Passivity-Based Control of Human-Robotic Networks with Inter-Robot Communication Delays and Experimental Verification
J. Yamauchi, M.W.S. Atman, T. Hatanaka, N. Chopra, M. Fujita
aa r X i v : . [ c s . S Y ] F e b Passivity-Based Control of Human-Robotic Networks with Inter-RobotCommunication Delays and Experimental Verification
J. Yamauchi , M.W.S. Atman , T. Hatanaka , N. Chopra and M. Fujita Abstract — In this paper, we present experimental studies ona cooperative control system for human-robotic networks withinter-robot communication delays. We first design a cooperativecontroller to be implemented on each robot so that theirmotion are synchronized to a reference motion desired by ahuman operator, and then point out that each robot motionensures passivity. Inter-robot communication channels are thendesigned via so-called scattering transformation which is atechnique to passify the delayed channel. The resulting roboticnetwork is then connected with human operator based onpassivity theory. In order to demonstrate the present controlarchitecture, we build an experimental testbed consisting ofmultiple robots and a tablet. In particular, we analyze the effectsof the communication delays on the human operator’s behavior.
I. I
NTRODUCTION
Complex robotic coordination tasks in highly uncertainenvironments require the system designers to take advantageof human operator’s strengths, high-level decision-makingand flexibility. Motivated by these needs, semi-autonomousoperation of robots is gaining increasing research interests[1].One of the most promising design tools for such semi-autonomous systems is passivity, as confirmed in the historyof a traditional semi-autonomous robot control problem,bilateral teleoperation [2]-[12]. In this research field, thehuman operator has been treated as a passive component andthen control architectures have been established while ensur-ing closed-loop stability based upon this assumption. Thisparadigm has also been taken in teleoperation of multiplenetworked robots [2]–[4]. Rodriguez-Seda et al. [2] presentan architecture such that the robotic network is controlled byoperating a leader robot so that the robots forms a specifiedformation while avoiding collisions. Liu [3] extends motionsynchronization on the joint space to the task space undertime-varying delays. Fully distributed control algorithms arepresented by Franchi et al. [4], where stability is ensuredin the presence of split and join events. Other interestingextensions of bilateral teleoperation are presented in [5] and[6]. Varnell and Zhang [5] employ a non-classical human-robot interfaces, namely a tablet, and discuss the stabilitywhile assuming a human pointing model. Saeidi et al. [6]introduce the notion of robot-to-human trust and mixed J. Yamauchi and M.W.S. Atman are with Department of Mechan-ical and Control Engineering, Tokyo Institute of Technology, Japan yamauchi.j.ab, [email protected] T. Hatanaka and M. Fujita are with Department of Systems and ControlEngineering, School of Engineering Tokyo Institute of Technology, Japan [email protected] N. Chopra is with Department of Mechanical Engineering, Universityof Maryland, USA Fig. 1. Information flows in the intended scenario of human-roboticnetwork system. initiative control scheme in order to improve the performanceand reduce workload of the operator.While the above papers consider robot dynamics togetherwith force feedback, the authors [13], [14] studied anotherproblem formulation focusing on interactions between ahuman operator and kinematic robots as in [15], [16]. Theschematic of the intended system is illustrated in Fig. 1.Then, we investigated motion synchronization of robots tohuman references under distributed information exchangebetween the human and robots, and among robots. To thisend, we presented a novel passivity-based control archi-tecture and proved synchronization under explicit bilateralconnections between the human and robotic network. Forimplementation on real robotic systems, both the human-robotic network and inter-robot interactions must be imple-mented using appropriate communication technology. In thiscase, the communication channels may suffer from delaysin the transmission of information, which is indeed one ofthe most important issues in bilateral teleoperation. However,[13], [14] did not address this issue explicitly.Our objective is thus to extend the results of [13], [14]to the case with time delays and its experimental stud-ies. Although both the human-robotic network and inter-robot communications may have delays, this paper inves-tigates the latter since this issue emerges in the one-human-multiple-robot interactions while the former has been in-depth studied in bilateral teleoperation. Delays in inter-robot communications have been extensively studied in thefield of cooperative control (See [7] and references therein).Among many approaches, this paper focuses on the schemepresented in [7], and synchronization is guaranteed despitethe delays. In this paper, the control architecture in [7] isshown to be successfully integrated with the cooperativecontrol for human-robotic networks presented in [13], [14].However, the integration is not straightforward and requiresnovel technical extensions in the formulation and this is ig. 2. The system configuration for human-robotic network. presented in this paper. Furthermore, as pointed out in [17],real deployments of robotic network is important from theviewpoint of difficulties to simulate each intended task andsituation faithfully. Therefore, we investigate our proposedarchitecture in a testbed and show the influences of commu-nication delays not only on a robotic network but also on areal human’s behaviour.The organization of this paper is as follows: SectionII presents the intended problem and briefly reviews theresults of [13], [14]. In Section III, we design a novelcontrol architecture based on the scattering transformation[7], and then, show passivity of the resulted system. Wealso show position synchronization to the reference values inSection IV. We demonstrate our results through experimentsin Section V, and finally, summarize the obtained results inSection VI. II. P
ROBLEM S ETTING
In this section, we start by reviewing the problem formu-lation and results presented in [13], [14]. Please refer to [13],[14] for more details.
A. System Configuration and Objectives
Let us consider a system with a human operator and n mobile robots V = { , · · · , n } located on a 2-D plane asshown in Fig. 1. We suppose that the motion of every i -throbot is described by the kinematic model ˙ q i = u i ∀ i ∈ V , (1)where q i ∈ R and u i ∈ R are the position and velocityinput of i -th robot, respectively.Every robot can interact with neighboring robots and theinter-robot information exchanges are modeled by a graph G = ( V , E ) , E ⊆ V ×V . Then, robot i has access to informa-tion of the robots belonging to the set N i = { j ∈ V| ( i, j ) ∈E} . Throughout this paper, we assume the communicationgraph is fixed, undirected and connected. Differently from[13], we assume that the inter-robot communication suffersfrom time delays, which will be discussed in Section II.In addition to the total robots set V , we define accessiblerobots set V h which is a subset of V (Fig. 2). Accessibility means that the operator can send a signal to and receivefeedback information from only the robots in V h . Here,we assume that the human operator determines a commandsignal u h based on certain information y h visually fed backfrom V h through a monitor in front of the operator. The command u h is then sent back to all the accessible robots.We also introduce the notation δ i such that δ i = 1 if i ∈ V h and δ i = 0 otherwise.In this paper, we address position synchronization. Letus assume that the human operator has a desired positiondenoted by q r . Then, the goal of the position synchronizationis defined by lim t →∞ k q i − q r k = 0 ∀ i ∈ V . (2)The objective here is to design the robot controller u i and theinformation y h displayed on the monitor so as to guaranteethe above control goal. B. Control Architecture without Time Delays
The authors [13], [14] take the control input u i as u i = u r,i + δ i u h i ∈ V . (3)Then, the signal u r,i to achieve inter-agent motion synchro-nization is designed as ˙ ξ i = X j ∈N i b ij ( q j − q i ) (4) u r,i = X j ∈N i a ij ( q j − q i ) − X j ∈N i b ij ( ξ j − ξ i ) (5)where a ij = a ji , b ij = b ji ∀ i, j ∈ V , a ij > , b ij > if ( i, j ) ∈ E and a ij = b ij = 0 otherwise.Then, the collective dynamics (1), (3) and (5) for all i ispassive from u h to z , where z is defined as z := 1 m X i ∈V h q i , (6)and m is the number of elements of V h . Based on thispassivity, we let the feedback information y h for the humanoperator be y h = z . Namely, the human operator can obtainthe average position of the accessible robots z . In [13], posi-tion synchronization is theoretically proved in the absence ofdelays under a passivity assumption on the human’s decisionprocess together with some additional assumptions. However,inter-robot communication delays may destabilize the abovecontrol system. This is why we present a system architecturewith robustness against inter-robot communication delays. Remark 1:
The system architecture (4), (5) can achievenot only position synchronization but also synchronizationof velocity at the same time, i.e., lim t →∞ k ˙ q i − v r k = 0 , lim t →∞ k q i − q j k = 0 ∀ i, j ∈ V , (7)where v r is a constant reference velocity. However, we omitthis part because of space limitations.III. C OOPERATIVE C ONTROL A RCHITECTURE UNDER I NTER -R OBOT C OMMUNICATION D ELAYS
A. Passivity of Robot Dynamics
In this section, we redesign the cooperative controllergenerating u r,i in order to guarantee stability and synchro-nization despite the inter-robot communication delays. ig. 3. Block diagram of i -th robot and its cooperative controller includingthe scattering transformation. In the presence of the delays, i -th robot cannot obtain q j ( t ) and ξ j ( t ) at time t . We thus replace these signals by r qij , r ξij ,respectively. Then, i -th robot’s dynamics is described by ˙ ξ i = X j ∈N i b ij ( r qij − q i ) (8) ˙ q i = X j ∈N i a ij ( r qij − q i ) − X j ∈N i b ij ( r ξij − ξ i ) + δ i u h (9)Let us now define p ij ∈ R as p ij := M ij (cid:18)(cid:20) r qij r ξij (cid:21) − (cid:20) q i ξ i (cid:21)(cid:19) = M ij (cid:20) r qij − q i r ξij − ξ i (cid:21) , (10)where M ij := (cid:20) a ij I − b ij I b ij I (cid:21) for all j ∈ N i and i . It iseasy to see from the definition that M ij is a passive map.Then, (8) and (9) is described as a feedback systemconsisting of (cid:20) ˙ q i ˙ ξ i (cid:21) = µ i + (cid:20) δ i (cid:21) u h (11)and the operation µ i := P j ∈N i p ij . Then, if there is nointeraction with a human operator, i.e., u h ≡ , and wedefine a storage function as S i := 12 k q i k + 12 k ξ i k , (12)the system (11) is passive from µ i to [ q Ti ξ Ti ] T .From the above discussions, the system (8) and (9) can bereduced to a feedback interconnection of passive systems anda collection of passive maps M ij j ∈ N i . Accordingly, wecan obtain the following inequality for each robot dynamics, ˙ S i = (cid:2) q Ti ξ Ti (cid:3) X j ∈N i p ij = − X j ∈N i a ij k q i − r qij k + X j ∈N i r Tij p ij ≤ X j ∈N i r Tij p ij . (13)The above inequality implies that each robot dynamics ispassive from the stacked vector of r ij to the stacked vectorof p ij from all neighbor robots with respect to the storagefunction (12). Fig. 4. The scattering transformation between robot i and robot j . B. Scattering Transformation and Passivity of Communica-tion Block
In this subsection, we present a novel control architecturebased on [7]. Hereafter, similarly to [13], [14], we assumethat reference q r is constant, which means that we areassuming that these signals are varying so slowly that theanalyses under the constant reference are applicable to theactual system. Time varying reference is also addressed in[14], however its extension to the case with delays is left asa future work.Following the architecture of [7], we let each agentexchange the variable p ij through scattering transformationinstead of directly sending q i and ξ i as illustrated in Fig. 3.In the present case, the scattering variables are defined as s + ij = 1 √ σ ( − p ij + σr ij ) , s − ij = 1 √ σ ( − p ij − σr ij ) , (14) s + ji = 1 √ σ ( p ji + σr ji ) , s − ji = 1 √ σ ( p ji − σr ji ) , (15)where r ij = [( r qij ) T ( r ξij ) T ] T and σ > is constant. Theoperation is illustrated in Fig. 4. It is immediate to see fromthis figure that s + ji ( t ) = s + ij ( t − T ) , s − ij ( t ) = s − ji ( t − T ) , (16)where T > is a delay in communication channel from i -th robot to j -th robot and it is assumed to be constant.Hereafter, we suppose that both of s + ji and s − ij are equal tozero during the negative time t < for all i, j .We define s q := [( p σ/ q Tr T ] T ∈ R and the storagefunction for the communication channel as S cij := 12 Z tt − T k s + ij − s q k dτ + 12 Z tt − T k s − ji + s q k dτ. Thus, if we define ¯ r qij := r qij − q r and ¯ r ij := [(¯ r qij ) T ( r ξij ) T ] T ,the time derivative of S cij is given by ˙ S cij = 14 σ ( k − p ij + σ ¯ r ij k − k p ji + σ ¯ r ji k + k p ji − σ ¯ r ji k − k − p ij − σ ¯ r ij k ) = − p Tij ¯ r ij − p Tji ¯ r ji . (17)Thus, if we interpret [ − p Tij − p Tji ] T and [¯ r Tij ¯ r Tji ] T as the inputand output respectively, the communication channel becomespassive with respect to S cij . ig. 5. Block diagram of the human-robotic network system. C. Passivity of Robotic Network
In this subsection, we show passivity of the roboticnetwork discussed above. First, we define the signals ¯ q i := q i − q r , for all i and ¯ z := z − q r . Then, the error dynamicson (8) and (9) is given by ˙¯ q i = X j ∈N i a ij (¯ r qij − ¯ q i ) − X j ∈N i b ij ( r ξij − ξ i ) + δ i u h (18) ˙ ξ i = X j ∈N i b ij (¯ r qij − ¯ q i ) , (19)where (18) is hold because q r is constant. From (18) and(19), (11) is rewritten as (cid:20) ˙¯ q i ˙ ξ i (cid:21) = µ i + (cid:20) δ i (cid:21) u h . (20)Then, we define the storage function for the error dynamicsas ¯ S i := 12 k ¯ q i k + 12 k ξ i k , i ∈ V . (21)From (13), the time derivative of ¯ S i along the trajectory of(20) is given by ˙¯ S i = (cid:2) ¯ q Ti ξ Ti (cid:3) X j ∈N i p ij + ¯ q Ti δ i u h = − X j ∈N i a ij k q i − r qij k + X j ∈N i ¯ r Tij p ij + ¯ q Ti δ i u h . (22)Hence, we define a total storage function for the roboticnetwork as S := 1 m X i ∈V ¯ S i + 1 m X ( i,j ) ∈E S cij . (23)From (22) and (17), the time derivative of S is given by ˙ S = 1 m X i ∈V ˙¯ S i + 1 m X ( i,j ) ∈E ˙ S cij = − m X i ∈V X j ∈N i a ij k q i − r qij k + ¯ z T u h ≤ ¯ z T u h . Thus, the robotic network is passive from human input u h to the average position of accessible robots ¯ z with respect to(23). In the next section, we close the robotic network witha human operator based on this passive property.IV. I NTERCONNECTED SYSTEM OF R OBOTIC N ETWORKAND P ASSIVE H UMAN O PERATOR
In this section, we prove position synchronization (2) byutilizing passivity.
A. Synchronization to Human’s Desired Position
First, we start by the description of a human operator.Similarly to [13], [14], we assume that the operator deter-mines the command u h based on the error q r − y h betweenthe reference q r and the feedback information y h = z . Then,the entire system is illustrated as Fig. 5, where the humandecision process is denoted by Φ . Then, we assume that ahuman operator’s decision process Φ is input strictly passivefrom q r − z to u h , i.e., there exists a storage function S Φ h and ǫ > such that ˙ S Φ h ≤ ( q r − z ) T u h − ǫ k q r − z k . (24)The validity of this assumption is examined in [13], [14]using experimental data obtained from a human-in-the-loopsimulator, where it is confirmed that the statement is trueover a prescribed frequency domain. We need to analyze theeffect of the communication delays on the human propertybut this exceeds the scope of this paper and we leave theissue as a future work.From this human passivity assumption, we have the fol-lowing result. Proposition 1:
Consider the system (18) and (19), and thescattering transformation (14) and (15) for all j ∈ N i andall i . Then, the feedback system achieves the condition (2) ifthe communication graph is fixed, undirected and connected,and the human decision process Φ is input strictly passive. Proof:
First, we define an energy function U as U := S + Z t (cid:0) − ¯ z ( τ ) u h ( τ ) − ǫ k ¯ z ( τ ) k (cid:1) dτ + β, (25)where β is a positive constant. From the passivity of roboticnetwork shown in Section III and human operator’s passivityassumed above, we obtain ˙ U = − m X i ∈V X j ∈N i a ij k q i − r qij k + ¯ z T u h − ¯ z T u h − ǫ k ¯ z k = − m X i ∈V X j ∈N i a ij k q i − r qij k − ǫ k ¯ z k ≤ . (26)Thus, it is guaranteed that the all states are bounded in spiteof communication delays.Let us define x it such that x it ( θ ) = x i ( t + θ ) for θ ∈ [ − T, . Then, the LaSalle’s invariance principle for timedelay systems [18] is applicable and any solution x t ofthe system converges to the largest invariant set in theset of functions satisfying ˙ U ≡ . Thus, ˙ U = 0 means q i ≡ r qij ( i, j ) ∈ E and ¯ z ≡ . Hence, we can concludeas follows. lim t →∞ ( r qij − q i ) = 0 ( i, j ) ∈ E (27) lim t →∞ ¯ z = 0 (28)Next, in order to analyze further, we need to follow thebehavior of ¯ r ij . First, we define e ij and e ji as ij := − σ { ( r qij − q i ) + ( r qji ( t − T ) − q j ( t − T )) } ,e ji := − σ { ( r qji − q j ) + ( r qij ( t − T ) − q i ( t − T )) } . Then, each element of (14)–(16) can be given as r qij = r qji ( t − T ) + 1 σ { b ij ( r ξij − ξ i )+ b ji ( r ξji ( t − T ) − ξ j ( t − T )) } + e ij , (29) r qji = r qij ( t − T ) + 1 σ { b ji ( r ξji − ξ j )+ b ij ( r ξij ( t − T ) − ξ i ( t − T )) } + e ji . (30) r ξij = r ξji ( t − T ) + b ij e ij , (31) r ξji = r ξij ( t − T ) + b ji e ji , (32)Furthermore, subtracting (30) at time t − T from (29) yields r qij + r qij ( t − T ) = 2 r qji ( t − T ) − b ij σ { ( r ξij − ξ i ) − ( r ξij ( t − T ) − ξ i ( t − T )) }− a ij e ij + a ji e ji ( t − T ) . (33)Utilizing the equations in (32), we have r ξij = r ξij ( t − T ) + e ij + e ji ( t − T ) . Now, according to (27), the signals e ij and e ji converge to , i.e., lim t →∞ e ij = lim t →∞ e ji = 0 (34)holds. Thus, taking the limit of (33) yields lim t →∞ ( r qij + r qij ( t − T ) − r qji ( t − T )) = 0 . (35)The same equation holds for k ∈ N i as lim t →∞ ( r qik + r qik ( t − T ) − r qki ( t − T )) = 0 . (36)On the other hand, because the signal r qij for all j ∈ N i converges to q i from (27), we obtain lim t →∞ ( r qij − r qik ) = 0 ∀ j, k ∈ N i . (37)Subtracting (36) from (35) and using (37), we have lim t →∞ ( r qji − r qki ) = 0 . (38)Because of (27), equation (38) implies lim t →∞ ( q j − q k ) = 0 ,which holds for ( j, k ) ∈ E . Then, we have lim t →∞ ( q i − q j ) = 0 for all i, j ∈ V . Furthermore, from (28), we have lim t →∞ ¯ z = lim t →∞ m X i ∈V h q i − q r ! = 0 . (39)Therefore, we can conclude that lim t →∞ ( q i − q r ) = 0 forall i ∈ V . This completes the proof. Remark 2:
As in the same way, the velocity synchro-nization (7) is achieved with the same control architecture.However, we omit the result because of space limitations.
Fig. 6. The architecture overview of experiment system.Fig. 7. The robotic network and obstacles on the field. The communicationgraph is shown in right bottom. The accessible robots are in grey, i.e., 3rdand 4th robots.
V. E
XPERIMENT
In this section, we show the experiment results of thediscussed control system. In this paper, we focus on theinfluence of the communication delay on the human oper-ator’s behavior. For that purpose, we conduct two types ofexperiments, without inter-robot communication delay andwith inter-robot communication delay. Then, we investigatethe differences by comparing the robots’ trajectories andhuman input. Although it is also important to investigate thehuman passivity assumption, as already mentioned in SectionIV, we leave this as a future work.
A. Experimental Setting
In this subsection, we introduce our experiment systemand the intended scenario. The architecture of experimentsystem is illustrated in Fig. 6. We use 6 omnidirectionalrobots named TDO48 from TOSADENSHI Inc. and obtainimage data by using a ceiling camera named Firefly MVfrom Point Grey. From image processing by C++, we obtainall robots positions. Even though the control architecture isimplementable by each robot processor, we artificially imple-ment all cooperative controller in a computer for simplicity.The inter-robot communication delays are also generated inSimulink and the delays set 0.5s. Simulink is running ondSPACE for the real time implementation. On the other hand,we show the average position of accessible robots and givenreference position via GUI programmed by C++. Then, theparticipant inputs velocity command through mouse. Finally,the velocity inputs are converted to motor angular velocities,and then, transmitted to each robot via Bluetooth. ig. 8. The experiment result without inter-robot communication delay.(top) The trajectories of all robots. The average position of accessible robotsare shown by blue curve, and each robot’s initial and last positions are shownby circle and cross, respectively. The reference position is shown by red dot.(middle) The trajectories in x-axis and y-axis. (bottom) Human input.
For the scenario, we ask the participant to control roboticnetwork to a given position, as shown by red dot in Fig. 7.The reference position is q r = [0 .
55 0 . T . Furthermore,we add the obstacles which the participant have to avoidcollision with them. In order to avoid the collisions betweeneach robot, we utilize the biases d i ∀ i ∈ V and denotereal position η i as η i = q i + d i ∀ i ∈ V . The biasesare given as d = [0 .
35 0 . T , d = [0 0 . T , d =[ − .
35 0 . T , d = [ − . − . T , d = [0 − . T , d = [0 . − . T . During this section, weshow all figures using the biased positions, rather than thereal positions η i . The communication graph of the roboticnetwork is shown in Fig. 7. The initial positions of all robotsare q i (0) = [2 . . T and ξ i (0) = 0 ∀ i ∈ V . The parametersare set as a ij = 0 . , b ij = 0 . and σ = 1 . . B. Experimental Results
First, the result without inter-robot communication delay isshown in Fig. 8. The human operator successfully control theaccessible robots, and all robots reached the target position.Note that non-accessible robots could close the distanceswith the accessible robots around 30s while the accessiblerobots are still moving. This shows one of the advantage inexchanging the integral value, ξ i , of − P j ∈N i b ij ( q i − q j ) .The human input is shown in the bottom part of Fig. 8. Theresult shows that the human operator smoothly controlled the Fig. 9. The experiment result with inter-robot communication delay andscattering transformation. (top) The trajectories of all robots. The averageposition of accessible robots are shown by blue curve, and each robot’sinitial and last positions are shown by circle and cross, respectively. Thereference position is shown by red dot. (middle) The trajectories in x-axisand y-axis. (bottom) Human input. robotic network.Next, we show the result with inter-robot communicationdelay and the scattering transformation in Fig. 9. In thesame way as the delay free case, all robots reached thetarget position. However, comparing the trajectories with theresult without delay, non-accessible robots couldn’t closethe distances with the accessible robots. As a result, theaccessible robots moved back and forth around the referenceposition. The arrival time is delayed by about 70s. Thehuman input is shown in the bottom of Fig. 9. After 50s, thehuman operator repeated adjustments because non-accessiblerobots followed late. Comparing to the result of delay freecase, the human input looks more fluctuated, which can beinterpreted as the deterioration of human’s operability.In summary, position synchronization by the proposedarchitecture is verified through this experiment. In additionto this result, since we observed performance degradation ofhuman, thorough investigation is needed regarding humanperformance. To this end, we need a criteria to measure theperformance qualitatively.VI. C
ONCLUSIONS
In this paper, we have investigated a cooperative controlarchitecture of human-robotic networks in the presence ofinter-robot communication delays, where the objective is touarantee position synchronization to human’s desired posi-tion. First, we proposed control architecture based on [13],[14] and the scattering transformation. Then, we showedpassivity of the robotic network. Next, by using humanpassivity assumption, we showed that the feedback systemachieves position synchronization. Finally, we demonstratedthe efficiency of the proposed architecture through experi-ments, which managed to move all robots to target positionin the same way as delay free case. Furthermore, we investi-gated the influences of inter-robot communication delays onhuman’s operability. R
EFERENCES[1] Y. Wang and F. Zhang (eds.),
Trends in Control and Decision-Makingfor Human-Robot Collaboration Systems , Springer, 2017.[2] E.J. Rodriguez-Seda, J.J. Troy, C.A. Erignac, P. Murray, D.M. Sti-panovic and M.W. Spong, “Bilateral Teleoperation of Multiple MobileAgents: Coordinated Motion and Collision Avoidance,”
IEEE Trans.Control Systems Technology , Vol. 18, No. 4, pp. 984–992, 2010.[3] Y. Liu, “Task-Space Bilateral Teleoperation Systems for Heteroge-neous Robots with Time-Varying Delays,”
Robotica , Vol. 33, No. 10,pp. 2065–2082, 2015.[4] A. Franchi, C. Secchi, H.I. Son, H.H Bulthoff and P.R. Giordano,“Bilateral Teleoperation of Groups of Mobile Robots with Time-Varying Topology,”
IEEE Trans. Robotics , Vol. 28, No. 5, pp. 1019–1033, 2012.[5] P. Varnell and F. Zhang, “Dissipativity-Based Teleoperation with Time-Varying Communication Delays,”
Proc. 4th Workshop on DistributedEstimation and Control in Networked Systems , pp. 369–376, 2013.[6] H. Saeidi, F. McLane, B. Sadrfaidpour, E. Sand, S. Fu, J. Rodriguez,J.R. Wagner and Y. Wang, “Trust-Based Mixed-Initiative Teleoperationof Mobile Robots,”
Proc. 2016 American Control Conference , pp.6177–6182, 2016.[7] T. Hatanaka, N. Chopra, M. Fujita and M.W. Spong:
Passivity-BasedControl and Estimation in Networked Robotics , Communications andControl Engineering Series, Springer-Verlag, 2015.[8] Y. Morita, Y. Ogawa, Y. Kawai, T. Imamura, T. Miyoshi and K.Terashima, “Design Method for Multilateral Tele-Control to RealizeShared Haptic Mouse,”
Proc. SICE Annual Conference 2013 , pp.2220–2226, 2013.[9] E. Nuno, L. Basanez and R. Ortega: “Passivity-Based Control forBilateral Teleoperation: A Tutorial,”
Automatica , Vol. 47, pp. 485–495, 2011.[10] S. Hu, C. Chan and Y. Liu, “Event-Triggered Control for BilateralTeleoperation with Time Delays,”
Proc. 2016 IEEE/RSJ InternationalConference on Advanced Intelligent Mechatronics , pp. 1634–1639,2016.[11] S. Islam, P.X. Liu, A.E. Saddik and Y.B. Yang, “Bilateral Controlof Teleoperation Systems With Time Delay,”
IEEE/ASME Trans.Mechatronics , Vol. 20, No. 1, pp. 1–12, 2015.[12] M. Shahbazi, H.A. Talebi and M.J. Yazdanpanah, “A Control Archi-tecture for Dual User Teleoperation with Unknown Time Delays: ASliding Mode Approach,”
Proc. 2010 IEEE/RSJ International Confer-ence on Advanced Intelligent Mechatronics , pp. 1221–1226, 2015.[13] T. Hatanaka, N. Chopra and M. Fujita, “Passivity-Based BilateralHuman-Swarm-Interactions for Cooperative Robotic Networks andHuman Passivity Analysis,”
Proc. 54th IEEE Conference on Decisionand Control , pp. 1033–1039, 2015.[14] T. Hatanaka, N. Chopra, J. Yamauchi and M. Fujita, “A Passivity-Based Approach to Human-Swarm Collaborations and Passivity Anal-ysis of Human Operators,”
Trends in Control and Decision-Making forHuman-Robot Collaboration Systems , Y. Wang and F. Zhang (eds.),Springer-Verlag, 2017.[15] M. Egerstedt, J.-P. de la Croix, H. Kawashima and P. Kingston,“Interacting with Networks of Mobile Agents,” Large-Scale Networksin Engineering and Life Sciences, pp. 199–224, Springer-Verlag, 2014.[16] D. Sieber, S. Music and S. Hirche, “Multi-Robot Manipulation Con-trolled by a Human with Haptic Feedback,”
Proc. 2015 IEEE/RSJInternational Conference on Intelligent Robots and Systems , pp. 2440–2446, 2015. [17] D. Pickem, P. Glotfelter, L. Wang, M. Mote, A. Ames, E. Feron and M.Egerstedt, “The Robotarium: A Remotely Accessible Swarm RoboticsResearch Testbed,” arXiv:cs.RO:1604.00640, 2016.[18] J.K. Hale and S.M.V. Lunel,