Preprint version 2012 IEEE International Conference on Robotics and Automation, St. Paul, MN

Bilateral Teleoperation of a Group of UAVs with CommunicationDelays and Switching Topology

Cristian Secchi, Antonio Franchi, Heinrich H. Bulthoff, and Paolo Robuffo Giordano

Abstract— In this paper, we present a passivity-based de-centralized approach for bilaterally teleoperating a group ofUAVs composing the slave side of the teleoperation system. Inparticular, we explicitly consider the presence of time delays,both among the master and slave, and within UAVs composingthe group. Our focus is on analyzing suitable (passive) strategiesthat allow a stable teloperation of the group despite presenceof delays, while still ensuring high flexibility to the grouptopology (e.g., possibility to autonomously split or join duringthe motion). The performance and soundness of the approach isvalidated by means of human/hardware-in-the-loop simulations(HHIL).

I. INTRODUCTIONGroups of mobile robots have proven to be very effectivein solving complex tasks like surveillance, exploration andsearch and rescue, and the problem of implementing adesired emerging behavior of a group has received a lot ofattention in the last years (see, e.g., [1], [2]). Nevertheless,when the task is very complex, autonomy of the fleetis far from being reached and the human intervention isstill necessary. Therefore, bilateral teleoperation of a semi-autonomous group seems a very promising solution. In fact,in this way the user can guide the robots by a master interfaceand receive an informative feedback on the status of thegroup. In particular, a force feedback should be includedsince it improves the skills of the human during teleoperationas shown in [3].

The bilateral teleoperation of a group of robots is anemerging research area in the telerobotics community andseveral works addressed this problem [4], [5], [6]. Becauseof their extreme flexibility and their high mobility, teleoper-ation of groups of Unmanned Aerial Vehicles (UAVs) (theso-called Aerial Teleoperation) has been addressed in [7],[8], [9], [10], [11]. In particular, in [9] a highly flexibledecentralized control strategy was proposed in which theUAVs were allowed to change the shape of the group bymeans of split and join maneuvers, while guaranteeing bothinter-agent and obstacle collision avoidance. In this way, theuser could simply focus on the motion of the group and feelthe state of the fleet and of its interaction with the remoteenvironment through a visual and force feedback.

C. Secchi is with the Department of Science and Methods of Engineering,University of Modena and Reggio Emilia, via G. Amendola 2, MorselliBuilding, 42122 Reggio Emilia, Italy cristian.secchi@unimore.it

P. Robuffo Giordano and A. Franchi are with the Max Planck Institutefor Biological Cybernetics, Spemannstraße 38, 72076 Tubingen, Germany{prg,antonio.franchi}@tuebingen.mpg.de.

H. H. Bulthoff is with the Max Planck Institute for Biological Cy-bernetics, Spemannstraße 38, 72076 Tubingen, Germany, and with theDepartment of Brain and Cognitive Engineering, Korea University, Anam-dong, Seongbuk-gu, Seoul, 136-713 Korea hhb@tuebingen.mpg.de.

However, as in any teleoperation setting, non-negligibletime delays can be present both in the communicationchannel between master and slave side, as well as within themembers of the group. Although both kinds of delays havedestabilizing effects if not properly handled, this problem israrely addressed in the multi-slave teleoperation literature.A notable exception are [4], [7] where the passifying PDaction proposed in [12] is used for handling the delayedcommunication between master and slave.

In this context, the goal of this work is to extend the(passivity-based) framework proposed in [9] so as to ex-plicitly consider communication delays between master andslave, and within the (multi-UAV) slave system. In orderto preserve the passivity of the teleoperation system andto deteriorate the quality of the force feedback as less aspossible, the interconnection between master and slave isimplemented by extending the two layer approach proposedin [13] to the multi-slave teleoperation case. This strategyallows to obtain the highest possible transparency allowedby the passivity constraint. Furthermore, in order to preservethe flexibility of the group of UAVs, we also detail twonew procedures for passively implementing split and joinmaneuvers in case of delayed communication among theagents at the slave side.

The paper is organized as follows: in Sec. II a briefsummary of the distributed control strategy proposed in [9]is summarized for the reader’s convenience. In Sec. III, anextension of the two layer framework for the multi-slaveteleoperation case is developed, and Sec. IV presents twoprocedures for implementing split and join maneuvers in caseof communication delays. After discussing human/hardware-in-the-loop simulations in Sec. V aimed at to validatingthe proposed approach, Sec. VI draws the conclusions andaddresses future perspectives.

II. BACKGROUND MATERIAL

In this Section, the passive and decentralized control strategyfor the teleoperation of a group of UAVs proposed in [9]is briefly summarized. Each UAV is modeled as a floatingmass in R3 and the slave side consists of a group of Nagents among which a leader is chosen. The motion of eachUAV depends on the motion of the surrounding vehicles,while the motion of the leader depends also on its couplingwith the master. In order to consider the difference betweenthe bounded workspace of the master and the unboundedworkspace of a UAV, the position of the master is treatedas a velocity setpoint for the leader at the slave side andthe difference between the position of the master and the

velocity of the leader generates a force at the master sidefor feeding back to the user an information about the motionstatus of the fleet.

A. The Master Side

The master can be a generic fully actuated mechanical systemdescribed by the following Euler-Lagrange equations:

MM (xM )xM + CM (xM , xM )xM +BM xM = FM (1)

where MM (xM ) represents the inertia matrix,C(xM , xM )xM is a term representing the centrifugaland Coriolis effects, and BM is a matrix representing boththe viscous friction present in the system and any additionaldamping injection via local control actions. We also assumethat gravity is locally compensated. The variables xM andvM := xM represent the position and the velocity of theend-effector. In order to passively couple the position ofthe master to the velocity of the leader, in [9] we proposeda local control loop that renders the master passive withrespect to the pair (FM , rM ) at the expense of possibleincreases in the master damping BM , where

rM = ρvM + ρλxM , ρ > 0, λ > 0. (2)

By properly choosing the design parameters ρ and λ , it ispossible to reduce the contribution of vM and to make thesecond term equal to KxM , where K is a desired scalingfactor. Thus, the rM variable approximates the (scaled)position of the master but, during fast motions, the velocityterm ρλvM may act as a disturbing effect.

B. The Slave Side

1) Model of the agents: The UAVs are assumed to beendowed with a Cartesian trajectory tracking controller (as,for instance, the one proposed in [14]) ensuring a closed loopbehavior close enough to that of a fully actuated floatingmass in R3. We then model each agent, and its local controlstructure, as:

pi = F ai + F e

i −BiM−1i pi

ti = (αi 1tiDi + wi)

yi =(M−1i piti

) i = 1, . . . , N. (3)

Here, pi ∈ R3 and Mi ∈ R3×3 represent the momentum andthe inertia matrix of agent i, respectively, Ki = 1

2pTi M

−1i pi

is the kinetic energy stored by the agent during its motion,and Bi ∈ R3×3 is a positive semidefinite matrix representingan artificial damping added for asymptotically stabilizingthe behavior of the agent. Forces F a

i ∈ R3 and F ei ∈ R3

represent the interaction of agent i with other agents andwith the external world (i.e., the obstacles or the master side),respectively.

The power dissipated by the agents because of their localdamping Bi, i.e.,

Di = pTi M−1i

TBiM

−1i pi, (4)

is monitored and stored back into the local energy variableTi = 1

2 t2i ∈ R called tank, whose state ti ∈ R augments the

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

90

dij [m]

V[J

]

d0 D

0 1 2 3 4 5 6 7 8−140

−120

−100

−80

−60

−40

−20

0

20

40

dij [m]

Fa ij

[N]

d0 D

Fig. 1: The shape of the interagent potential as a function of thedistance (left), and its corresponding coupling force (right).

agent dynamics in (3). The quantity αi ∈ {0, 1} in (3) is acontrol parameter used to disable/enable the storage of Di

into the tank. In fact, because of the reasons reported in [15],the energy stored in the tanks needs be bounded by abovein order to avoid the implementation of practically unstablebehaviors. Thus, αi is set to 0 if the energy stored in the tankreaches an upper bound Ti to be selected depending on theparticular application. We also set a small threshold ε > 0below which energy extraction from the tank is prevented,in order to avoid singularities in (3).

The quantity wi ∈ R in (3) is an additional input usedto exchange energy with the tank through the port (wi, ti).Finally, the outputs of the overall system (3) are the velocityof the agent vi = M−1

i pi and the tank state ti. It is possibleto prove that system (3) is passive w.r.t. its input/output ports,see [9].

2) Decentralized inter-agent interactions: Two agents areassumed to sense each other and to communicate (i.e., theyare considered as neighbors) if their relative distance dij isless than D ∈ R+. Furthermore, agents can measure thedistance from any obstacle located within the range D. Theagents are coupled so as to achieve a flexible, cohesive andcollision free behavior by means of a set of interaction forces

F ai =

∑j 6=i

F aij . (5)

For each neighboring agent j, agent i computes an inter-agent interaction force F a

ij whose magnitude and directiondepends on the relative distance and bearing respectively.This force is designed so as to regulate the distance betweenthe agents to a desired value d0, to prevent collisions betweenthe agents, and to vanish as the distance among the agentsbecomes larger than D. Figure 1 depicts the shape of apossible inter-agent force and associated scalar potential asa function of the inter-robot distance dij .

As explained in [9], such interaction force can be ex-pressed as a nonlinear spring whose lower bounded potentialenergy function V depends on the relative position amongthe agents xij := xi − xj ∈ R3. Formally,{

xij = vijF aij = ∂V (xij)

∂xij

(6)

where vij = vi−vj is the relative velocity among the agents.We note that the overall interaction force (5) can be computedin a decentralized way since, if agent j is not detected, i.e.,it is not a neighbor, it is considered as being farther than Dand a null force is implemented.

Preprint version 2 2012 IEEE ICRA

01

23

45

67

80

10

20

30

40

50

60

70

80

90

dij

[m]

V [J]

d0

D

obstacle

UAV1

UAV2

Split Join Esplit Ejoin > EsplitNo interaction

Fig. 2: When two agents split, the energy Esplit is stored in thespring, while when they join the energy Ejoin > Esplit is neededto implement the new desired coupling. In this case, without properstrategies, an amount Ejoin − Esplit > 0 of energy would beintroduced into the system, thus violating passivity.

3) Split and join decisions: In order to enable the fleet toreshape its formation and/or to vary its topology in a flexibleway, the agents are allowed to autonomously implement splitand join decisions based on suitable strategies dependingon the particular situation. We then refer to a split as thecancelation of the coupling force F a

ij between a pair of agentsi and j even though dij ≤ D. A join is the (re-)establishmentof the coupling, e.g., after a split. Clearly, a join can happenonly if dij ≤ D. Intuitively, a split between two agentsmimics the disconnection from the virtual elastic element Vijthat represents their coupling. The spring becomes isolatedand keeps on storing the same energy that was storing beforethe split decision, while the agents keep on interacting withthe rest of the system. Thus, a split is a passivity preservingdecision.

A join decision, on the other hand, can lead to a violationof passivity: when two agents i and j join, they instanta-neously switch from a state characterized by no interaction,to the inter-agent interaction represented by (6). Some extraenergy can be produced during the join procedure, possiblythreatening the passivity of the system. In fact, in the generalcase, the relative distance of two agents at the join decisioncan be different from their relative distance at the splitdecision, and this can result in a non passive behavior: theillustrative example of Fig. 2 shows this situation.

To remedy this problem, we exploit the energy in thetanks Ti in order to passively implement join decisions thatwould otherwise violate the passivity constraint. In short, inthe critical case of Fig. 2, agents i and j implement a joindecision only if the sum of the energy stored in their tanksis greater than the energy produced by the (re-)establishmentof the coupling. When this is not the case, tanks are suitablyrecharged by increasing the local damping Bi (or by moresophisticated techniques) until there is enough energy forimplementing the join. This procedure can be modeled as anexchange between the tanks and the nonlinear springs thatcouple the agents through the inputs wi1.

4) Passivity of the overall slave side: Since the forcesF aij are symmetric, the interactions among the agents can

be modeled as an undirected graph G = (V, E) where thevertices represent the agents and an edge (i, j) representsthe presence of a spring coupling agent i with agent j.

1Full details of this strategy, as well as of additional techniques to suitablyredistribute the tank energies among the agents, can be found in [9].

Defining p = (pT1 , . . . , pTN )T ∈ R3N , B = diag(Bi), x =

(xT12, . . . , xT1N , x

T23, . . . , x

T2N , . . . , x

TN−1N )T ∈ R3

N(N−1)2 ,

v = (vT1 , . . . , vTN )T ∈ R3N and F e = (F eT1 , . . . , F eTN )T ∈

R3N , the overall slave side (agents-tanks-springs) can beshown to take the compact form:

0@pxt

1A =

240@ 0 I 0

−IT 0 ITγ0 −Iγ 0

1A−0@ B 0 0

0 0 0−αPB 0 0

1A35∇H +GF e

v = GT∇H(7)

where ∇H =(∂TH∂p

∂TH∂x

∂TH∂t

)Tand

H =N∑i=1

Ki +N−1∑i=1

N∑j=i+1

V (xij) +N∑i=1

Ti (8)

represents the total energy of the overall slave side. More-over, I = IG⊗I3, with IG being the incidence matrix of thegraph G whose edge numbering is induced by the entries ofthe vector x. Matrix G =

((IN ⊗ I3)T 0T

)T, with I3 and

IN being the identity matrices of order 3 and N respectively,0 represents a null matrix of proper dimensions, and ⊗denotes the Kronecker product. The matrix Iγ = Γ◦(1⊗IG),where ◦ is the element-wise product, 1 =

(1 1 1

)T,

and Γ is a matrix of proper dimensions whose elementsrepresent an energetic interconnection between tanks andsprings mediated by the inputs wi in (3). Matrix P describesthe storage of energy into the tanks and takes the expression

P = diag(1tipTi M

−Ti ) i = 1, . . . , N (9)

Finally, α = diag(αi)is the matrix containing the switchingparameters, t = (t1, . . . , tN )T , and c = (c1, . . . , cN )T . It ispossible to show that that the system represented in (7) ispassive with respect to the pair (F e, v) using H as a storagefunction.

C. The Teleoperation System

Let the agent L be the leader. It is possible to decomposeF eL = Fs + F env

L , where F envL is the component of the

force due to the interaction with the external environment(obstacles) and Fs is the component due to the interactionwith the master side. Similarly, we can decompose FM in (1)as FM = Fm + Fh, where Fh is the component due to theinteraction with the user and Fm is the force acting on themaster because of the interaction with the slave.

For achieving the desired teleoperation behavior, masterand slave sides are joined using the following interconnec-tion: {

Fs = −bT (vL − rM )Fm = bT (vL − rM ) (10)

where bT > 0 is a design parameter. This is equivalentto joining the master and the leader using a damper whichgenerates a force proportional to the difference of the twovelocity-like variables of the master and the leader. SincerM is “almost” the position of the master, see Sect. II-A, theforce fed back to the master and the control action sent tothe leader are the desired ones. The complete teleoperation

Preprint version 3 2012 IEEE ICRA

FhviFm

Masterrm

Slave

Fs

ObstacleF e

j

vjrm Leader

(robot i)

Followers

robot j

Fig. 3: The overall teleoperation system.

system, represented in Fig. 3, consists then of the intercon-nection of a passive master side, a passive interconnectionand a passive slave side. Recalling that the interconnectionof passive systems is again passive, we can conclude that theteleoperation system is passive w.r.t. external actions (humanforce Fh and environment).

III. A TWO LAYER APPROACH FOR DELAYEDMASTER-SLAVE COUPLING

In this Section, we will extend the bilateral control strategysummarized in Sec. II in order to guarantee a passivebehavior in case of non negligible communication delaysbetween master and slave sides. To this end, we will adaptthe two layer approach proposed in [13] for the followingreasons: first, thanks to its flexibility, this approach can beeasily adapted to our framework, and, second, it allows topassively implement any desired coupling force in presenceof master/slave communication delays. Therefore, besidesproviding robustness against delays, it will also be possible toavoid the use of the rM variable in (10) and to implement themaster/slave coupling by directly using the master positionxM .

Consider the Lagrangian model of the master in (1) whichcan be rewritten in a port-Hamiltonian form [16] as:8>>><>>>:„pM

xM

«=

»„0 −II 0

«−„BM 0

0 0

«– ∂HM∂pM∂HM∂xM

!+ (Fh + FM )

vM = ∂HM∂pM

(11)where pM is the momentum and HM = 1

2pTMM

−1M (xM )pM

is the kinetic energy.Similarly to what done for the agents within the slave

side, we propose to keep track of the energy dissipated bythe master using a local tank variable tM ∈ R. Thus, theaugmented dynamics of the master becomes:8>>>>>>>>>>>>><>>>>>>>>>>>>>:

0@pMxMtM

1A =

240@ 0 −I −wMI 0 0

wTM 0 0

1A −0@ BM 0 0

0 0 0−αMPMBM 0 0

1A350BB@∂HM∂pM∂HM∂xM∂TM∂tM

1CCA +

0@ Fh0

1tM

(αMMPin −MPout)

1Av =

∂HM∂pM

(12)

where TM = 12 t

2M , PM = 1

tMpTMM

−TM (xM ), and the

quantities MPin and MPout represent power flows that allowthe master tank to exchange energy with the external world.The energy dissipated by the master is given by:

DM = pTMM−TM BMM

−1M pM (13)

Using (12) it can be seen that

TM = αMDM + wTM∂HM

∂pM+ (αMMPin −MPout) (14)

Master

Tm TL

Leader

F1

F2

Fn

CommunicationChannelmPin

mPoutsPin

sPout

Fh

vm

vm tm v1 t1Passivity  Layer

Transparency  Layer

Fmd Fsd

Fig. 4: The two layer architecture for the multi-slave teleoperation.

As before, the parameter αM ∈ {0, 1} disables the storage ofenergy in the tank when TM (tM ) is greater than a selectedupper bound TM . The variable wM ∈ RN is a controlparameter that allows to exploit (i.e., to extract or inject)the energy of the tank for reproducing the desired controlaction Fm from (10) by setting wM = −FmtM . In order toavoid singularities (tM = 0), it is necessary to set a lowerthreshold εM > 0 under which energy cannot be extractedfrom the tank (either using wM or MPout).

Now consider the leader: this is subject to three forces,i.e., the master/leader coupling force Fs, the inter-agent forceF aL and the external (obstacle) force F extL . In order to couplethe leader with the master in presence of delays, we extendagain the model reported in (3) for allowing the leader toimplement Fs using the energy stored in its tank. Thus, theleader model becomes:

pL = −BLM−1L pL − wstL + F ∗

tL = αLtLDL + 1

tL(αLsPin − sPout) + wTs vL + wL

yL =(vLtL

)(15)

where F ∗ = F envL + F aL and the term ws ∈ R3 is usedfor implementing the desired coupling force Fs by settingws = −FstL . As for the input wL, this is still used to couplethe tank with the rest of the fleet as explained in the previoussection. Finally, the power flows sPin and sPout are usedto model an exchange of energy with external entities (themaster in our case).

Let T be the constant delay characterizing the communica-tion channel along which the master and leader exchange in-formation. Following the idea discussed in [13], we proposea teleoperation architecture, illustrated in Fig. 4, in whichthe exchange of information between master and slave sidetakes place over two distinct layers. In the passivity layer,energy is exchanged between the tanks using the signals ?Pinand ?Pout, where ? = M, s. Ensuring a proper exchange ofenergy at this layer is sufficient for guaranteeing the passivityof the teleoperation system. In particular, we propose tointerconnect the tanks over the communication channel by:

sPin(t) = MPout(t− T )

MPin(t) = sPout(t− T )(16)

Preprint version 4 2012 IEEE ICRA

The desired coupling forces are then generated locally usingonly the energy available in the tanks: therefore, one canuse the exact position of the master xM instead of the rMvariable in (10). Over the transparency layer, the leader sendsits velocity vL to the master which computes FM (t) =bT (vL(t − T ) − xM (t)), the desired force to feedback tothe robot. Similarly, the master sends its position to theslave which computes the desired coupling force Fs =−bT (vL(t) − xM (t − T )). These forces are implementedusing the energy stored in the tank as shown in (12) and(15).

The tanks of the leader and of the master need to bealways “full enough” for allowing to passively reproduce thedesired control action. Therefore, for each tank, we definethe quantities T e• where • = M,L and ε < T e• < T•, torepresent a predefined emergency threshold below which thetank needs to be refilled. In order to control the exchange ofenergy along the communication channel, the master sendsto the leader an energy request signal MEreq(t) defined as:

MEreq(t) ={

1 if TM (t) < T eM0 if TM (t) ≥ T eM

(17)

In a similar way, the leader sends an energy request signalsEreq(t) to the master. The overall power extracted from themaster tank and sent to the leader is then given by:

MPout(t) = (1− αM )DM )t) +s Ereq(t− T )τ(TM (t),e TM )P(18)

where τ(TM (t),e TM ) is a threshold function which is 0if TM (t) <e TM and 1 if TM (t) ≥e TM . When thetank has reached its maximum level, αM = 0 and allthe energy dissipated is sent to the tank of the leader. Ifthe master receives a request of energy of from the tank(reqEs(t − T ) = 1) and if the tank is above the emergencythreshold (τ(TM (t),e TM ) = 1) a constant flow of powerP > 0 is extracted from the tank of the master and sent tothe slave. Similarly, the overall power sent from the leaderto the master is

sPout(t) = (1− αL)DL +M Ereq(t− T )τ(TL(t),e TL)P (19)

Remark 1: It can happen that the energy stored in the tankapproaches to ε either because the power flow from the otherside has not arrived yet or because there is not enough energyin the system. In this case, the only option for refilling thetank is to augment the local damping. The price to pay is aspurious dissipative force temporarily acting on the system.

Proposition 1: The system consisting of the master repre-sented in (12) and of the the leader represented in (15) thatexchange energy as indicated in (16) is passive.

Proof: The power flow along the communication chan-nel is given by

Hc(t) =M Pout(t)−M Pin(t) +s Pout(t)−s Pin(t) (20)

Using (16) in (20) we have that

Hc(t) =d

dt

∫ t

t−T(MPout(τ) +s Pout(τ))dτ (21)

Thus, the energy exchanged by the tanks is stored in thecommunication channel and is described by the followinglower bounded energy function

Hc(t) =∫ t

t−T(MPout(τ) +s Pout(τ))dτ > 0.

Consider now the combined master/leader/channel energyfunction:

H(t) = HM (t) + TM (t) +HL(t) + TL(t)(τ)

+∫ t

t−T(MPout(τ) +s Pout(τ))dτ (22)

Deriving (22) and using (12), (15) we obtain:

H = −(1−αM )DM−(1−αL)DL+αMPin(t)−sPout(t)++αL

sPin(t)− sPout(t)+FTh vM +F ∗vL+wTs tL+Hc(t)(23)

Since αM , αL ∈ {0, 1} the first and the second term arenegative. Using (20), we have that

αMMPin(t)−s Pout(t) + αLsPin(t)− sPout(t) ≤ −Hc(t)

(24)Thus, (23) can be rewritten as

H ≤ FTh vM + F ∗vL + wTs tL (25)

which proves the passivity of the system.Remark 2: In case of unreliable channels, some informa-

tion can be lost during the communication or the delay can bevariable. The passivity of the system can be preserved usingthe null packet strategy proposed in [17] and replacing with0 any unreceived information. It is straightforward to adaptthe proof proposed in [17] to our master-leader case.

The system composed by the master, the leader andthe communication channel is passive independently of thedelay. The system has three ports it can interact with the restof the world. The port (Fh, vM ) allows to interact with theuser, the port (vL, F ∗) allows to interconnect the leader withthe rest of the fleet and with the environment and the port(wL, tL) allows to interconnect the leader to the interagentpotential elements for passively implementing split and joinmaneuvers.

Thus, since the group of followers is a passive system andsince the interconnection of passive systems is still passive,the overall teleoperation system, obtained by interconnectingthe leader with the rest of the fleet, is passive independentlyof the communication delay.

IV. INTER-AGENT DECISIONS WITH DELAYSEvery agent is assumed to measure its relative positionw.r.t. neighboring agents by means of a position sensor, butinter-agent communication is still needed in order to agreeon the split and join decisions. Mobile wireless networksare the most suitable way for implementing a distributedcommunication among the UAVs but at the cost of somedelay, usually variable, in the exchange of information.We will indicate with ∆ > 0 an upper bound on themaximum communication delay between any two agents.

Preprint version 5 2012 IEEE ICRA

The implementation of the split and join maneuvers stronglyrelies on the exchange of information between the agents.Therefore, in this Section we will analyze the effect of thedelay during split/join decisions, and we will detail twoprocedures for still (passively) executing them in presenceof communication delay.

We will assume that the agents share a common clock(this can be done using any standard time synchronizationalgorithm, see e.g. [18]). Furthermore since the communi-cation happens only among neighboring agents, congestionproblems are very limited and we can assume that data isalways delivered.

Notice that, since the delay associated to the sensing isassumed negligible, the inter-agent behavior described in (5)can be safely implemented since it only depends on relativeposition measurements.

A. Delayed Split

In the non-delayed case described in [9], when agent idecides to split from agent j, it sends its decision to agent jso that both are able to implement the decision synchronouslysince the information is delivered instantaneously. The syn-chronicity guarantees the passivity of the split whose ener-getic meaning is that the agents get disconnected from thevirtual spring representing their coupling.

If the same strategy was implemented in the delayed case,passivity would not be preserved anymore. In fact, whenagent i splits, agent j keeps on generating a force F aji untilit receives the split decision. During this period the couplingcannot be modeled as a spring anymore because |F aij | 6= |F aji|and, therefore, the passivity of the fleet is threatened.

In order to ensure the passivity preservation during splitdecisions, we force agent i and agent j to plan and executea split at the same time instant in the future. In particular, ifagent i decides to split from j, then it sends, at time τ is, asplit notification to agent j with attached the time τ is + ∆.This represent the future time at which they are supposedto split. Since the delay is bounded by ∆ and the packet isalways delivered, agent j will be certainly able to performthe split at the required time. Nevertheless the split may beanticipated in two particular situations. First, in the case thatagent j decided also to split from i and sent a previous splitnotification at time τ js < τ is In this case, the split is performedat τ js + ∆. Second, whenever the two agents are not able toperceive their relative position anymore, because they movedout of the range of their sensors. In this last case the splitis synchronous since we assumed the sensing delay to benegligible.

Both agents store in the local variable Eij the energystored in the virtual spring at the moment of the split. Thisis done by measuring the relative distance using the onboardsensing.

B. Delayed Join

In the non-delayed case, when agent i decides to join withagent j, it sends a request which contains the amount ofenergy Ti, stored in its tank, to the agent j, which in turnreplies communicating to i the amount of energy stored in

the tank Tj . Since there is no delay, they can synchronouslycompute the amount of energy available, the amount ofenergy necessary for implementing the join, and decidewhether further refilling the tanks or to conclude the joinprocedure. This synchronous procedure is crucial for thepassive implementation of the join.

If the delay in the communication is not negligible, eachagent would receive an outdated information about the storedenergy. In fact, during the time necessary for delivering theinformation, the agent keeps on interacting with the rest ofthe fleet and the energy in the tank can change, e.g., candecrease. This makes the information not suitable for takinga decision about a passive implementation of the join. Aredesign of the join procedure is then necessary in order toensure the passivity of the decision.

In the delayed case the join procedure cannot be in-stantaneous and must be implemented with an handshakingmechanism. If at time τsi an agent i decides to join withagent j then it sends to agent j a join request with attachedthe amount of energy stored in its tank at time τsi , namelyTi(τsi ). Then agent i waits until the response of j arrivesat time τ ri ≤ τsi + 2∆. If the response is positive, then itcontains also the amount of energy stored in the tank ofj at the time τ rj when the response has been sent, namelyTi(τ rj ). The two agents then will try to join exactly at timeτsi +2∆. The amount of energy needed for implementing thejoin at time τsi + 2∆ is computed simultaneously by i andj using the sensed inter-distance. If this energy is less thanTi(τsi ) +Ti(τ rj ), then both the agents decide simultaneouslyto join since they have all the needed information to updatetheir tanks. Otherwise the join procedure is aborted and thehandshaking has to be started again if agent i is still willingto join with agent j. This last case (the abortion) applies alsoto the situation when the response from j is negative.

A few clarifications are needed for the proposed algorithm:1) : A locking mechanism ensures that, in case of join,

Ti(τsi + 2∆) + Tj(τsi + 2∆) ≥ Ti(τsi ) + Ti(τ rj ), i.e., theamount of energy considered available for the join is actuallypresent in the tanks. In fact, we assume that the agent i andj will reply negatively to any other join request from anotheragent k while they are waiting for the join response (in thecase of i) or they are about to try to join (for both agents).This is clearly a conservative strategy which could be inprinciple improved at the cost of an increased complexity(and fragility) of the join algorithm.

2) : If the join failed due to the absence of enough energyin the tanks, then the two agents may also temporary increasethe damping in order to refill their tanks before attemptingthe join another time.

3) : If agent j sent a join request before receiving the oneof agent i, then agent j has the precedence and the roles inthe description are exchanged.

4) : During the join negotiation, and in case the decisionis refused or aborted, no coupling force is implementedbetween pairs of agents and, therefore, there is the risk ofa collision. This can be avoided by augmenting the localdamping for “braking” an agent when it is too close and

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obstacles

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Fig. 5: Human-Hardware-in-the-loop setup

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Fig. 6: Results of the HHIL simulation. Left: superimposition of theleader velocity vL (solid lines) and the master position xM (dashedlines). Right: force cue Fm applied on the master and displayed tothe human operator

decoupled from another agent.5) : The tank of the leader can decrease even during a

join negotiation because of the interaction with the master.This problem can be solved dividing the tank into two parts:one reserved to the interaction with the fleet and the otherto the coupling with the master.

Using this strategy, a synchronous knowledge of theenergy available for implementing the join is reproduced.The price to pay to meet the passivity constraint is a moreconservative behavior with respect to the non delayed case.

V. HARDWARE-IN-THE-LOOP SIMULATIONS

In this section we report the results of a human/hardware-in-the-loop simulation (HHIL) aimed at validating the pas-sive teleoperation framework developed so far. Figure 5shows a snapshot of our setup which consists of a 3-DOFforce-feedback device, the Omega.32. As for the UAVs, theywere simulated in a physically realistic 3D environmentbased on the Ogre3D engine and the PhysX libraries forsimulating the interaction between the UAVs and the envi-ronment.

We considered N = 8 agents and simulated a master/slavedelay T = 1 [s] and a maximum inter-agent communicationdelay ∆ = 1 [s]. At every message sent by an agent, theactual communication delay δ was randomly drawn from auniform distribution taking values in (0, ∆]. Furthermore, inorder to show the generality of our approach, we did notconsider a particular strategy for taking split and join deci-sions, but implemented them as completely random eventswith independent probabilities of 1% of being triggered atevery simulation step.

Figure 6(a) shows the behavior over time of the threecomponents of the leader velocity vL(t) (solid lines), andthe corresponding (delayed) master command xM (t − T )

2http://www.forcedimension.com

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Fig. 8: Results of the HHIL simulation. Top left: energy flow sentfrom the master to the leader. Bottom left: energy request signalfrom the leader to the master. Top and bottom right: symmetricsignals from the leader to the master and viceversa

(dashed lines) during the HHIL simulation. We can notethe following: the leader is in general tracking the mastervelocity commands with a persistent steady-state error whichis especially visible when xM ' const. This is an expectedand desired behavior of our teleoperation framework due tothe ‘drag’ force exerted by the agents on the leader becauseof their local damping Bi, see [9], [11] for more details.In fact, it can be proven that this mismatch results into aforce cue informing the human operator about the absolutevelocity of the agents in the group. Still because of theinteraction of the leader with the other agents, one can notethe occasional small jerky behaviors in vL: these are mainlydue to the random split/join decisions over time taken by theleader and by its neighbors, and are also reflected as smallspikes in the force cue displayed to the human operator, asdepicted in Fig. 6(b). Here, one can also note how Fm iscorrectly representing the ‘steady-state’ mismatch betweenvL and xM (t−T ). As a final remark, note how all quantitieskeep bounded, proving the stability of the system despite thecommunication delays.

Figure 7(a) reports the behavior of the N = 8 tankenergies Ti over time, while Fig. 7(b) the behavior of TM ,the master tank energy. Note the frequent negative jumpsinto the the tanks Ti: these are the energy amounts extractedfrom the tanks in order to passify unsafe join decisions,as explained in Sect. II-B. Note also how the tanks getrefilled over time thanks to the energy dissipated by everyagent during its motion. The same also holds for the mastertank TM , although, since the master was kept almost fixedfor large portions of the simulation, its tank replenishmentproceeded at a slower rate compared to the agents. It is

Preprint version 7 2012 IEEE ICRA

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Fig. 9: Results of the HHIL simulation. Random values of δ, thecommunication delay applied to the messages sent by agent 7 atevery split/join request

interesting to note that at about t ≈ 36 [s] one of the agenttanks (the one of the leader) dropped below the emergencyvalue T eL = 5 [J ], therefore triggering the energy requestsignal sEreq of Sect. III. To illustrate this point, Figs. 8(a–b) show the time behavior of MPout and sEreq (left column),and sPout and MEreq (right column). Note how at t ≈36 [s], after an energy request is sent from the leader tothe master (sEreq = 1), a corresponding energy flow issent back from the master to the leader (MPout = P ). Thisis also reflected in the sudden increase of the leader tank(Fig. 7(a)) and corresponding decrease in the master tank(Fig. 7(b)). Because of this energy exchange, also the mastertank drops at its emergency value T eM = 1.5 [J ] at aboutt ≈ 41 [s], triggering the energy request signal MEreq = 1.This is followed by an energy flow from the slave to themaster (Fig. 8(b)) which allows to exit from this undesirablesituation.

As a final plot, we show in Fig. 9(a) the values of therandom communication delay δ at every split/join messagesent by agent 7. Note how (i) the split/join decision takesplace in a random way, and how (ii) the values of δ arerandomly distributed over (0, ,∆] as expected.

We finally encourage the reader to watch the video at-tached to the paper where a complete HHIL simulation isshown.

VI. CONCLUSIONS AND FUTURE WORKIn this paper, a passive teleoperation strategy for a group

of UAVs with switching topology was presented. Buildingupon previous results in this area, we focused our attentionon an often overlooked but actual issue in many teloperationsystems, that is, presence of time delays. Specifically, weconsidered presence of time delays among the master andslave system and within the agents composing a group. Thepotentially destabilizing action of such delays was dealt withby suitably monitoring the energy flows within the systemso that no excess of energy is created over time. This wasdone by means of passive and decentralized procedures andat the minimum possible expense for the transparency of theteleoperation system.

Although an experimental evaluation of the general tele-operation approach shared by this paper has already beengiven in [11] in the case of negligible delays, in the futurewe aim at experimentally testing the procedures discussedin this paper in more realistic settings involving significantcommunication delays as those discussed in the reportedsimulations.

ACKNOWLEDGEMENTSThis research was partly supported by WCU (World ClassUniversity) program funded by the Ministry of Education,Science and Technology through the National ResearchFoundation of Korea (R31-10008).

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