology as shown in (Fig. 4.45(e)) was adopted, in which only up sidecable is actuated. In this morphology, the down-side driven-cable is replaced by a linear springand the side parts of the spine are kept in natural condition. Based on this configuration, thespinal structure becomes partially actuated and partially passive. Absolute value of sine wavewas taken to control the only one motor in the spine. The motors in sides of spine are stillkept constant value 0, which means it neither pulls the cable, nor pushes the cable. The betterparameter set is in the following Tab. 10.

Amplitude of motor controlling up side of spine 120degFrequency of the save wave 3

Table 10: Control for walking forward

ResultsWe observed that the robot with this configuration can walk half as fast as the one with partialactuated and passive spine in Tab. 11.

Ave speed (cm/s) 6.17101Std speed 0.843323

Table 11: Results of the experiment for forward motion

The upward movement of spine doesn’t exhibit as shown in Fig. 4.50, because the springdownside plays a passive role and is unable to pull the downward cable through the spinewhich contributes mostly to the upward movement. The results showed that the locomotion

46


can also be achieved by spine featuring one actuated cable and one passive linear spring onthe opposite side.

Figure 4.50: Sequential pictures of the locomotion in 2 cycles when Aup =120deg, Freq=3. Red linesrepresent the length of springs below it over time.

4.3.3 Conclusion

A biological spinal model has been analyzed in terms of the effect of the spinal morphologicalfeatures on the locomotion. A novel highly-compliant, multi-joint artificial spine has been de-veloped based on this biological analysis. The development of a robot called kitty embeddingthis biologically inspired spine helps biological and robotics researchers better understand themechanism of spinal engine behind the locomotion.

A series experiments have been conducted to test the effect of the spine on locomotion undertwo kinds of spinal morphology. The first one is fully actuated spine and the second is partialactuated and partial passive. These preliminary experiment results showed that the robot withfully actuated spine is able to move forward fast with obvious up-down movement in the spineand the speed is up to 11cm/s, as well as turn left or right stably. It also showed that therobot with partial actuated and passive one can achieve the movement of moving forward aswell, but the movement of spine is just oscillating from initial position to down, which mightcontribute to the slow speed which is only half as fast as the fully actuated one. All the resultsemphasize the concept of spinal engine and demonstrate that only by the movement of thespine can the robot achieve locomotion.

47

References

References

[1] B. Shetty and M. Ang Jr, “Active compliance control of a PUMA 560 robot“, Proc IEEEInt. Conf. On Robotics and Automation, vol. 4, 1996.

[2] J. Sulzer, M. Peshkin, and J. Patton, “MARIONET: An exotendon-driven, rotary serieselastic actuator for exerting joint torque“, International Conference on Robotics for Reha-bilitation (ICORR 2005), 2005, pp. 103-108.

[3] B. Zinn, M. Roth, O. Khatib, and J. Salisbury, “A new actuation approach for humanfriendly robot design“, The International Journal of Robotics Research, vol. 23, no. 4-5,pp. 379-398, 2004.

[4] T. Morita and S. Sugano, “Development of a new robot joint using a mechanicalimpedance adjuster“, IEEE International Conference on Robotics and Automation (ICRA1995), vol. 3, May 1995, pp. 2469-2475.

[5] G. Pfreundschuh, T. Sugar, and V. Kumar, “Design and control of a three-degrees of-freedom, in-parallel, actuated manipulator“, Journal of Robotic Systems, vol. 11, no. 2,1994.

[6] G. A. Pratt and M. M. Williamson, “Series Elastic Actuators“, IEEE International Work-shop on Intelligent Robots and Systems (IROS 1995), Pittsburg, USA, 1995, pp. 399-406.

[7] J. E. Pratt, B. T. Krupp, C. J. Morse, and S. H. Collins, “The roboknee: an exoskeletonfor enhancing strength and endurance during walking“, EEE International Conference onRobotics and Automation (ICRA 2004), vol. 3, 2004, pp. 2430- 2435.

[8] A. Bicchi and G. Tonietti, “Fast and soft arm tactics: Dealing with the safety-performancetrade-off in robot arms design and control“, IEEE Robotics and Automation Magazine,vol. 11, no. 2, 2004, pp. 22-33.

[9] S. Au and H. Herr, “On the design of a powered ankle-foot prosthesis: The importance ofseries and parallel motor elasticity“, IEEE Robotics and Automation Magazine, 2008

[10] A. Jafari, N. Tsagarakis, B. Vanderborght, D. Caldwell “An Intrinsically Safe Actua-tor with the Ability to Adjust the Stiffness“, The Seventh IARP Workshop on TechnicalChallenges for Dependable Robots in Human Environments (DRHE 2010).

[11] A. Jafari, N.G. Tsagarakis, B. Vanderborght, and D. G. Caldwell, “AwAS: a novelactuator with adjustable stiffness“ IEEE Int. Conf. on Intelligent Robots and Systems(IROS2010), Taipei, Taiwan, 2010, pp. 4201 - 4206.

[12] A. Jafari, N. G. Tsagarakis and D. G. Caldwell “Giunto rotante a rigidezzaregolabile(AwAs II:Rotational Joint with variable stiffness)“, Patent Number:TO2010A000779.

[13] A. Jafari, N. G. Tsagarakis and D. G. Caldwell, “AwAS-II: A New Actuator with Ad-justable Stiffness based on the Novel Principle of Adaptable Pivot point and VariableLever ratio“ IEEE Int. Conf. on Robotics and Automation (ICRA2011), Sanghai, China.

48

References

[14] N. G. Tsagarakis, A. Jafari and D. G. Caldwell, “A Novel Variable Stiffness Actuator:Minimizing the Energy Requirements for the Stiffness Regulation“ 32nd Annual Inter-national Conference of the IEEE Engineering in Medicine and Biology Society (EMBC2010), Anchorage, Alaska, 2010.

[15] K. Hollander, T. Sugar and D. Herring, “Adjustable robotic tendon using a ”jack spring”“ International Conference on Robotics for Rehabilitation (ICORR 2005), 2005, pp. 113-118.

[16] R. Van Ham, M. Van Damme, B. Verrelst, B. Vanderborght, and D. Lefeber, “MAC-CEPA, the Mechanically Adjustable Compliance and Controllable Equilibrium PositionActuator: A 3DOF Joint with 2 independent Compliances“ International Applied Me-chanics, Vol. 4, April 2007.

[17] N. Hogan “Adaptive control of mechanical impedance by coactivation of antagonist mus-cles,“ IEEE Trans. Aut. Cont., vol. AC-29, no. 8, pp. 681-690, August 1984.

[18] C.P. Chou and B. Hannaford “Measurement and modelling of McKibben Pneumatic Ar-tificial Muscles“ IEEE Trans. Robotics and Automation, vol. 12, no. 1, pp. 90-102, 1996.

[19] G. Tonietti, R. Schiavi and A. Bicchi “Design and control of a variable stiffness actuatorfor safe and fast physical human robot interaction“, IEEE International Conference onRobotics and Automation, pp. 528-533, 2005.

[20] J. Hurst, J. Chestnutt and A. Rizzi “An actuator with mechanically adjustable seriescompliance“, Robotics Insitute, Carnegie Mellon University, Pittsburgh, PA, 2004.

[21] R. Schiavi, G. Grioli, S. Sen and A. Bicchi “VSA-II: a Novel Prototype of VariableStiffness Actuator for Safe and Performing Robots Interacting with Humans“, IEEE In-ternational Conference on Robotics and Automation, Pasadena, CA, 2008.

[22] A. De Luca, A. Albu-Schaeffer, Sami Haddadin, G. Hirzinger ”Collision Detection andSafe Reaction with the DLR-III Lightweight Manipulator Arm”, IEEE International Con-ference on Intelligent Robots and Systems, Beijing, China, 2006.

[23] G. Hirzinger, N. Sporer, A. Albu-Schaeffer, H. Maehnle and A. Pasucci, ”DLR’s Torquecontrolled lightweight robots III - are we reaching the technological limits now?”, IEEEInternational Conference on Robotics and Automation, 2001.

[24] A. Albu-Schaeffer, C. Ott, U. Frese, G. Hirzinger, ”Cartesian impedance control of re-dundant robots: recent results with the DLR-light-weight-arms”, IEEE International Con-ference on Robotics and Automation, 2003.

[25] A. Albu-Schaeffer, M. Fischer, G. Schreiber, E. Shoeppe and G. Hirzinger, ”SoftRobotics: What Cartesian Stiffness Can We obtain With Passively Compliant, UncoupledJoints?”, IEEE International Conference on Intelligent Robots and Systems, 2004.

[26] S. Haddadin, A. Albu-Schaeffer, A. De Luca and G. Hirzinger, ”Evaluation of Col-lision Detection and Reaction for a Human-Friendly Robot on Biological Tissue”, 6thIEEE/IARP - RAS/EURON Workshop on Technical Challenges for Dependable Robots inHuman Environment, Pasadena, CA, USA, 2008.

49

References

[27] N. Hogan, ”Impedance Control: an approach to manipulation: parts I-III”, Journal ofDynamic Systems, Measurement and Control, Vol. 107, 1985.

[28] A. Albu-Schaeffer, C. Ott, G. Hirzinger, ”A Unified Passivity-based Control Frameworkfor Position, Torque and Impedance Control of Flexible Joint Robots”, The InternationalJournal of Robotics Research, vol. 26, no. 1, pp. 23-39, 2007.

[29] S. Haddadin, A. Albu-Schaeffer, A. De Luca and G. Hirzinger, ”Collision Detectionand Reaction: A Contribution for Safe Physical Human-Robot Interaction”, InternationalConference on Intelligent Robots and Systems, Nice, France, 2008.

[30] M. Laffranchi, N. Tsagarakis, F. Cannella and D. G. Caldwell , ”Antagonistic and SeriesElastic Actuators: a Comparative Analysis on the Energy Consumption”, InternationalConference on Intelligent Robots and Systems, St Louis, USA, 2009.

[31] J. Tak-Man Cheung, M. Zhang, K.N. An, ”Effects of plantar fascia stiffness on thebiomechanical responses of the ankle-foot complex”, Clinical Biomechanics 19, 2004.

[32] M. Ishikawa, P.V. Komi, M.J. Grey, V. Lepola, G.P. Bruggemann, ”Muscle-tendon in-teraction and elastic energy usage in human walking”, Journal of applied physiology 99,2005.

[33] S. Wolf and G. Hirzinger, ”A new variable stiffness design: matching requirements ofthe next robot generation”, IEEE International Conference on Robotics and Automation,Pasadena, CA, USA, 2008.

[34] S. A. Migliore, E.A. Brown, S.P. DeWeerth, ”Biologically Inspired Joint Stiffness Con-trol”, IEEE International Conference on Robotics and Automation, 2005.

[35] M. Van Damme, R. Van Ham, B. Vanderborght, F. Daerden and D. Lefeber, ”Design of a’Soft’ 2-DOF Planar Pneumatic Manipulator ”, Climbing and Walking Robots, Part 9, pp.559-566, 2006.

[36] B. Verrelst, R. Van Ham, B. Vanderborght, F. Daerden, D. Lefeber and J. Vermeulen”The Pneumatic Biped ’Lucy’ Actuated with Pleated Pneumatic Artificial Muscles”, Au-tonomous Robots, vol. 18, no. 2, pp. 201-213, 2005.

[37] F. Daerden and D. Lefeber, ”The concept and design of pleated pneumatic artificial mus-cles”, International Journal of Fluid Power, vol. 2 no. 3 pp. 41-50, 2001.

[38] H. Kazerooni, P. Houpt and T. Sheridan, ”The fundamental concepts of robust compliantmotion for robot manipulators”, IEEE International Conference on Robotics and Automa-tion, 1986.

[39] http://yobotics.com/.

[40] J. Pratt, B. Kupp and C. Morse ”Series Elastic Actuators for high fidelity force control”,Industrial Robot: An International Journal, Vol. 29, Issue 03, pp. 234-241 2002.

[41] G.A. Pratt, ”Low Impedance Walking Robots”, Integ. and Comp. Biol., 42:174-181(2002).

50

References

[42] N. Tsagarakis, G. Metta, G. Sandini, D. Vernon, R. Beira, F. Becchi, L. Righetti, J.Santos-Victor, A. J. Ijspeert, M. C. Carrozza and D. G. Caldwell, ”iCub - the designand realization of an open humanoid platform for cognitive and neuroscience research.Advanced Robotics, vol. 21, 2007.

[43] N.G. Tsagarakis, L. Zhiin, J.A. Saglia and D.G. Caldwell, ”The Design of the LowerBody of the Compliant Humanoid Robot ”cCub”. International Conference on Roboticsand Automation, Shanghai, China, 2011.

[44] N.G. Tsagarakis, F. Becchi, L. Righetti, A. Ijspeert, and D.G. Caldwell. ”Lower bodyrealization of the baby humanoid - ’icub”’, Proc. of IEEE IROS 2007, pp. 3616-3622.

[45] N.G.Tsagarakis, Bram Vanderborght, Matteo Laffranchi and D.G.Caldwell, ”The Me-chanical Design of the New Lower Body for the Child Humanoid robot ’iCub”’, IEEE/RSJInternational Conference on Intelligent Robots and Systems, IROS 2009

[46] S. Rutishauser, A. Sproewitz, L. Righetti, and A. J. Ijspeert, ”Passive compliantquadruped robot using central pattern generators for locomotion control,” in 2008 IEEEInternational Conference on Biomedical Robotics and Biomechatronics, 2008.

[47] M. Raibert, M. Chepponis, and H. Brown, ”Running on four legs as though they wereone,” Robotics and Automation, IEEE Journal of, vol. 2, no. 2, pp. 70-82, 1986.

[48] H. Witte, R. Hackert, W. Ilg, J. Biltzinger, N. Schillinger, F. Biedermann, M. Jergas, H.Preuschoft, and M. Fischer, ”Quadrupedal mammals as paragons for walking machines,”in Proc AMAM - Adaptive Motion in Animals and Machines, pp. TuA-II-2.1 - TuA-II-2.4,2003.

[49] M. Fischer and R. Blickhan, ”The tri-segmented limbs of therian mammals: kinemat-ics, dynamics, and self-stabilization-a review,” Journal of Experimental Zoology. Part A,Comparative Experimental Biology, vol. 305, pp. 935-952, Nov. 2006.

[50] M. Kalakrishnan, J. Buchli, P. Pastor, M. Mistry, and S. Schaal, ”Learning, planning, andcontrol for quadruped locomotion over challenging terrain,” vol. 30, pp. 236-258, 2011.

[51] F. Iida, ”Cheap design approach to adaptive behavior: Walking and sensing through bodydynamics,” in International Symposium on Adaptive Motion of Animals and Machines,2005.

[52] M. S. Fischer and H. Witte, ”Legs evolved only at the end!,” Philosophical Transactionsof the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 365, no.1850, pp. 185-198, Jan. 2007.

[53] F. Wyffels, M. D’Haene, T. Waegeman, K. Caluwaerts, C. Nunes, and B. Schrauwen,”Realization of a passive compliant robot dog,” in Biomedical Robotics and Biomecha-tronics (BioRob), 2010 3rd IEEE RAS and EMBS International Conference on, 2010, pp.882-886.

[54] C. Semini, N. G. Tsagarakis, E. Guglielmino, and D. G. Caldwell, ”Design and experi-mental evaluation of the hydraulically actuated prototype leg of the HyQ robot,” in Intelli-gent Robots and Systems (IROS), 2010 IEEE/RSJ International Conference on, 2010, pp.3640-3645.

51

References

[55] F. Roos, H. Johansson, and J. Wikander, ”Optimal selection of motor and gearhead inmechatronic applications,” Mechatronics, vol. 16, no. 1, pp. 63-72, Feb. 2006.

[56] R. Playter, M. Buehler, and M. Raibert, ”BigDog,” in Proceedings of SPIE, 2006, vol.6320.

[57] Gracovetsky SA, Iacono S, ”Energy transfers in the spinal engine”, J Biomed Eng, 9:99-114 (1987).

[58] Gracovetsky SA, ”An hypothesis for the role of the spine in human locomotion: a chal-lenge to current thinking”, J Biomed Eng, 7(3):205-216 (1985).

[59] Nicol J. G. and Waldron K. J., ”Biomemetic leg design for untethered quadruped gallop”,Proc. Of the CLAWAR Int.Conf. on Climbing and Walking Robots, Paris, France, 2002.

[60] Alexander R. M., ”Principles of Animal Locomotion”, Princeton university press,Princeton NJ, 2003.

[61] Boszcyk, Bronk M., Alexandra A. Boszczyk and Reinhard Putz., ”Comparative andFunctional Anatomy of the Mammalian Lumbar Spine”, Anatomical Record Part A 264 ,(2): 157-168, 2001.

[62] Spine biomechanics. MER/BIO SOFT TISSUE MECHANICCS: SB1-SB11.

[63] http://en.wikipedia.org/wiki/Zygapophyseal-joint

[64] http://artistik.pl/

[65] Augustus A. White, Manohar M. Panjabi, Clinical biomechanics of the spine Lippincott,1990.

52

Compliant Actuators - facts | AMARSi Projectamarsi-project.eu/system/files/D21.pdf · Fixed...

Documents

Transcript of Compliant Actuators - facts | AMARSi Projectamarsi-project.eu/system/files/D21.pdf · Fixed...