Design, Realization and Control of Soft Robot Armsfor Intrinsically Safe Interaction with Humans

Antonio Bicchi and Giovanni ToniettiCentro Interdipartimentale di Ricerca “E. Piaggio”

Universita di Pisa - Italia

R obots designed to share an environment withhumans, such as e.g. in domestic or enter-

tainment applications or in cooperative material-handling tasks ([1, 18]), must fulfill different re-quirements from those typically met in industry.It is often the case, for instance, that accuracyrequirements are less demanding. On the otherhand, a concern of paramount importance is safetyand dependability [11] of the robot system. Ac-cording to such difference in requirements, it canbe expected that usage of conventional industrialarms for anthropic environments will be far fromoptimal.

The inherent danger to humans of conventionalarms can be mitigated by drastically increasingtheir sensorization (using e.g. proximity–sensitiveskins such as those proposed by [7]) and changingtheir controllers. However, it is well known in therobotics literature that there are intrinsic limita-tions to what the controller can do to modify thebehaviour of the arm if the mechanical bandwidth(basically dictated by mechanism inertia and fric-tion) is not matched to the task (see e.g. [27]). Inother words, making a rigid, heavy robot to be-have gently and safely is an almost hopeless task,if realistic conditions are taken into account.

One alternative approach at increasing thesafety level of robot arms interacting with hu-mans is to introduce compliance right away at themechanical design level. Accuracy in positioningand stiffness tuning would then be recovered bysuitable control policies. This approach is clearlycloser in inspiration to biological muscular appara-tuses than to classical machine-tool design, whichhas inspired most robotics design thus far.

Several projects are being pursued in researchlabs towards the design of passively compliant, bi-ologically inspired arms. Particular attention hasbeen devoted to the development of suitable actu-ators (see e.g. [15, 16, 6, 25, 24, 2]). Studies on theorganization of motor control in humans (see e.g.

[17, 12, 10, 22, 3]) have been used to inspire con-trol architectures of anthropomorphic robots (e.g.,[23, 19]).

In this paper, we describe our approach to in-trinsically safe robot arm design, and a prototypearm built in our laboratory. The main charac-teristic of the arm is that it introduces relativelyhigh, controllable compliance at the mechanicallevel. The arm is designed to achieve positiontracking in 3D with variable effective complianceat the joints. Rather than achieving complianceby methods based on controller synthesis, in ourdesign we have compliant nonlinear actuatorsthat offer intrinsic compliance (hence safety),even in cases where the controller may fail. Onthe other hand, modern control techniques areadopted to recover accuracy in positioning and intuning the arm compliance to accomplish taskswhich require those features.

1 Compliance of Robot Arms

M ethods for achieving compliance in robotmanipulators have been studied since very

early in the robotics literature.Most of the work has been concerned with

task–space specifications of compliance of theend–effector with respect to a desired posture, orreference trajectory ([26, 14]). The basic idea ofis that the rigid nature of robotic arms is com-pensated by control by suitably setting the gainsof joint position servos so as to achieve a desiredeffective compliance at the end–effector (see fig.1,top). However, these approaches may not proverobust with respect to such model nonidealities ase.g. friction and backlash in transmission ([27]),by the simple reason that the insufficient me-chanical bandwidth of the actuators/transmissionsubsystem does not allow the controller to takesuitable countermeasures to unexpected collisionsof the arm or delays in feedback (fig.1, middle).

Figure 1: The classical approach to stiffness andimpedance control amounts to independently tun-ing the set-point and the gains of a position con-troller (top). If applied to a rigid arm, the in-sufficient mechanical bandwidth of actuators andtransmission may not allow the controller to takesuitable contermeasures to unexpected collisionsof the arm (middle). To guarantee higher priorityto safety than to performance, a certain amountof passive (mechanical) compliance can be pur-posefully introduced in the system, while advancedcontrol can be used to recover accuracy (bottom).

As a consequence, severe harm to persons dealingwith the robot arm can ensue if the robot is usedin anthropic environments. In such applications,it seems to be preferrable that the arm is designedto be passively compliant, by e.g. includingcompliant transmission so as to prevent buildingup of excessive forces in the transients. Passivecompliance, along with low inertia, are the twobasic elements of inherently safe mechanismdesign (fig.1, bottom.). The role of control designwith passively compliant arms is in some senseconverse to that described above, and consistsof compensating compliance of the mechanicalstructure of the arm, to achieve acceptable levelsof accuracy in positioning.

A first possibility to realize robot arms with

a low damaging potential to interacting humansis to have large mechanical compliance of thetransmission between actuators and arm joints.By these means, indeed, the effective inertia atan impact of the arm is reduced with respect torigid transmission, by decoupling the contributeof actuators’ moving parts. This is particu-larly important for electrical motors using highreduction-rate gearboxes, also in view of theirusually high static friction, which may preventbackdrivability. In many applications, however,the arm may have to perform different tasks,for which different compliance may be necessary.Hence, the need for a different type of robot armdesign, with passive and tunable compliance.Robots arms of this type will be referred to as“soft”, and will be considered in detail in the restof this paper.

Perhaps, the simplest configuration of a softjoint actuation system is that illustrated in fig.2.Here, two actuators are connected to the samejoint in an agonistic-antagonistic arrangementthrough mechanically compliant elements (de-picted as springs). It is important to notice thatactuators are conservatively assumed here to be“position sources”, rather than “force sources”:in other words, we assume that set-point posi-tions θ1, θ2 are maintained by the actuators despitechanges of the applied forces. In other words, theeffective compliance of the manipulator arm willnot rely on any closed-loop control on actuators(although the set-points can be changed by thecontrollers, we do not want to rely on this to en-sure safety). The torque τ applied to the joint,

Figure 2: An agonistic-antagonistic arrangementof two actuators on a joint to control joint positionand stiffness independently.

corresponding to a joint angle q, actuator angular

positions θ1 and θ2, is given by

τ = R [k1(rθ1 − Rq) + k2(rθ2 + Rq)] (1)

with R the radius of the joint pulley, r the radiusof the actuator pulleys, and k1(q, θ1), k2(q, θ2) de-note the transmission stiffness functions. The ef-fective joint compliance is defined as the infinites-imal variation of the joint angle corresponding toan infinitesimal change of external torque at thejoint, while actuator inputs are held constant. Theinverse of this quantity, i.e. the effective joint stiff-ness σ, is simply evaluated as

σ = ∂τ∂q =

R2(k1 + k2) + R[

∂k1∂q (Rq − rθ1) − ∂k2

∂q (Rq + rθ2)] .

It can be easily observed that, if transmission stiff-nesses ki are constant, the joint stiffness is inde-pendent of the actuator inputs. In this case, in-deed, only joint position regulation would be al-lowed, while the joint stiffness remains constant(σ = R2(k1 + k2)), independently from θ1, θ2 (andfrom q). On the other hand, a nonlinear transmis-sion stiffness ki(q, θi) may allow the simple passivecompliance scheme above to allow tunable compli-ance.

More generally, we will refer to a whole class ofpossible agonistic-antagonistic actuator arrange-ments by defining the characteristic function of ajoint,

τ = φ(q, θ) (2)which models the generation of the effective torqueat the joint, τ , as a function of the joint position,q, and of the m joint actuators commands, col-lected in the joint reference vector θ ∈ IRm. Forsuch a model, the open-loop joint stiffness is de-fined as the infinitesimal variation of joint torquecoresponding to an infinitesimal variation of thejoint position, while actuator inputs are kept con-stant, i.e.

σ =∂φ(q, θ)

∂q(3)

Let [τσ

]= Ψq(θ)

denote the map IRm → IR2 from actuator inputsto joint torque and stiffness. In general, it will bepossible to control the torque and the stiffness in-dependently in the vicinity of an equilibrium con-figuration q with inputs θ, if ψq(θ) is injective,hence the condition

rank∂Ψq(θ)

∂θ= 2.

Assuming this condition is met, and that two ac-tuators are connected to the joint (m = 2), thejoint characteristic functions can be inverted (atleast locally) to obtain

θ = Ψq(τ, σ)

Actuator commands can be distinguished be-tween effective torque-generating commands θt,i.e. those which modify τ leaving unaffected σ;and co-contraction commands θc, which modifythe joint stiffness without affecting joint balance.Explicitly, we let

θt(τ) = Ψq(τ, σ = const.)θc(σ) = Ψq(τ = const., σ)

When building a “soft” robot arm with tunable,passive compliance, multiple actuators have to beconnected to the arm’s joints. Several arrange-ments are in general possible to map actuatorsto joint torques: for instance, the Salisbury hand[21] achieved a single-parameter tunable compli-ance for each of its fingers by actuating the threejoints of the fingers by four independently driventendons. In our design, however, we are interestedin the capability of tuning the compliance of alljoints independently, and will hence refer to thecase that an arrangement of (at least) two actua-tors per joint is adopted.

2 Actuators for passive compliancecontrol.

In this paragraph we consider the design of actu-ators systems that could be used to control in-

dependently joints position and stiffness of a robotarm, providing two examples that can be easilyimplemented in practical devices.

A first type of passive, tunable compliance jointcan be obtained by the use of conical compressionsprings. The force-length relationship of conicalsprings, such as that depicted on the left in fig.3,is a function of several design and material param-eters (such as upper and lower coil diameters, wirediameter, spring length, number of coils, elastic-ity and shearing moduli of the steel, etc.), whichcan be accurately evaluated by mechanical engi-neering CAD software packages. An example ofthe characteristic line (force path diagram) of aconical helical compression spring obtained by theHexagon c©Spring Software [13], is reported on theright of fig.3. Notice that the characteristic linebecomes progressively steeper at the point wherethe larger coils begin to touch. By careful de-

Figure 4: A possible arrangement of electrical actuators, tendons and conical springs to achieve tunablecompliance at a robot joint.

Figure 3: Conical compression spring: force-length characteristics and design.

sign and suitable preloading, conical springs canbe made to work in the nonlinar region, wherethe force path is approximately parabolic. No-tice that the nonlinear behaviour can only be ob-tained by compression of a conical spring. A pos-sible scheme to apply conical springs to actuaterobot joints using flexible tendons is reported infig.4. To compute the joint characteristic functionfor the arrangement in fig.4, let us assume that inthe working region the force path of each conicalspring can be simply modeled by a parabolic lawas

Fs = γs2,

where Fs represents the spring force, γ is a con-stant parameter that depends on constructive de-tails, and s is the contraction of the spring.

The inputs to the joint are the angular positions

of the two motors, i.e. θ = (θ1, θ2)T . Hence, thejoint torque characteristic function is

τ = φ(q, θ) = γR(s21 − s2

2),

where s1 = (θ1r − qR) and s2 = (θ2r + qR) arethe spring deformations (positive if compressive).The joint stiffness is easily evaluated as

σ =∂τ

∂q= 2γR2(s1 + s2).

That the compliance can be tuned independentlyfrom the applied torque can be checked by verify-ing that

det

[2γRrs1 −2γRrs2

−2γR2r −2γR2r

]= −4γ2R3r2(s1 + s2)

is not zero, provided that both springs are incompression (which has of course to be the case,in order for the tendons to be in tension in thearrangement of fig.4). Indeed, for this arrange-ment, the inverse map Ψ : (τ, σ) �→ θ providingthe motor angular positions corresponding to adesired torque and stiffness, can be explicitlyevaluated as{

θ1 = Rr q + R2τ

σ + σ4γR2

θ2 = −Rr q − R2τ

σ + σ4γR2

(4)

Another possibility to build tunable complianceis to use McKibben actuators (fig.5). As it iswell known, these are pneumatic actuators con-sisting of an inner inflatable tube, closed at the

ends and surrounded by braided cords. Chou andHannaford [8] provided a detailed analysis and anaccurate, yet simple model of McKibben actua-tors, which can be summarized as

f = (kL2 − b)p

where p denotes the pressure in the inner tube,L the actuator length, f the force applied at itsends, k and b two constant parameters dependingon constructive details. The model is valid underthe condition that

√b/k < Lmin ≤ L ≤ Lmax,

which implies f > 0. We will henceforth assumeactuators to work in such operating region. For

Figure 5: A McKibben pneumatic artificial musclebuilt in our laboratory.

a robot joint actuated by two identical McKibbenactuators in antagonistic arrangement as shownin fig.6, the joint characteristic functions for jointtorque τ and stiffness σ, assuming commands tobe control pressures, θ = (p1 p2)T , are obtained as

τ = φ1θ1 − φ2θ2

σ = φ′1θ1 − φ′

2θ2(5)

whereφ1 = Rk(L2

1 − L2min)

φ2 = Rk(L22 − L2

min)φ′

1 = −2R2kL1

φ′2 = −2R2kL2

In this case, it holdsd = det ∂Ψq(θ)

∂θ = −2R3k2[L2(L21 − L2

min) + L1(L22 − L2

min)]which is strictly less than zero in the operatingregion for the actuators, where they are stretched

Figure 6: Model of a joint actuated by two antag-onistic McKibben actuators.

to less than their minimum length. Hence, themap (5) from control pressures to joint torqueand stiffness is invertible:

θ =[ −1

d2R2kL21d2R2kL1

]τ +

[ 1dRk(L2

2 − L2min)

1dRk(L2

1 − L2min)

]σ.

(6)The linearity of this inverse ensues that the spaceof actuator commands can be regarded as thecartesian product of the two subspaces of torque-generating commands and co-contraction com-mands.3 Problems in controlling passively

compliant arms

In this section, we will review some of the prob-lems that are encountered when controlling pas-sively compliant arms, providing pointers to pa-pers where these problems have been solved, orpointing at important open problems.

The problem of controlling flexible arms hasbeen studied extensively in the robotics literaturesince early times, in relation to both link flexibil-ity ([29]) and joint compliance [30]. Techniques foraccurately controlling positions in these cases ex-ist, which are based on advanced nonlinear controltechniques (see e.g. [9]). These typically assumeknowledge of accurate models of compliance andinertial parameters.

If such knowledge is not available, adaptive con-trol methods that could cope with such uncertain-ties should be used. The problem of adaptationto uncertain inertial parameters, in the presenceof known elasticity, has been widely studied (seee.g. [5]). Adaptation to unknown stiffness pa-rameters is a tougher problem, though, due to thefact that compliance parameters enter nonlinearlyin the dynamic equations.

Some preliminary results in this directions havebeen recently obtained ([4]), showing that un-known but constant flexible joint models can be

identified measuring only link positions. This ca-pability can be used to build an adaptive controllerfor position tracking with robot arms that havelarge unknown joint compliance. Another possibleapproach, explored e.g. in [20], is to use learningcontrol techniques.

Although accurate control of arms with large,constant (or mechanically adjustable) joint flexi-bility is to be considered an important directionfor research, we already pointed out that in manyapplications robots may have to perform differ-ent tasks, for which different compliance may benecessary. Hence, the need for soft arms with apassive but tunable compliance.

The general model of an n degrees of freedomrobot arm, actuated by a tunable compliance ac-tuation system, can be given as

Bq + h(q, q) = φ(q, θ) (7)

where q and θ will be regarded, from now on, asthe vector of joint angles and of actuator commandvalues, respectively. Actuator dynamics shouldin general be considered to be coupled with (7),which may have the form

x = f(x, q)Θ = h(x, q) (8)

For instance, in nonlinear spring actuator arrange-ments, one would have to consider for the latter{

J1θ1 + γS21R = τ1

J2θ2 + γS22R = τ2

with s1, s2, R, r as above specified, J1, J2 the mo-ments of inertia of the electric motors and τ1, τ2

the actuator torque vectors. For the McKibbenactuator arrangement, the dynamics of the elec-trovalve and air conduits should be considered. Insome cases, for the sake of simplicity, it may beassumed that the response of actuators to com-mands is locally regulated by a quick and accurateinner control loop (as e.g. in fig.7), so that one canassume Θ to be directly available as a control in-put. An important control objective is to guaran-tee that arbitrary trajectories of the end–effectorcan be controlled while stiffness is controlled todesired values, without the two specifications inte-fering with each other (decoupled control). Someresults in this direction have been presented in [4].

Naturally, the dynamic control of tunable com-pliant arms inherits many of the problems with thecontrol of flexible arms, but only partially can they

enjoy solutions provided in that field. A key dif-ference is the presence of essential nonlinearities inthe model of soft arms, which obviously make con-trol much harder. This is particularly true whenan exact model of the system parameters is notavailable, and adaptation is necessary.

A possibility to independently control the po-sition and the stiffness of a soft robot arm is toadopt the Internal Model approach used in thebiomechanical theory of human motion [17]. Thistheory admits the existence of a (learned) dynamicmodel of the human arm in its sensory-motor con-trol. Such model, with unknown constant param-eters, is continuously adapted by a feedback adap-tive control, that generates the model parametersestimation [28].

4 Design, realization and preliminaryexperiments with a “Soft Arm”

As discussed in the previous sections, our ap-proach at designing intrinsically safe robot

arms is to use agonistic-antagonistic, compliantarrangements of actuators, in a rather anthropo-morphic fashion.

The three degrees of freedom robot arm devel-oped in our laboratory presents also has anthropo-morphic kinematics (fig.8), lightweight structure.The current version employs McKibben artificialmuscles, and is endowed with a simple light-weightgripper (see fig.9)

The control hardware of the Soft Arm is repre-sented by a 333Mhz PC Workstation, three po-sition feedback linear potentiometers, an ADCADAC 5803HR and a DAC Advantech PCL726boards. The pressures are controlled in the pneu-matic muscles by six pneumatic servovalves SMCITV2050. The arm has no sensors, except forjoint position encoders: in particular, all interac-tion tasks are performed without measuring con-tact forces, which are kept within acceptable limitsby virtue of the compliant structure of the arm.

Preliminary experiments in human–robot inter-action, with disturbances at different frequenciesinduced by the operator in the structure (fig.10),have been focused on testing the mechanical ro-bustness of the robot arm and the capability of thecontrol system to varying the system bandwidth(in other words, the robot capability to interactwith the environment with more or less sensibilitywith respect to external unpredictable distubancesor controller delays or failures). One importantresult is that the use of intrinsic compliant actua-tors, instead of “rigid actuators”, such as electric

Figure 7: Nonlinear actuators control system where, in particular, qd, θd are, respectively, vectors con-taining the desired joints and motors positions and Ψ represents the map between the joint torques andstiffness in equation (4). The fast inner control loop of the actuators is highlighted.

motors, and the possibility to varying the “open–loop” joints compliance (the variable σ in the pre-vious sections), increase the robot arm robustnesswith respect to unmodelled disturbances.

Figure 8: The Soft Arm is a lightweight structureactuated by McKibben artificial muscles in antag-onistic pairs with an antropomorphic kinematics.

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