On the Scheduling of Systems of Heterogeneous UAVs and Fuel Service Stations for Long-Term Mission Fulfillment

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1 On the Scheduling of Systems of Heterogeneous UVs and Fuel Service Stations for Long-Term Mission Fulfillment Jonghoe Kim, Byungduk Song, and James R. Morrison*, Member, IEEE bstract The duration of missions that can be accomplished by unmanned aerial vehicles (UVs) is limited by the battery or fuel capacity of its constituent UVs. However, a system of UVs that is supported by automated refueling bases may support long term or even indefinite duration missions in a near autonomous mode. The UVs can return to a base, replenish their resources and resume their duties. We develop a mixed integer linear program model to formalize the problem of scheduling such a system that includes multiple bases in disparate geographic locations that are shared between the UVs. The system consists of a heterogeneous fleet of UVs (each with different travel speed and distance capabilities), refuel stations and mission trajectories that must be followed by at least one UV. UV may hand off the mission to another in order to return to base for a fuel recharge. For two example problems, a state of-the-art MILP solver such as CPLEX is sufficient to create a schedule for the model. This is the first time that a generic scheduling model has been developed that allows mobile agents to return to service after refueling across multiple bases. In practice, the approach allows for a long-term mission to receive uninterrupted UV service by successively handing off the task to replacement UVs served by geographically distributed shared bases. I. INTRODUCTION Missions of unmanned aerial vehicles (UVs) that require long term UV autonomy, such as indefinite border patrol or building construction, must resolve the limitation imposed by the finite UV energy source. While battery energy density optimization or UV efficiency improvements are Jonghoe Kim, Byungduk Song and James R. Morrison are with the Department of Industrial and Systems Engineering, KIST, Guseong-dong, Yuseong-gu, Daejeon , Republic of Korea. *Corresponding author ( james.morrison@kaist.edu; homepage: phone: ; fax: ). necessary, the issue of refueling is fundamentally one of logistics. Here we develop a scheduling model allowing a fleet of UVs and fuel service station to provide long term support of mission objectives. This is accomplished by allowing our UVs to be replenished and return to the field. The scheduling models developed appear to be the first of their kind allowing UVs to recharge at a collection of shared, geographically distributed base stations and then return to work. While our focus is on UVs, the model works just as well for any system of finite duration mobile robots or agents that can be redeployed following recharge. While high-cost military UVs such as the Predator can remain in flight for as long as 24 hours, commercial UVs, micro-uvs and nano-uvs are not as capable. s such, practical applications are limited. With greater autonomy, UV fleets could be employed for long-term missions and serve as a perimeter patrol, security escort, fire monitor, communication relay and environmental monitor. To resolve the limitation imposed by the finite energy source on board each UV, we propose a system of UVs, shared refueling stations distributed across the field and a scheduling algorithm to coordinate their activities. To accomplish the mission, the UVs can refuel at any station and return to service. The missions are assumed to be space-time trajectories that at least one UV must follow without fail. Figure 1 depicts an example system with three service stations, five UVs and three objectives (objects). The system must allocate resources to provide one UV at all times to each objective (object). Objects 1 and 2 are stationary and Object 3 follows a trajectory throughout the time horizon. The general system that we will consider consists of a

2 collection of N UVs (each with possibly different traveling speed and maximum flight distance), M refueling stations and T objectives (fixed or moving in a given time window). Throughout, we assume that the service stations can provide sufficient fuel or battery replacements to accomplish the mission. The contributions of this work are as follows. For what is to our knowledge the first time, we: Propose the conceptual idea that UVs be supported by a collection of shared service stations distributed over the field in disparate locations to conduct missions of indefinite duration. Develop an MILP scheduling model that allows a mobile robot to return to the field following a visit to any shared base for energy resupply. Here a collection of mobile robots must follow a specific time-space trajectory where the presence of any one at each time of the mission is sufficient. Demonstrate that the MILP formulations can be employed to direct the actions of a system of UVs and service stations on long-term missions that use multiple stations. The second is accomplished by discretizing the time-space trajectory (path) of the objectives, or jobs, into smaller pieces, or split-jobs. The ideas and models proposed might be considered to fall within the area of mobile robot logistics. The rest of the paper is organized as follows. In Section II, we review related scheduling research. Section III develops our mixed integer linear program (MILP). Numerical examples of our MILP are presented in Section IV. Concluding remarks and future directions are provided in Section V. II. LITERTURE REVIEW In recent years, considerable attention has been devoted to the development of various UV capabilities. To wit, target classification and tracking (c.f., [1-3]), decision support tools for Figure 1. system of three service stations, five UVs and three tasks human operators (c.f., [4-5]), automatic systems for landing control (c.f., [6-7]) and battery replacement systems (c.f., [8-9]) have been developed. In [10], a functioning prototype battery replacement system was employed with UV flight tests. There, they also developed software to guide the UVs to use the station. (It is not however a generic scheduling algorithm.) The design of a service station to provide an indefinite supply of batteries was considered in [9]. This is particularly relevant to our study at it will enable an automated service platform to indefinitely supply freshly charged batteries for weary UVs. The UV and service station system may then aspire to prosecute missions of indefinite duration. Much research has focused on UV scheduling. Some has developed scheduling methods for UVs without including a travel time or distance restriction. mathematical scheduling

3 model to allocate and aggregate the available UVs was developed in [11]. nonlinear integer program was proposed and validated in a small scale problem. The authors in [12] posed the problem of assigning multiple UVs to simultaneously perform cooperative tasks on consecutive targets. They considered a team of UVs acting as a sensor and communication network to cooperatively track and attack moving ground targets. mathematical program formalized the problem and a genetic algorithm was developed to obtain good solutions. The scheduling of capacitated UVs with limited flight duration has also been studied. Capacitated UVs should finish their tasks before their fuel (battery) runs out. UV scheduling based on the vehicle routing problem with time windows was proposed in [13]. There, each UV had a different maximum travel time and returned to the depot after their tasks. Tasks are defined by their location, required service time and time window (earliest and latest time to begin service). MILP was suggested to find an optimal schedule. Shima et al [14] developed an optimization algorithm for assigning multiple UVs to task tours. The scenario of interest was one where multiple micro-aerial vehicles are launched from a small UV in order to investigate selected targets in an urban setting. The time to finish serving all the targets was minimized via objective function and a solution was obtained by a search algorithm based on the branch and bound concept. scheduling model with n tasks and m UVs, each with a capacity limit q, was developed by Kim et al [15]. They considered two situations: no UV return and UV return. model for balancing workloads across the UVs was suggested. lidaee et al. [16] improved on the model in [15] to reduce the number of variables and constraints. The authors in [17] developed a scheduling method for a system of UVs and multiple home bases (with disparate locations) where each UV must return to its base at the end of its flight. There is no refueling. Research on capacitated UV scheduling is necessary because UVs have a fundamental duration of service limitation due to their dependence upon batteries or a liquid fuel. The issue of scheduling for persistent operation has been addressed in [18-20]. There, the concept of using a service station (possibly with multiple connection points) at a single location for persistent UV operations was studied. In this paper, we propose a UV scheduling model allowing UVs to recharge and return to service at multiple shared service stations distributed throughout the field. To our knowledge, this is the first such effort at persistence that allows distributed shared service stations. Due to the inclusion of the refuel/recharge process, it may be considered as a study on mobile robot logistics. III. UV SCHEDULING FOR LONG-TERM MISSIONS We discuss the idea that shared service platforms distributed across the field and a collection of UVs can be employed to prosecute missions of long duration. With this goal in mind, we develop a mathematical programming model that will schedule UVs and service platforms seeking to provide uninterrupted service to long term missions.. System to Provide Indefinite Duration Service Due to their dependence on a fuel source, a single UV can only prosecute a mission of limited duration. However, a fleet of UVs with well stocked or self-replenishing energy source can be exploited to provide a mission of indefinite duration. The idea is to allow a weary UV to handoff its mission to a refreshed UV. The weary UV will return to the service station for refueling (or battery recharge or replacement) and then return to the field. It will then accept a mission from a weary UV via handoff and replace that UV in

4 providing the desired service. This process may repeat indefinitely. The coordination of the activities of such a system would allow for the missions to be pursued without interruption. Such a coordinated process is enabled by the presence of service stations that can supply batteries at a desired rate indefinitely. The design of such a service station is discussed in [9] using elementary Petri net models. B. Mathematical Program to Schedule the System We next formulate a mixed integer linear program (MILP) that schedules a fleet of heterogeneous UVs with fuel limitations to serve time constrained jobs and minimize total travel distance. To schedule a UV tracking a moving target or patrolling an area, we break the space-time mission trajectories into pieces that we refer to as split jobs. This is required because one UV may not be able to cover the entire task due to a fuel or battery constraint. We assume that the specific times are known. Therefore, we can divide the trajectory of the moving target into several split jobs that may be served by different UVs. Each split job has a strict start time and end time. Split jobs for a moving target or patrol path are depicted in Figure 2. The number of split jobs and their start and end times are considered as fixed constants in the MILP formulation. They are not decision variables and must be determined in advance. This approach serves to discretize each mission. Using more split jobs may enable an improved objective function value but will increase computational complexity. We use i, j to index jobs and s to index recharge stations. Let k be the index for the UVs. We assume that a UV starts its travel from a recharge station and processes several split jobs. fter finishing its split jobs, it should return to a travel defines one UV flight. UVs can have multiple flights during the time horizon and r is introduced to index a th flight. Let d = N J +1 be the index that represents a dummy split job. dummy split job is required for a UV that does not process any split jobs. Let N J, N UV, N ST and N R be the number of split jobs, the number of UVs in the system, the number of recharge stations and the maximum number of flights per UV during the time horizon, respectively. recharge station can recharge multiple UVs simultaneously. Let M be a large positive number. Each split job has two (x,y) coordinate points which are start location (x i,y i ) and finish location (x j,y j ). UV starts the split job at the start point and completes it at the finish point. The travel distance from split to split ij ) is calculated using the Euclidean distance. That is, D ij = ((x i -x j ) 2 +(y i -y j ) 2 ) 1/2, where (x i, y i ) are the coordinates of split and (x j, y j ) are the coordinates of split point or station j. Note that D ij is not equal to D ji (the start and end points change). Let P i denote the process time of split job i or recharging time at station i. We assume that the recharge time for a UV is constant. Since we assume that the target movement or patrol path and times are known, split job i has a strict time constraint. Each split job i should start at time E i (and thus end at time E i + P i ). Note that since the start/end times and start/end locations for all split jobs are known, these are not our decision variables. The decision variables will simply tell us which UV is assigned to each split job and provide certain key event time instants. UV k can fly for at most q k units of time in one flight. We assume that initially all UV batteries or fuel tanks are empty (this is convenient for our model and is immediately rectified in the first moments of the schedule). UV does not use its fuel when they wait for a split job at the split job start point (perhaps they rest on the ground). Define S ok and TS k to be the initial location of k, respectively. The input parameters such as N J,

5 N UV, N ST, N R, D ij, P i, E i, q k, S ok and TS k are known constants. The notation for set indices follows: UV flight index: r in R = {1,, N R }; UV index: k in K = {1,, N UV }; Split job index: i, j in J = {1,, N J }; Set of split jobs and dummy jobs: = {1,, N J +1}; Set of UV flight start recharge stations: SS = {N J +2, N J +4,, N J N ST }; Set of UV flight end recharge stations: SE = {N J +3, N J +5,, N J N ST +1}; Set of all job and recharge stations = U SS SE ) = {1,, N J N ST +1}. The decision variables for our mathematical program are given as follows: X ijkr = 1 if UV k processes split job j or recharges at station j after processing split job i or recharging at station i during the r th flight; 0, otherwise. C ikr is th flight i; otherwise its value is 0. Y ikr = 1 if UV k processes split job i during its r th flight; 0, otherwise. If we use one index for each recharge station, C ikr cannot be determined in the case that UV k starts its flight at station i and finishes its flight at the same station during the r th flight. Therefore, we assign two indices to each recharge station. Station s is allocated indices N J +2s and N J +2s+1. The first index for recharge station s in W SS is used when a UV moves from station s to a job. The second index SE is used when UV moves from a split job to station s. We assume that the UV travel speed does not affect its fuel consumption. Fuel consumption is proportional to travel time. (It is easy to adjust the formulation so that fuel consumption is proportional to travel distance instead. This may be a more natural way to treat fuel consumption.) Our mixed integer linear program (MILP) for the UV scheduling problem is as follows: Figure 2. Split jobs for a moving target subject to (initial recharge station constraint) X s, jk11 ( k K), (2) j ok (recharge station constraints) X 1 ( k K, r R), (3) s SS j s SE i i X sjkr X 1 ( k K, r R), (4) iskr iskr s1, ikr1 i X ( k K, r1... N 1, s ), (5) C C ( kk, r1... N 1, s ), (6) skr s1, kr1 R SE (split job assignment constraints) X 1 ( j ), (7) kk rr i j i ijkr J X X 0 ( i, k K, r R),(8) ijkr jikr j X 0 ( k K, r R, s ), (9) iskr (start time constraints) C P D / TS C M (1 X ) ikr i ij k jkr ijkr ( i, j, k K, r R),(10) j SE Minimize D X kk rr i j SS SE R X Y ( i, k K, r R), (11) ijkr ikr J MY C ( i, k K, r R), (12) ikr ikr J ij ijkr, (1) SS SE

6 Figure 3. Example layout for tracking a moving ground target kk rr C E ( i ), (13) ikr i J (fuel and battery constraint) D / TS X P X q ij k ijkr i ijkr k i j i j ( k K, r R), (14) (dummy job constraints) Xsdkr Xd, s1, kr ( kk, rr, sss ), (15) X dikr X idkr 0 ( k K, r R, ij ), (16) (variable nonnegativity and integrality constraints) C 0 ( k K, r R, i ), (17) ikr X {0,1} ( kk, rr, i, j ), (18) ijkr Y {0,1} ( k K, r R, i ). (19) ikr The objective function (1) is to minimize the total travel distance of the UV fleet. Initial recharge station constraint (2) ensures that every UV should start its first flight from its initial recharge station. Recharge station constraint (3) guarantees that UV k can have only one starting recharge station per flight. Constraint (4) indicates that UV k can have only one ending recharge station per flight. Constraint (5) requires that if UV k finishes its r th flight at station s, its r+1 th flight starts at station s. Constraint (6) states that the finish time of a th flight is equal to the th flight. Job assignment J to be processed by a UV. Constraint (8) is a flow balance constraint that ensures a UV does not finish its flight at a job. Constraint (9) ensures that a UV cannot finish its flight at the starting station. (This is not a restriction, just a notational issue related to each station having two indices.) Start time constraint (10) gives the relationship between the split job start time or recharge start time and that of its successor for the same UV during its r th flight. Constraints (11), (12) and (13) imply that every split j J starts its process at the pre-determined start time of the split job. Fuel and battery constraint (14) states that the total flight time, including travel time and process time for split jobs, capacity. Dummy job constraint (15) ensures that a UV cannot go to the start recharge station in SS after processing a dummy split job. Constraint (16) prevents a dummy split job from having a successor and predecessor split J. Constraints (17), (18) and (19) define the ranges of the decision variables. The mathematical model proposed for UV scheduling requires N R > 1 due to constraints (5) and (6). Since, N R is just the maximum number of flights allowed for each UV; this is not in any way a restriction on the modeling capability. IV. NUMERICL EXPERIMENT In this section, we present two numerical examples to illustrate the application of the MILP

7 Split Job TBLE 1. SPLIT JOBS FOR EXMPLE 1 Start point Finish point Process time Split Job start time 1 50, ,250 1 min 6 min 2 150, ,250 1 min 7 min 3 250, ,250 1 min 8 min 4 350, ,250 1 min 9 min 5 450, ,250 1 min 10 min 6 550, ,250 1 min 11 min 7 650, ,250 1 min 12 min TBLE 2. OPTIML ROUTE OF UVS DURING FIRST FLIGHT UV Split Job Served Start station End station q k (min) None N/ N/ 8 3 None N/ N/ 8 4 None N/ N/ 8 5 2,3,4,5,6, ,9,10,11,12,13, Obj. value = 1846m 8 750, ,250 1 min 13 min 9 850, ,250 1 min 14 min , ,350 1 min 15 min , ,450 1 min 16 min , ,550 1 min 17 min , ,650 1 min 18 min , ,750 1 min 19 min in Section III. The two examples were tested on a personal computer with Intel(R) Core(TM)2 Quad CPU Q8400, 2.66GHz and 4.00GB ram using ILOG CPLEX 11.0 and OPL Development Studio Example 1: Tracking a Moving Ground Target. UVs can be used to track a moving target. The layout of Example 1 is provided in Figure 3. There are three recharge stations located at coordinates (250m, 550m), (650m, 550m), (750m, 150m), and each station has two empty UVs initially. The moving target will start its travel at time 6 min at coordinate (50m, 250m) and finish its travel at moving speed is 100m/min and constant. The target should be observed at all time during its travel by UVs. UVs 1, 2, 3, 4, 5 and 6 are initially located at stations 1, 1, 2, 2, 3 and 3, respectively. UVs 1, 2, 3 and 4 have 100 m/min travel speed at maximum. UV 5 and 6 can fly up to 150 m/min. We allocate 14 split jobs for the moving target tracking; their start point coordinate, finish point coordinate and duration are given in Table 1. For example, Split Job 1 starts at time 6 min at location (50m, 250m) and ends at location (150m, 250m) after 1 minute. We set the maximum number of UV flights to two for all UVs. We set the maximum travel time for UVs 1, 2, 3 and 4 to 8 minutes and UVs 5 and 6 to 13 minutes. We solve the resulting MILP using CPLEX. In the optimal solution, UV 1 starts its first flight from station 1 to serve split job 1 and then returns to station 1. UVs 2, 3 and 4 do not process any split job. UV 5 starts its first flight from station 3 to serve split jobs 2, 3, 4, 5, 6 and 7. fter that, it returns to station 3 and stays at station 3. UV 6 flies from station 3 to split job 8 to process split jobs 8 14 and returns to station 2 after its flight. It stays at station 2. ll split jobs are served in a flight. The minimized total travel distance is 1846 m. The result is summarized in Table 2. We conduct sensitivity analysis by adjusting q k. The tuple Q is (q 1,q 2,q 3,q 4,q 5,q 6 ) and the unit of q k is minutes. We increase or decrease q k for all UVs by the same amount. It is observed that as q k increases, the number of UVs used, objective function value and computational time decrease. The detailed results of our sensitivity study are shown in Table 3. B. Example 2: UV Border Patrol. One can construct an automatic area patrol system using camera equipped UVs, automatic recharge stations and the mathematical model

8 TBLE 3. SENSITIVITY NLYSIS BOUT MXIMUM TRVEL TIME OF UV Q Used UVs Obj. value (m) (7,7,7,7,12,12) Infeasible Computational time (sec) (8,8,8,8,13,13) 1,5, (9,9,9,9,14,14) 1,2, (10,10,10,10,15,15) 1,2, (11,11,11,11,16,16) 1, (12,12,12,12,17,17) 1, (13,13,13,13,18,18) 1, developed in this study. The configuration of Example 2 is depicted in Figure 4. There are two recharge stations located at coordinates (300 m, 600 m) and (600 m, 300 m). Each station has one UV (they initially require a recharge due to our formulation, but this happens immediately at the beginning of any feasible schedule). There are four fixed patrol paths the UVs must follow. Each start point and end point of the patrol paths are depicted in Figure 4. Patrol paths 1, 2, 3 and 4 should be started at times 6, 18, 6 and 18 minutes. UVs 1 and 2 are initially located at stations 1 and 2, respectively. We set the maximum number of flights for each UV to two. The maximum travel speed of UVs 1 and 2 is 150 m/min. We create 8 split jobs to describe the patrols (effectively discretizing the patrol paths); their details are shown in Table 4. We set the maximum flight duration q k of both UVs to 15 minutes. CPLEX is sufficient to obtain a solution. In the optimal solution, flight starts at station 1, processes split jobs 1, 2, 3 and 4, then enters station 2. UV 2 starts its first flight from station 2, processes split jobs 5, 6, 7 and 8 and enters station 1. ll split jobs are served by the during the flights. The total travel distance is 2048m. The result is summarized in Table 5. If we change q k of the UVs to 14 minutes, the Figure 4. Layout configuration of auto patrol system UVs cannot serve all jobs during their first flights due to limited fuel capacity. The optimal schedule of UVs during their first and second flights is summarized in Table 6. UV 1 serves job 1 and 2 during its first flight and returns to station 1 for recharging. fter recharging it serves jobs 5 and 6. Finally it heads for recharge to station 2. Similarly, UV 2 serves jobs 5, 6 during its first flight and serves jobs 7, 8 during the second flight. If the patrol schedule were of longer duration, this process would repeat. V. CONCLUDING REMRKS UV missions are limited by the battery life (or fuel life) of their robots. However, by incorporating into the system a collection of service stations that can replace the batteries (or fuel) for a long duration of time, the mission may be conducted much longer. The UV can refuel at the station and return to service. This would enable a UV service that is not limited by the battery life of a single UV. Further, service station concepts have been proposed in the literature that would (subject to a throughput limitation) allow for

9 Split Job TBLE 4. INFORMTION OF SPLIT JOB OF EXMPLE 2 Start point Finish point Process time Split Job start time 1 300,900 0,900 2 min 6 2 0,900 0,600 2 min 8 3 0,300 0,0 2 min ,0 300,0 2 min ,0 900,0 2 min ,0 900,300 2 min , ,900 2 min , ,900 2 min 20 batteries to be supplied indefinitely. With such a service station, the mobile robot missions might be conducted without interruption for an indefinite duration of time. Incorporating such mobile robot logistics issues into the mobile robot system has the potential to increase the capabilities, autonomy and practical applicability of such systems. With an eye toward supporting the delivery of such increased autonomy, we developed mixed integer linear programming (MILP) scheduling models. The models allow the mobile robots to visit any of a number of shared bases distributed throughout the field, refuel and then return to service. They allow the mobile robots to follow a specific trajectory through space at required times. This is accomplished by breaking the path into so-called split jobs that each mobile robot may service. To our knowledge, the features of persistence and multiple shared service stations (distributed throughout the field) have not previously been incorporated into scheduling models in the literature. The MILP scheduling model developed is implemented on two examples. The optimization problems are solved with CPLEX. brief sensitivity study on the maximum duration that a UV can be in flight is conducted. The examples demonstrate that as the UV battery life decreases relative to the mission duration, it is optimal to travel to the service TBLE 5. OPTIML ROUTE OF UVS DURING FIRST FLIGHTS UV Split Job Served Start station station, recharge and return to service. Future research should delve into methods that allow efficient computation of a schedule. For example, heuristic approaches such as genetic algorithms may help to address large size problems in reasonable computational time. In addition, studies that develop scheduling methods for indefinite duration missions, such as perpetual border patrol, should be pursued. REFERENCES End station q k (min) 1 1,2,3, ,6,7, Obj. value = 2048 m [1] target classification and tracking from real-time video, in Proc. IEEE Workshop on pplications of Computer Vision, Princeton, 1998, pp [2] using a micro air vehicle with a fixed angle camera,in Proceedings of the merican Control Conference (CC 8), June 2008, pp [3] V. N. Dobrokhodov, I. I. Kaminer, K. D Jones, and R. -based tracking and motion estimation for moving targets using small UVs, In Proc. of the I Guidance, Navigation, and Control Conference and Exhibit, Keystone, 2006 (Paper no. I ). [4] -UV scheduling for human operator target identification,in Proc. merican Control Conference (CC), San Francisco, C, June 2011, pp [5] M.L. Cummings and.s. Brzezinski, decision support for multiple independent UV schedule management, International Journal of pplied Decision Sciences, Vol. 3, No. 3, 2010, pp [6] -off and landing control for small UVs,In Proc. Control Conference, th sian, Melbourne, Victoria, ustralia, July 2004, pp in Vol.2. [7] G. Xu, Y. Zhang, S. Ji, Y. Cheng and Y. Tian, -based for UV autonomous landing on a ship, Pattern Recognition Letters, vol.30, no.6, 2009, pp

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