Spill detection and perimeter surveillance via distributed swarming agents


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Spill detection and perimeter surveillance via distributed swarming agents

  1. 1. IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 18, NO. 1, FEBRUARY 2013 121 Spill Detection and Perimeter Surveillance via Distributed Swarming Agents Guoxian Zhang, Gregory K. Fricke, and Devendra P. Garg Abstract—The problem of perimeter detection and monitoring UAV. This movement continued and the movement of the UAVshas a variety of applications. In this paper, a hybrid system of finite formed a latency. This method could easily adapt to a changestates is proposed for multiple autonomous robotic agents with the in the fire size and the number of UAVs needed during thepurpose of hazardous spill perimeter detection and tracking. In thesystem, each robotic agent is assumed to be in one of three states: process. Clark and Fierro [13] and Cruz et al. [14] utilized asearching, pursuing, and tracking. The agents are prioritized based hybrid control algorithm [15] to achieve the perimeter searchon their states, and a potential field is constructed for agents in each and monitoring in an unknown environment; this method isstate. For an agent in the tracking state, the agent’s location and susceptible to cases in which a single perimeter would split intovelocity as well as those of its closest leading and trailing agents are multiple distinct perimeters. Bruemmer et al. [16] utilized theutilized to control its movement. The convergence of the trackingalgorithm is analyzed for multiple spills under certain conditions. social potential field generated by different kinds of sensors onSimulation and experiment results show that with the proposed each agent to avoid collision and attract agents to the perimeter.method, the agents can successfully detect and track the spills of Related research in multiple robots is in formation control.various shapes, sizes, and movements. Olfati-Saber [17], [18] proposed a method to control a flock Index Terms—Autonomous agents, mobile agents, multirobot while maintaining its geometric formation along the way. Asystems. potential function achieved local minima when the distances between each pair of agents in the flock reached a preset value. The stability of flocking of a group with fixed and dynamic I. INTRODUCTION topologies was studied by Tanner et al. in [19] and [20]. A social potential field was used to control the distances between agents, HE development of swarm robotics has emerged as a toolT for mobile sensor networks in a variety of areas, suchas environment monitoring [1], foraging [2], [3], target detec- and each agent’s velocity was controlled by the difference in the velocity from its neighbors. In these cases, the distance between each pair of agents converged to a preset value that istion [4], and target tracking [5]. Two different kinds of con- not suitable in cases where the desired distance between twotrol (centralized and decentralized) can be implemented for the neighbors changes with time.robot group. In centralized control, all agents in the group are In this paper, inspired by flocking agents, a control law isassumed to be able to share their information [6]. This kind proposed for a group of agents whose purpose is to search for,of control suffers from computational burden if the number of detect, and track a hazardous spill in an unknown environment.agents is relatively large. More often, decentralized control is Each agent is assumed to have limited and specific sensingused for swarm robotics with information shared only among and communication ranges. It is shown that the group can suc-agents within a local network [1], [7]–[11]. In this paper, we cessfully detect the spill and track its boundary when the spill’spropose a method for the problem of perimeter detection and location and size are changing. Simulation results showed excel-tracking via swarm robots, which has a variety of applications lent performance in tracking multiple spills that come togethersuch as forest fire surveillance [12], oil leakage tracking [13], or split during the process. The control algorithm proposed inand animal herd monitoring. Section III is modified to fit the requirement of real experiments Some of the previous studies in this area have been reported in and the performance is verified with a group of robotic agents.literature as follows. Casbeer et al. [12] proposed a decentralizedmultiple unmanned aerial vehicle (UAV) approach to monitora forest fire. Each UAV flew along the perimeter of the fire in II. PROBLEM FORMULATIONone direction, and then, reversed direction upon meeting another A group of autonomous mobile agents A1 , A2 , . . ., An is as- sumed to be initially deployed in the area W. At time t, the con- figuration of agent i is represented as qi (t) = [ri (t)T , θi (t)]T , where ri (t) = [xi (t), yi (t)]T denotes the position of Ai at time Manuscript received September 30, 2010; revised March 9, 2011; acceptedJune 27, 2011. Date of publication September 12, 2011; date of current version t and θi (t) denotes its orientation. Each agent is assumed toSeptember 12, 2012. Recommended by Technical Editor P. X. Liu. This work be equipped with a sensor whose field of view (FOV) is Si ,was supported in part by the Army Research Office under Grant W911NF-08- and communication range is Mi . For simplicity’s sake, in our1-0106 and Grant W911NF-09-0307. G. Zhang is with Microstrategy, Inc., Tysons Corner, VA 22182 USA (e-mail: paper, we assume that both Si and Mi are circles whose cen-zhangguoxian@gmail.com). ters are located at ri (t), and are of constant radii rS and rM . G. K. Fricke and D. P. Garg are with the Pratt School of Engineer- Similar assumptions are commonly used by other researchersing, Duke University, Durham, NC 27708 USA (e-mail: gkf4@duke.edu;dpgarg@duke.edu). (for example, see [17] and [21]). A number of spills Ωj (t) with Digital Object Identifier 10.1109/TMECH.2011.2164578 the boundary ∂Ωj (t) exist in W. A spill Ωj (t) is defined as a 1083-4435/$26.00 © 2011 IEEE
  2. 2. 122 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 18, NO. 1, FEBRUARY 2013connected subspace in R2 . Each agent is assumed to be ableto measure the length of the spill boundary within its FOV.This length may be computed in a variety of ways. One wayis to utilize pattern classification technology to detect the spillboundary from a visual sensor as implemented in [22]. Then,the detected spill boundary is represented by a series of pointson it and a straight line segment is generated with each pair ofadjacent points. The spill boundary length is approximated bysumming the lengths of all the straight line segments. When∂Ωj (t) changes, it would be beneficial that the agent group canuniformly distribute along the spill boundary since the changeof a part on ∂Ωj (t) could be detected by an agent quickly. A method is proposed to control the movement of each agenttracking a spill. Only the positions and linear speeds of an agent’sclosest leading and trailing neighbors along its way may beutilized to generate a potential field to control its movement. Fig. 1. Sample layout of the multiple agent system.An influence distance along the spill boundary, denoted by L,controls how the closest neighbor affects an agent’s potentialfield. This assumption guarantees the scalability of the proposedmethod and will be discussed in Section III. The problem can be formulated as follows: given a groupof agents A1 , A2 , . . . , An and their initial configurationsq1 (0), q2 (0), . . . , qn (0), find the path for each agent i, wherei = 1, 2, . . . , n, such that ∀ > 0, there exists a time T > 0and a spill index j, for t > T agent i tracks Ωj (t), and ri (t), rN (r i (t)) (t) ∂ Ω j = Lj (t) satisfies ⎧ ⎪ |L (t) − ∂Ωj (t) | < , if n (t) > ∂Ωj (t) ⎪ j ⎨ nj (t) j L (1) ⎪ ⎪ ∂Ωj (t) ⎩ L (t) >= L − , if nj (t) ≤ . j LHere, a, b ∂ c is the distance from a to b along the curve ∂c in theforward direction; N (ri (t)) is the index of the closest neighbor Fig. 2. State transition diagram.of Ai in the forward direction; nj (t) is the number of agents thatare tracking Ωj at time t; and ∂Ωj (t) is the length of ∂Ωj (t). individual robot are shown in Fig. 2. This hybrid hierarchy isFurthermore, the velocities of agents tracking the same spill consistent with the embedded software principles of Alur etconverge to the same value. Mathematically speaking, assume al. [15]. The system described herein exhibits architectural hi-that agents i and j are tracking the same spill, ∀ > 0, ∃T > 0, erarchy in its basic construction; the controller employs behav-such that ∀t > T , we have |vi (t) − vj (t)| < . When there is ioral hierarchy in its state transitions. In contrast to the hybridno ambiguity, we simplify each variable without writing time controller of Clark and Fierro [13] and Cruz et al. [14], theexplicitly; for example, ∂Ωj represents ∂Ωj (t). controller presented here requires only a single tier of mode The communication among the mobile agents can be repre- switching with no submodes or substates for obstacle or vehiclesented as a set of connected undirected graphs, each of which avoidance. The potential functions, developed next, allow a con-can be defined as Gk (Vk , Ek ), where Vk = {al 1 , al 2 , . . . , al k } tinuous calculation and application of control authority that isare the agents in Gk , and Ek = {(al i , al j ) ∈ Vk × Vk |al i , al j ∈ consistent with the goals of each state and yet robust to collisionVk , al j ∈ Ml i }. The information, such as a detected point of the avoidance.spill boundary by an agent, is assumed to be able to be shared The agents are assumed to have a unicycle model in whichwithin the graph with no time delay. A typical example of the ⎧agent system with ten agents and one spill is shown in Fig. 1. ⎪ xi = vi cos θi ⎪˙ ⎪ ⎪ ⎨ yi = vi sin θi ˙ III. SOLUTION (2) ⎪ vi = ai ⎪ ˙ ⎪ ⎪ A hybrid hierarchical control technique is used to control the ⎩˙agents. Three behaviors are used for perimeter detection and θ i = ωitracking: searching, pursuing, and tracking. An agent switches where vi is the linear velocity of the ith agent, ai is its linearamong these states based on the agent and its local group acceleration, and ωi is its angular velocity. The control inputsmembers’ situations. The algorithmic state transitions for an of each agent are set up as [ui wi ], where ui = ai and wi = ωi .
  3. 3. ZHANG et al.: SPILL DETECTION AND PERIMETER SURVEILLANCE VIA DISTRIBUTED SWARMING AGENTS 123A. Perimeter Search In the proposed method, the robotic agents are initially ran-domly deployed in an unknown environment. The geometry ofeach agent is ignored in the system, i.e., two agents collide onlywhen their positions are the same. To avoid collision, we assumethat there is a repulsive potential field generated by each agent,denoted as Ui [23] ⎧ 2 ⎪1 ⎨ η 1 1 1 − , if ρ(r, ri ) ≤ ρ0 Ui (r) = 2 ρ(r, ri ) ρ0 (3) ⎪ ⎩ 0, if ρ(r, ri ) > ρ0where η1 is a scaling parameter, ρ0 is the influence distanceof each agent, ri is the ith agent position, and ρ(r, ri ) is the Fig. 3. Location, forward movement direction, and distance between adjacentdistance between r and ri . mobile agents along the spill perimeter. The agents in different states are assumed to have differentpriority levels for avoidance. The agents in the searching state Ud (r) is constructed for the agent moving toward rd . It is givenare assumed to be at the lowest level, and the agents in the bytracking state are at the highest level. Let the index sets Is , Ip ,and It represent the indices of agents in searching, pursuing, 1 Ud (r) = η2 ρ(r, rd )2 (7)and tracking states, respectively. Assume that an agent in the 2searching state is at r, and let Ns (r) = {i|∀i, r ∈ Mi } denote where η2 is a scaling parameter and ρ(r, rd ) is the distancethe indices of agents in which communication range r lies. When between r and rd . Let Np (r) = {i|∀i ∈ Ip ∪ It , r ∈ Mi } de-Ns (r) = ∅, the following potential field is constructed for the note the set of indices of agents in pursuing or tracking state,agent: in which communication range r lies. The following potential Us (r) = Ui (r) (4) field is constructed for the agent: i∈N s (r) Up (r) = Ud (r) + Ui (r). (8)and the force implemented on the agent is computed as i∈N p (r) Fs (r) = −∇Us (r). (5) The negative gradient Fp (r) of the potential Up (r) is utilized to navigate the agent in pursuing state. In practice, we assume thatHere, Fs (r) is utilized as control ui for the agent, and ωi there is a maximum velocity vm ax to bound the movement ofis set at the value with which the orientation of the agent in each agent.the next time step is consistent with the direction of Fs (r).Since the travel distance and search time are not consideredin the objective of our problem, when Ns (r) = ∅, a random C. Tracking the Spill Boundarysearch technique in discrete time with the input [ur (k), wi (k)] i r Assume that the agent i is in the pursuing state. When ri −is utilized to navigate the agent at q with searching state rd < d, where d is a capture distance defined by the user, the agent changes into the tracking state. It will then move ur (k + 1) = ur (k) + b(k)Δt i i along the spill boundary with the interior of the spill on its left. r r wi (k + 1) = wi (k) + c(k)Δt (6) The forward direction of the agents’ movement is as shown in Fig. 3.where b(k) is a random variable having uniform distribution When an agent moves away from the forward direction, itswith the support assigned by the user, c(k) is a random variable velocity is negative. In this case, the unicycle model in (2) canhaving normal distribution with a zero mean, and variance speci- still be used by simply adding π to the orientation. For agentfied by the user, and Δt is the discrete time period. When another i, li is defined as follows. Assume that at time t, the ith agentobjective such as travel distance is included, collaboration be- is tracking Ωj . It will measure the length of the perimeter andtween agents may be used to improve the search efficiency (e.g., positions of other agents in the tracking state within its FOV.see Franchi et al. [8]). Alternatively, task allocation such as that Practically, this measurement may be performed by calibrateddeveloped by Viguria and Howard [24] may be implemented. webcams (low cost, but low accuracy), laser rangefinders (higher cost and high accuracy), or a system such as that developed byB. Pursuit Pugh et al. [25]. Then, if the closest neighbor in the forward When a point lying on the boundary of the spill is within direction, whose index is represented by N (ri ), is inside its FOV,the ith agent’s sensor FOV, a detection occurs. The ith agent set li = ri , rN (r i ) ∂ Ω j ; otherwise, li is unknown to the agent.changes to a pursuing state if a detection occurs either in its Assume that ∂Ωj can be represented by a function s = f (r),FOV or by a member of its local communication graph. The where s ∈ [0, ∂Ωj ] indicates the length of the perimeter fromlocation of the detected point is denoted by rd . A potential field a reference point to r along the forward direction. Write f (ri )
  4. 4. 124 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 18, NO. 1, FEBRUARY 2013as si and s(rN (r i ) ) as si+1 , then when li is known to the agenti, it can be computed as follows: si+1 − si , if si+1 ≥ si li = (9) si+1 − si + ∂Ωj , if si+1 < si .Define a virtual distance Li between agent i and N (ri ) as li , if li < L Fig. 4. Change in θi at each time step. (a) Movements of agent and spill have Li = (10) intersection; if Δsi > 0, angular change is Δθi ; if Δsi < 0, angular change L, if li ≥ L or li is unknown is Δ θi . (b) Movements of agent and spill have no intersection; agent moves toward the closest boundary point of the spill.where L is the influence distance between agent i and agentN (ri ), and is set as L = rS in our paper. where ˆi is the noisy measurement by agent B. This case will be l Assuming that L0 = Ln j , i.e., the last agent wraps to the first studied in our future study.agent, a potential function [26], [27] is proposed for agents i,which is given by D. Stability Analysis Li−1 Vi (Li , Li−1 ) = k1 2ln(Li ) + (11) To investigate the system’s stability, we consider a time t > T Li in which we assume that all agents are in the tracking state, andwhere k1 is a positive constant. When Li < L and Li−1 < L, the spills stop changing in size and location. Another assump-using (9)–(11), the derivative of Vi with respect to si is tion is that the number of agents is large enough so that each dVi 1 Li−1 agent is connected with its leading and trailing neighbors during = −k1 − 2 (12) tracking. Without loss of generality, we relabel the agents so that dsi Li Li the first n1 agents track Ω1 , the (n1 + 1)th–(n1 + n2 )th agentswhere Vi has a minimum at Li = Li−1 . Including the control of track Ω2 , and so on. Let l = [L1 , L2 , . . . , Ln ]T . The collectivevelocity for the agents, the following controller is proposed to potential of the system can be given bybe used as the linear acceleration input of the ith agent: ⎛ ⎞ p n 0 +···+n jui = ⎝⎧ V (s) = V (l) = Vi ⎠ (15)⎪k 1 Li−1⎪ 1⎪ − 2 if Li < L, Li−1 < L j =1 i=n 0 +···+n j −1 +1⎪⎪ Li Li⎪⎪⎪⎪ where s = [s1 , . . . , sn ]T ; p is the number of spills when the⎪⎪ +(vi+1 − 2vi + vi−1 ),⎪⎪ spills stop changing; n0 equals zero; and M1 , M2 , . . . , Mp are⎨ 1 Li−1 k1 − 2 +(vi−1 − vi ), if Li = L, Li−1 < L the lengths of the p spill boundaries; L1 , L2 , . . . , Ln satisfies⎪⎪ L L ⎧⎪⎪ ⎪ L1 + L2 + · · · + Ln 1 = M1⎪⎪ ⎪ ⎪⎪⎪ k1 1 L ⎨L⎪⎪ − +(vi+1 − vi ), if Li < L, Li−1 = L n 1 +1 + Ln 1 +2 + · · · + Ln 1 +n 2 = M2⎪⎪ Li L2⎪⎩ i ⎪ ⎪··· 0, if Li = L, Li−1 = L. ⎪ ⎩ Ln 1 +···+n p −1 +1 + Ln 1 +···+n p −1 +2 + · · · + Ln = Mp . (13) (16) The collective dynamics of the system is given byFrom (12) and (13), it is evident that when Li goes to zero,ui approaches minus infinity. This guarantees that the ith agent ˙ s=v (17)does not surpass the (i + 1)th agent, which implies that the order Tof the agents is maintained when they are moving. ∂V1 ∂V2 ∂Vn v=− ˙ , ,..., − L(s)v (18) The angular velocity of the ith agent is also controlled dis- ∂s1 ∂s2 ∂sncretely. Assume that the change in distance traveled by the ith where v = [v1 , . . . , vn ]T and L is the graph Laplacian as de-agent during Δt is Δsi . The change in θi , denoted as Δθi , is scribed in [17] and [28].computed in different situations, as shown in Fig. 4. By using Lagrange Multipliers, (15) has an extremum point If another kind of agent, denoted as B, which has a much larger atmeasurement range, (e.g., an airborne agent) is available to ⎧monitor the spill, while the multiple robotic agents are tracking ⎪ M ⎪ L1 = L2 = · · · = Ln 1 = 1 ⎪the spill, its measurement can be used as a coarse measure of ⎪ ⎪ n1 ⎪ ⎪li . This measurement of li is likely to have a lot of associated ⎪ ⎨ M2 Ln 1 +1 = Ln 1 +2 = · · · = Ln 1 +n 2 =noise due to the low resolution of the global measurement. In n2 ⎪··· ⎪that case, (10) may be changed to ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ Ln +···+n +1 = Ln +···+n +2 = · · · = Ln = Mp . li , if li < L ⎩ 1 p −1 1 p −1 Li = (14) np ˆi , l if li ≥ L (19)
  5. 5. ZHANG et al.: SPILL DETECTION AND PERIMETER SURVEILLANCE VIA DISTRIBUTED SWARMING AGENTS 125 ˙ In this case, H equals zero when v is an eigenvector of L cor- responding to eigenvalue zero. Then, v will be in the space with basis containing p vectors, denoted by bi = [c1 , c2 , . . . , cn ], where 1, n0 + · · · + ni−1 + 1 < j ≤ n0 + · · · + ni cj = 0, otherwise (23) for i = 1, 2, . . . , p, and v = λ1 b1 + λ2 b2 + · · · + λp bp (24) where λi , i = 1, 2, . . . , p, is an arbitrary parameter that in this case represents the steady linear velocity of all agents on ∂Ωi . This shows that the velocities of all agents tracking the same spillFig. 5. Example of the collective potential value changing with L 1 and L 2 . converge to the same value. Since v is bounded, the convergent velocity is also bounded. When H achieves a minimum, V is also at its local minimum. From previous analysisAlthough it is analytically difficult to show that this point is theonly minimum for (15), numerical simulations with MATLAB Ln 1 +···+n j −1 +1 = · · · = Ln 1 +···+n j , for j = 1, 2, . . . , psupport this assumption. For example, when n = 3, M = 24, (25)p = 1, and k = 1, the value of V is shown in Fig. 5, where is a local minimum for V . Hence, the system achieves the stablethe minimum of V appears at L1 = L2 = L3 = 8 and satisfies state with equal distance between adjacent agents and equal(19). Other values of n, M , and p also satisfy (19) as verified velocity for all agents tracking the same spill.by simulations. Consider a case that after all agents change to tracking state, Let H(s, v) represent the energy of the system, i.e. spill Ω1 does not have enough agents tracking along its bound- ary, i.e., n1 < ∂Ω1 /L. We claim that all agents tracking Ω1 n 1 2 converge to the same velocity and the distance between each H(s, v) = V (s) + vi . (20) pair of adjacent agents converges to a value no less than L. The 2 i=1 energy of the agents tracking Ω1 is presented asThen, n1 1 2 T H1 (s1 , v1 ) = V (s1 ) + vi . (26)˙ ∂V1 ∂Vn 2H(s, v) = ∇V (s) v − T ,..., v − v L(s)v T i=1 ∂s1 ∂sn Similarly, ∂Vn 1 ∂V2 ∂Vn −1 ∂Vn −n p +1= + ,..., + v − vT L(s)v ˙ 2 Ln 1 −1 1 ∂s1 ∂s1 ∂sn ∂sn H(s1 , v1 ) = − 2 − ,..., Ln 1 Ln 1 L2 2 Ln 1 −1 1 2 Ln −2 1= − 2 − ,..., − 2 − v 2 Ln −2 1 Ln 1 Ln 1 L2 Ln −1 Ln −1 Ln −n p +1 × − 21 − v1 − v1 L(s1 )v1 T Ln 1 −1 Ln 1 −1 L1− vT L(s)v (21) (27)where L has the form where s1 = [s1 , . . . , sn 1 ] and v1 = [v1 , . . . , vn 1 ]. Without loss ⎛ ⎞ of generality, we assume that at time t, L1 is a block diagonal L1 ⎜ L2 ⎟ matrix containing two blocks L11 and L12 . In view of the dis- ⎜ ⎟ L=⎜ ⎟ (22) cussion before, if no connection between L11 and L12 holds, ⎜ .. ⎟ ⎝ . ⎠ the velocity of agents in L11 converges to v 1 and the velocity of agents in L12 converges to v 2 . If v 1 = v 2 , the two connected Lp graphs will connect with each other some time since they arewhich is a positive semidefinite block diagonal matrix with rank tracking a perimeter. Then, (27) is likely to be negative and ˙n − p, and Lj has dimension nj . In general, H may be positive, cause the energy of the system to decrease again until either thebecause the potential function for agent i is based on only the graph splits into several connected graphs or the velocity of allclosest leading and trailing neighbors. agents converges to the same value. Since different velocities Therefore, for agent i, no information on Vi−1 and Vi+1 is of agents in various connected graphs cause a decrease of theavailable. However, with bounded v and the control in (13), system energy, the system energy achieves a local minimumeach Li , where i = 1, 2, . . . , n, tends to be close to each other, when the agents within all connected graphs tracking Ω1 haveand then, the first set of terms in curly brackets on the right side the same velocity. In this case, the first agent at the forward ˙of (21) gets close to zero. Thus, the sign of H is dominated by direction of each connected graph will have a leading virtual−v L(s)v and is negative. T distance equal to L (i.e., the distance between this agent and
  6. 6. 126 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 18, NO. 1, FEBRUARY 2013its leading adjacent agent is larger than L), which causes thedistance between adjacent agents within its graph to be L tohave a minimal energy as well. Therefore, the distance betweeneach pair of adjacent agents tracking Ω1 is not less than L. IV. SIMULATION AND EXPERIMENT RESULTS In this section, simulations and experiments are described totest the performance of the proposed method based on differentconditions. The influence of spill locations, size, and numbersas well as the agent group size is studied.A. Simulation Results In this section, we build a simulation to see how the agentgroup adapts to the change of the spill number as well as itslocation and size. In this environment, we assume that thereare two spills at the beginning. As time goes on, the two spillsmerge into one spill, and then, again split into two spills. Thenumber of agents is varied from 6 to 46, W is a square arenawith sides of length 40 m, rS = 5 m, rM = 8 m, vmax = 8 m/s,and Δt = 0.01 s. All simulation results are averaged over 30runs. The result of one run with 26 agents is shown in Fig. 6. From the time snapshots of the simulation process, we cansee that the agents successfully search, pursue, and track thespills no matter if they are merged or split into pieces. After thespills stop changing, the velocities of agents tracking the samespill converge to the same value as well as maintaining constantdistance between adjacent agents. Readers are referred to [29]for the results of examples with other spills. Fig. 7 shows the average time required for all agents to reachtracking state as a function of the number of agents. Five separatesimulations, using, respectively, 6, 16, 26, 36, and 46 agents,were run with all other parameters set to the same values usedin the simulation, as shown in Fig. 6. The results show that as thenumber of agents increases, the group requires less time for allagents to change the tracking state. This is because with more Fig. 6. Simulation result with changing number of spills. (a) Snapshot at timeagents, it is more likely that several agents will be connected in step one. (b) Snapshot at time step 52. (c) Snapshot at time step 400. (d) Snapshot at time step 682. (e) Snapshot at time step 690. (f) Snapshot at time step 5000.a local graph and that the possibility for an agent in the group (g) Distance between each agent and the closest agent ahead of it. (h) Velocityto detect a spill is increased. This decreases the time that the of each agent.agent group needs to explore the environment to detect spills.For more than 26 agents, the improvement in time decreasesas the number of agents increases. The reason is that when thenumber of agents is large, most agents are connected in the localgraph and immediately achieve the pursuing state as soon as oneagent in the local graph detects a spill; adding more agents tothe group does not decrease the time to detection as much as itdoes when the number of agents is small. To demonstrate how the size of the sensor FOV can affect theprocess time for all agents to change the tracking state, anothersimulation is conducted utilizing 16 agents, with different rS val-ues of 1, 3, 5, 10, 15, 20, and 30. The results are shown in Fig. 8.The results show that as the sensor FOV increases, the neededtime decreases. The rate of decrease tends to be small when rSis larger than 15. The reason is that as rS increases, the possi- Fig. 7. Average time needed for all the agents to change the tracking state forbility for the robotic sensor to detect a spill increases; however, different numbers of agents. The results are averaged over 30 runs.when rS is large enough compared to the size of the workspace,
  7. 7. ZHANG et al.: SPILL DETECTION AND PERIMETER SURVEILLANCE VIA DISTRIBUTED SWARMING AGENTS 127 Fig. 9. (a) Experimental configuration of Create robot with Dell Mini10 net- book, Logitech Quickcam Pro 9000, and Hokuyo URG-04LX-UG01 scanning laser rangefinder. (b) Perspective from camera no. 5 within the system.Fig. 8. Average time needed for all of the agents to change the tracking stateunder different sizes of sensor FOV. The results are averaged over 30 runs. A sample active-IR image of multiple robots captured by camera no. 5 is shown in Fig. 9(b). The markers are clearly vis- ible in this full-frame image, as are the spill and robot shapes.the agent could easily find the spill in a short time, and further The robots in this experiment are constrained to a plane; thus,increase of rS will not shorten the search time significantly. the out-of-plane distance measurement and the roll and pitch orientation measurements are unnecessary (and should be un-B. Experiment Results changing). For more details, the reader is referred to [22]. For each experiment, the robots were distributed about the Several experiments using real robots in a mixed simulation laboratory space away from the spill, with no particular arrange-setting have been conducted. The agents in these experiments ment or pattern. Results for two experiments are presented hereare iRobot Create robots. Dell Mini10 netbook computers are although several different configurations of spills have been con-mounted to each robot, sending drive commands to and receiving sidered in this paper, including convex and nonconvex shapes,sensor data from the Create base. shapes with different areas, and contiguous or noncontiguous ar- Each robot is equipped with reflective markers in a unique eas. Both experiments presented here utilized five robots in thepattern for identification to allow tracking via NaturalPoint Op- configuration discussed; several other experiments were con-tiTrack V100R2 cameras and customized Tracking Tools soft- ducted with three or four robots, as well.ware on a centralized computer (see [30] and [31] for alter- For the experiments reported here, the communication rangenatives) . The tracking data, akin to “indoor GPS,” are avail- is rM = 2 m, the avoidance influential range is η1 = 1 m, andable to each individual robot via wireless ethernet (WiFi) from track-state influence range is rS = L = 1 m.this central switchboard. The laboratory space is approximately In the preliminary experiments, it was observed that in track3 m × 6 m, which is well within WiFi range; use of the switch- state, the robots occasionally converged to a commanded speedboard computer enables the simulation of limited communica- that is too close to zero to be realized. Thus, in these experiments,tion range by allowing (respectively, blocking) the communi- a minimum velocity Vm in = 50 mm/s was imposed to preventcation between robots that are inside (respectively, outside) a the robots from coming to a stop while attempting to reachspecified range. equilibrium. The spills are simulated by covering an area of the floor with The first experiment presented utilizes a stationary rectan-a material of contrasting color. The spill sensor on each robot gular spill with a perimeter length of 4.7 m. With five robots,is a set of four downward looking IR sensors mounted on the and rS = L = 1 m, this should yield equal spacing along thefront bumper. The robot cannot detect the spill until it is already perimeter once all robots achieve the track state. The results ofsufficiently close to enter tracking state. If no other spill sensor this experiment are shown in Fig. 10.is equipped, the time spent in pursuit state in these experiments From the figure, it can be seen that the first four robots quicklywill be only one time step if the robot has directly detected the transition to track state. However, as the robots are not points butspill. The only case in which a robot remains in pursuit state for rather extended bodies, some additional time is required for theextended time is when spill detection occurs by another member fifth robot to reach the perimeter. This is due to the avoidanceof the local communication graph. hierarchy that forces a nontracking robot to yield to one that The downlooking IR sensors of the Create robot are thus used is tracking. Thus, a sufficient gap must be present before theas the primary sensors for actually tracking the spill; when the robot can merge onto the perimeter. Once all five robots are onspill is detected in these sensors, the robot switches into track the perimeter, the speeds do indeed converge, and the spacingstate.1 reaches an equilibrium. The second experiment presented utilizes the same stationary 1 For these experiments, the robots do not make use of on-board cameras spill of the first experiment, but with a second smaller spillalthough this capability has since been implemented for these robots. The with a perimeter length of 2.5 m that moves over time. Therobots are now equipped with Logitech webcams and Hokuyo scanning laserrangefinders, and relatively localize to their neighbors using methods described results of this experiment are shown in Fig. 11. Initially, the twoin [31] and [32]. spill components are overlapping; thus, the initial evolution is
  8. 8. 128 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 18, NO. 1, FEBRUARY 2013Fig. 10. Experimental result for five robots with a stationary large spill. (a)–(e) Snapshots of selected time points indicating the location of the spill and theagents. (f) Linear speeds of all agents.similar to that of the first experiment. Beginning at time step500, the smaller spill is gradually moved away from the largerspill, increasing the perimeter length and eventually separatinginto a second small spill; snapshots of this transition are seen inFig. 11(d)–(e). During the growth phase of the spill, the robots Fig. 11. Experimental result for five robots with a large spill that grows, splits into two spills, and then collapses to one large spill. (a)–(g) Snapshots of selecteddynamically increase their spacing to accommodate the longer time points indicating the location of the spill and the agents. (h) Linear speedsperimeter. Once the smaller spill separates, one robot continues of all agents.to track it with no change in its velocity; on the larger spill, theremaining four adjust their relative spacing to accommodate the and track a number of spills in an unknown environment. Ashorter perimeter and lost robot. hierarchical potential field is designed for agents in different At time step 700, the smaller spill rejoins the larger spill. states to control their movement that provides a simpler controlThis increased perimeter length, as illustrated in Fig. 11(f), is law for collision avoidance. Simulation and experiment resultsdetected by the next-passing robot around time step 730. This demonstrate that the agents can successfully detect and trackcauses a large increase in its speed because its leading robot spills whose location, shape, size, and number may change overis suddenly much further away along the perimeter. As seen time. Significantly, this adaptation occurs automatically within Fig. 11(h), the speeds of most of the robots briefly increase no need to specify a predetermined distance between adjacent(around k = 700) when the smaller spill rejoins the larger spill. agents. Further focus on search efficiency and optimal conver-The reintroduction of the fifth robot into the network causes a gence rates is ongoing. Additional enhancement of the robots’disruption to the equilibrium, which quickly settles out. Finally, sensing ability continues.the small spill is completely engulfed by the larger spill, againresulting the convergence as seen in the first experiment. ACKNOWLEDGMENT Videos of the presented experiments and simulations, as well The authors gratefully acknowledge the laboratory supportas other experiments not included here, can be found at the Duke provided by A. W. Caccavale and S. W. Li.RAMA Lab YouTube channel [33]. REFERENCES V. CONCLUSION [1] E. Sahin, Ed., Swarm Robotics (Lecture Notes in Computer Science, vol. 3342). Heidelberg, Germany: Springer, 2005, ch. 2, pp. 10–20. In this paper, a hybrid system of finite states with feedback [2] T. H. Labella and M. Dorigo, “Division of labor in a group of robotscontrol is advanced for a group of agents with a limited sensor inspired by ants’ foraging behavior,” ACM Trans. Auton. Adapt. Syst.,FOV and a limited communication range to search for, detect, vol. 1, no. 1, pp. 4–25, Sep. 2006.
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Blackwell, “Particle swarm optimization. An multiagent systems, Bayesian statistics, and decision overview,” Swarm Intell., vol. 1, no. 1, pp. 33–57, 2007. making under uncertainty.[12] D. Casbeer, D. Kingston, R. Beard, T. Mclain, S. Li, and R. Mehra, Dr. Zhang has been a member of the ASME since “Cooperative forest fire surveillance using a team of small unmanned air 2008. vehicles,” Int. J. Syst. Sci., vol. 37, no. 6, pp. 351–360, 2006.[13] J. Clark and R. Fierro, “Mobile robotic sensors for perimeter detection and tracking,” ISA Trans., vol. 46, pp. 3–13, 2007.[14] D. Cruz, J. McClintock, B. Perteet, O. Orqueda, Y. Cao, and R. Fierro, Gregory K. Fricke received the B.Sc. degree in en- “Decentralized cooperative control—A multivehicle platform for research gineering and applied science with mechanical con- in networked embedded systems,” IEEE Control Syst. Mag., vol. 27, no. 3, centration from the California Institute of Technol- pp. 58–78, Jun. 2007. ogy, Pasadena, in 2000, and the M.Sc. degree in me-[15] R. Alur, T. Dang, J. M. Esposito, R. B. Fierro, Y. Hur, F. Ivancic, V. Kumar, chanical engineering in 2009 from Duke University, I. Lee, P. Mishra, G. J. Pappas, and O. Sokolsky, “Hierarchical hybrid Durham, NC, where he is currently working toward modeling of embedded systems,” in Proc. First Int. Works., Embedded the Ph.D. degree in mechanical engineering, focused Softw., Tahoe City, CA, 2001, pp. 14–31. on the control of multirobot systems using minimalist[16] D. Bruemmer, D. Dudenhoeffer, M. Anderson, and M. McKay, “A robotic behavioral control laws. swarm for spill finding and perimeter formation,” in Proc. ANS Spectrum., His current research interests include system engi- Aug. 2002. neering, controls, and embedded software with sev-[17] R. Olfati-Saber, “Flocking for multi-agent dynamic systems: Algorithms eral years of experience with The Boeing Company and Hughes Space & Com- and theory,” IEEE Trans. Automat. Contr., vol. 51, no. 3, pp. 401–420, munication. Mar. 2006. Mr. Fricke is a student member of the ASME Dynamic Systems and Controls[18] R. Olfati-Saber and R. Murray, “Flocking with obstacle avoidance: Coop- Division. eration with limited communication in mobile networks,” in Proc. 42nd IEEE Conf. Decis. Control, Maui, HI, 2003, pp., 2022–2028.[19] H. Tanner, A. Jadbabaie, and G. Pappas, “Stable flocking of mobile agents, part I: Fixed topology,” in Proc. 42nd IEEE Conf. Decis. Control, Maui, HI, 2003, pp., 2010–2015. Devendra P. Garg received the B.Sc. degree in me-[20] H. Tanner, A. Jadbabaie, and G. Pappas, “Stable flocking of mobile agents, chanical engineering from Agra University, Agra, part II: Dynamic topology,” in Proc. 42nd IEEE Conf. Decis. Control, India, in 1954, the B.Eng. degree from the Univer- Maui, HI, 2003, pp., 2016–2021. sity of Roorkee, Roorkee, India, in 1957, the M.Sc.[21] Z. Yang, Q. Zhang, and Z. Chen, “Choosing good distance metrics and degree in mechanical engineering from the Univer- local planners for probabilistic roadmap methods,” IEEE Trans. Robot. sity of Wisconsin, Madison, in 1960, and the Ph.D. Autom., vol. 16, no. 4, pp. 442–447, Aug. 2000. degree in mechanical engineering from New York[22] G. Fricke, G. Zhang, A. Caccavale, W. Li, and D. P. Garg, “An intelligent University, New York City, NY, in 1969. sensing network of distributed swarming agents for perimeter detection He is Professor of Mechanical Engineering and Di- and surveillance,” in Proc. 3rd ASME Dyn. Syst. Control Conf., Cam- rector of the Robotics and Manufacturing Automation bridge, MA, Sep. 2010, pp. 741–748. (RAMA) Laboratory at Duke University, Durham,[23] J. C. Latombe, Robot Motion Planning. Norwell, MA: Kluwer, 1991. NC. He previously taught at the University of Roorkee (now, IIT/Roorkee),[24] A. Viguria and A. Howard, “An integrated approach for achieving multi- New York University, and MIT. He also served as Director of the Dynamic robot task formations,” IEEE/ASME Trans. Mechatronics, vol. 14, no. 2, Systems and Control Program at the National Science Foundation for six years. pp. 176–186, Apr. 2009. He was a Guest Editor of two Special Issues of ASME Transactions. He is an[25] J. Pugh, X. Raemy, C. Favre, R. Falconi, and A. Martinoli, “A fast onboard author of two books and numerous research publications in technical journals relative positioning module for multirobot systems,” IEEE/ASME Trans. in the U.S. and abroad. His research interests include control system synthesis, Mechatronics, vol. 14, no. 2, pp. 151–162, Apr. 2009. vehicle dynamics, robotics and automated manufacturing, and application of[26] N. Leonard and E. Fiorelli, “Virtual leaders, artificial potentials and coor- control theory to socioeconomic systems. dinated control of groups,” in Proc. IEEE Int. Conf. Decis. Control, 2001, Prof. Garg is a Life Fellow of the American Society of Mechanical Engineers pp., 2968–2973. (ASME). He is a Past Chairman of the ASME’s Dynamic Systems and Con-[27] M. Kumar, D. Garg, and V. Kumar, “Segregation of heterogeneous units trol Division (DSCD), and has served as Chairman of the Advisory Panel, and in a swarm of robotic agents,” IEEE Trans. Automat. Contr., vol. 55, no. 3, Chairman of the Honors and Awards Committee of the DSCD. He has received pp. 743–748, Mar. 2010. the ASME’s Dedicated Service Award, the DSCD Leadership Award, and the[28] U. Luxburg, “A tutorial on spectral clustering,” Statist. Comput., vol. 17, 2003 Edwin F. Church Medal. no. 4, pp. 395–416, 2007.