A Multi-Perspective Optimization Approach to UAV Resource Management for Littoral Surveillance

Transcription

1 A Multi-Perspective Optimization Approach to UAV Resource Management for Littoral Surveillance Héctor J. Ortiz-Peña Moises Sudit CUBRC, Inc. Buffalo, NY USA Michael Hirsch Raytheon, Inc. Orlando, FL USA Mark Karwan Rakesh Nagi University at Buffalo, SUNY Buffalo, NY USA Abstract Accuracy and timeliness of collected information by sensors (e.g., humans, unmanned vehicles, etc.) to prevent the illegal movement of drugs across the U.S. border has become critically important to create a safe and secure border environment. Efficient coordination of limited and distributed resources to gather the information necessary to (a) predict potential drug-related activities and (b) provide the protection to law enforcement authorities on the border has become paramount in this effort. We have developed a multi-perspective mathematical programming model to maximize the information gain from a team of unmanned vehicles performing surveillance around a region of interest. Routes of each vehicle are defined at its Control Station. Disruption of communication between each vehicle and its control station is minimized. Each control station considers its perspective of the environment (i.e., situational assessment) and mission, represented by a potential information gain map, resulting from the information gathered by its vehicle and received from other control stations on the same communication network. Routes of the vehicles are further constrained to be within pre-defined air corridors or shipping channels and may support (overlap in sensors coverage area) or complement (disjoint sensors coverage areas) different missions while surveilling the border. Using a small, simulated scenario, the applicability of the mathematical programming model for this type of operations is presented. I. INTRODUCTION Surveillance operations include collecting information from a variety of sensors, usually visual imagery or video, to monitor the activities on a particular area. This has been a long recognized priority of security agencies as an important operation for border security to prevent the illegal movement of drugs and to create a safe and secure border environment []. In many situations, littoral surveillance relies on the use of border patrol agents, video cameras, ground sensors and manned aircrafts to adequately monitor the border. Unmanned Aerial Vehicles (UAVs) can improve coverage along remote sections of the border and be used in situations where manned operations are too risky, too tedious, or prolonged periods of loiter time are required. The goal of several U.S. agencies, for example, is to begin using UAVs for collection of environmental data and to improve operational mission capabilities (including surveillance for search and rescue) and other essential components of national security to help safeguard the oceans from the Alaskan coast []. In this research, we look at the problem of routing a team of autonomous vehicles to maximize the resultant information gain over a region of interest. Our mathematical modeling development enables the unmanned vehicle system, consisting of the unmanned vehicle (UxV) equipped with on-board sensors and its off-board Control Station (CS), to develop flight plans that simultaneously adapt to the perceived environment and support Intelligence, Surveillance and Reconnaissance (ISR) mission objectives in a decentralized framework. The mathematical formulation considers each UxV s perspective of the environment (i.e., situational assessment) and mission, as information is only exchanged when UxVs are part of the same communication network. Each UxV perspective of the environment forms the basis of our multi-perspective optimization approach. The main strategy is to discretize space and time to represent the potential information gain on specific areas and time instances during the operation. Potential information gain refers to a measure of the available information, relevant to certain features on a particular situation, that might be derived from collected data. The developed mathematical programming model and applied concepts can be easily extended to analyze other unmanned or manned systems. In our model, each CS requires line-of-sight to communicate with its UxV. The range for this communication is limited. UxVs are responsible for sensing the environment. Each CS is responsible for determining the flight plan of its UxV over the planning horizon, considering mission objectives, its perspective of the environment, and the potential collected information from its UxV. Each CS can also exchange information with other neighbor CSs. This communication, however, is also limited. The primary objective of routing the UxVs is then to maximize the overall expected information gain considering available sensing capabilities; simultaneously, CSs need to maximize the network connectivity with other CSs to enable information sharing over the planning horizon in the decentralized framework. Our proposed approach accomplishes these objectives, enabling unmanned vehicle systems to autonomously develop and follow flight plans that, simultaneously, adapt to the perceived environment and support mission objectives. Using a small, simulated scenario,

2 the applicability of the mathematical programming model for this type of operations is presented. The rest of this paper is organized as follows: Section II-A describes, in general, different frameworks for planning and control of autonomous systems. Section II-B describes recent research for planning and control assuming decentralized frameworks. In section III our proposed mathematical programming model is described. Section IV presents the results for two representative scenarios related to littoral surveillance. Finally, in Section V, conclusions and future research directions are discussed. II. LITERATURE REVIEW A. Frameworks for Planning and Control of Autonomous Systems Frameworks for planning and control of autonomous systems for many cases, similar to information fusion systems, have been classified into three types of topologies [], []: () centralized, () decentralized, and () hierarchical. Central Decision Making node Broadcasted Messages from Central Node Messages to Central Node Fig. : Centralized Framework for Planning and Control Systems Decision Making Node Messages from Fusion Node Messages to Fusion Node Fig. : Hierarchical Framework for Planning and Control Systems In a centralized architecture, the information is propagated from node to node in the network until it reaches a central node responsible for determining and disseminating expected decisions (e.g., path definition, tasks assignments) to all lower nodes (Figure ). This requires high computational burden at the central node and a robust and reliable communication network that allows virtually perfect information flow among all the agents in the system and the central node. Decentralized frameworks (Figure ) rely on local (i.e., by each agent) processing of information, including information from nearby agents, and local decision-making. This framework reduces the computational and communication requirements of a centralized framework, allowing scalability of the system to large group sizes [5]. Jameson, in [], compared a few distributed architectures based on a set of general requirements for distributed information fusion. In his work, nodes on the network consisted of fusion centers (e.g., command and control centers) and/or sensors. In addition to the centralized and decentralized frameworks, Jameson describes the Distributed Hierarchical Information Fusion architecture. The nodes on this network correspond to military units in a command and control hierarchy. Each node is responsible for propagating the collected information to its parent and children nodes. Since data is propagated only to adjacent fusion nodes (Figure ), flow of information is faster than in certain centralized architectures (e.g., Figure ). Most planning and control algorithms assume a centralized framework. When the challenges of decentralized frameworks are addressed, architectures such as the one implemented by CEC are usually assumed: each UxV collects information from on-board sensors and, over a low latency network, information is exchanged with neighbor UxVs (i.e., peer nodes). Information is processed and trajectories are updated, as appropriate. Decision Making Node Messages to Near-by Nodes Fig. : Decentralized Framework for Planning and Control Systems B. Algorithms for Planning and Control Systems Research in the area of planning and control systems has resulted in the development of algorithms assuming, mostly, a centralized framework [7], [8]: information is collected in a single, central node and optimal or near-optimal plans are defined and communicated back to the agents (e.g., UxVs)

3 in the system. A smaller fraction of the research in this area has been concerned with the coordination of resources in a decentralized environment. Jin, Minai and Polycarpou, in [9], considered two classes of UAVs, target recognition UAVs and attack UAVs, for the search-and-destroy problem over an area. All UAVs were assumed to have sensors needed for search. A distributed assignment, mediated through centralized mission status information was developed. At each potential target location (environment was discretized as a set of cells), UAVs can Search, Confirm, Attack, perform Battle Damage Assessment (BDA), or Ignore. A centralized information base kept essential information updated for the coordination of the UAVs. Information included, for each target location, the target occupancy probability, certainty, task status, and assignment status. In addition, the information base included state information for each UAV. A set of rules, based on the information contained in the information base, determined the assignment of tasks to UAVs. Each UAV accessed and updated the information base at each step. Two measures of performance were considered to evaluate the proposed algorithm: the time needed to neutralize all a priori known (stationary) targets, and the total number of steps needed to bring all cells to the Ignore status. Shetty, Sudit, and Nagi, in [0], considered the routing of multiple unmanned (combat) vehicles to service multiple potential targets in space. They formulated this problem as a Mixed-Integer Linear Program (MILP), and decomposed the problem into: () the vehicle to target assignment problem, and () determining the tour for each vehicle to service their assigned targets. Each problem was solved using a tabu-search heuristic. A modeling framework for the dynamic rerouting of a set of heterogeneous vehicles was presented by Murray and Karwan in []. Vehicles were constrained by fueland payload- capacity. The defined MILP maximized overall mission effectiveness and minimized changes to the original vehicle task assignments (i.e., the previous solution). Tasks were characterized by priority values, service duration, limits on the number of resources that may perform them, precedence relationships among tasks, and multiple time windows in which resources could be assigned to the tasks. In addition, tasks were classified as required or optional. Vehicles were characterized by a value indicating the resource s relative capability for performing a task. Several authors (e.g., [], []) have taken an informationtheoretic approach to the resource allocation problem. From this perspective, the purpose of the resource management algorithm is to reduce the uncertainty about the environment. In [], McIntyre and Hintz demonstrated the effectiveness of this approach for sensor management on the problem of searching and tracking targets. Hirsch, et al., in [], mathematically formulated the problem of dynamically tracking targets of interest by a set of autonomous UAVs in a centralized cooperative control framework. A decentralized control approach for UAVs with the goal of tracking moving ground targets was developed by Hirsch, Ortiz-Peña and Eck in [5]. Targets and UAVs were moving through an urban domain, simulated as a set of buildings. The shape and location of each building was assumed to be known by each UAV. Areas in the urban domain in which an accurate representation of the ground targets was of interest were represented by an importance function. The vehicles operated in a decentralized manner, in which each UAV was responsible to plan its route to maintain an accurate representation of the targets. A non-linear optimization problem was defined and solved at each time step. A Continuous Greedy Randomized Adaptive Search Procedure (C-GRASP) [], [7] was utilized to approximately solve this optimization problem. Each UAV operated its own dynamic feedback loop in which, at each time step, it moved according to its current flight plan, sensed the environment with on-board sensors, received and shared collected information of the environment with neighbor UAVs (if any) and, when required, planned its next flight path for a fixed number of time steps. In [8], Hirsch and Ortiz-Peña extended their work in [5] by considering the decentralized control of two sets of UAVs (determined a priori): a set of low-level UAVs responsible for sensing the environment with the goal of accurately tracking targets of interest in the urban domain, and a set of high-level UAVs responsible for providing the communication back-bone for the autonomous low-level UAVs tracking the targets of interest. III. MODEL DESCRIPTION AND ASSUMPTIONS Effective utilization of a set of unmanned vehicle systems, with limited capabilities, is required in order to fulfill a set of mission objectives efficiently. Following the approach studied in [8], we considered a set of unmanned vehicle systems consisting of an unmanned vehicle and a control station. The UxV is assumed to follow, autonomously, the trajectories defined at its CS. It is further assumed that the UxV has to remain within communication range of its CS and cannot communicate with other CSs in the area of operation. The control station is responsible for receiving information from the sensors on-board its controlled UxV and from neighbor CSs. The communication range to share information with other CSs might be different than the required communication range to control and receive its UxV s collected information. In our algorithmic development, we assumed the effectiveness of each sensor, for each mission, is known a priori. This effectiveness may vary over time. The area of interest (i.e., area of operation) is represented by a grid in which each cell represents a specified region. Time is discretized and, at each time slice, the UxV may be assigned one (and only one) cell of a subset of all cells in the grid, depending on its previous assignments. A. Parameters The following parameters are defined: I set of UxVs i, j = indexes of UxVs,,..., I } T set of time slices t = index of time slices,,..., T } K set of grid cells k, k, k = indexes of grid cells,,..., K } R set of collection requirements (i.e., mission) r = index of collection requirements x ik0 r,,..., R } if UxV i is at cell k at the time of planning

4 x ik, if UxV i was at cell k a time slice prior to the time of planning w rt weight (priority) of r at t η kk distance between k and k, η kk 0 k, k CR i communication range to aircraft of UAS i s Control Station, CR i 0, i CR i communication range of UxV i s Control Station to other Control Stations, CR i 0, i if UxV i at cell k at time t, at cell k ψ ik k k = at time t can be assigned to cell k at time t if UxV i s CS at cell k at time ϕ ik k k = t, at cell k at time t can be assigned to cell k at time t e irkk t effectiveness of the team of UxVs on k for r at time slice t, when i is assigned to k B. Main Decision Variables The following decision variables are considered in mathematical program: if UxV i is assigned to cell k at x ikt = time slice t if UxV i s Control Station (CS) is assigned to cell k at time slice t y ikt = Ω ijrt value of information gain for r by j, when CS i is connected to CS j at time slice t f rkt potential information gain from k for r at t d rkt increase in information value for r from k at t g rkt reduction of information value due to the sensor effectiveness of the team of UxVs for r from k at t ijt distance from i s CS to j s CS at t c ijt = if UxV j s CS and UxV i s CS are within communication range at time slice t C. Objective function and constraints ) Objective function: Consider the following mathematical formulation β max i α max w rt g rkt + () r t k } ( α) min max frk T + r,k w rt Ω ijrt j j i r where α and β are weighting parameter on the different objectives. The objective function in equation () consists of three terms: t (i) (ii) (iii) max r t w rt k g rkt, maximizes the potential information to be gained by the set of UxVs, for all collection requirements over the planning horizon; } min max r,k frk T, minimizes the maximum value of potential information in the area of interest at the end of the planning horizon; this term is required to prevent the UxVs from loitering on cells with low potential information gain until other cells increase their value; and max i j j i r t w rt Ω ijrt, maximizes the connectivity of CSs by considering the collected information of its UxVs. ) UxV Assignment Constraints: x ikt =, i, t () k Constraint () ensures that each UxV is assigned a (single) cell each time slice t. l ik k kt =, i, t (a) k k k k,k,k ψ ik k k = l ik k kt x ikt + x ik,t + x ik,t, (b) i, k, k, k ψ ik k k =, t Constraints () ensures that each UxV i is assigned to a cell that can be reached at time slice t, given its assignment x ik,t and x ik,t at times t and t, respectively. The use of constraints () allow us to approximate a Dubins vehicle ([9]) by considering, not only the platform s last location but the turning radius to reach it. η kk x ikt y ik t CR i, i, t () k K k K Constraint () ensure that UxV i remains within communication distance of its CS. ) CS Assignment Constraints: Similar to constraints () - (), the assignment of CS to a cell k is constrained by y ikt =, i, t (5) k where constraint (5) ensures that each CS is assigned a (single) cell each time slice t. k k k k,k,k ϕ ik k k = o ik k kt =, i, t (a) o ik k kt y ikt + y ik,t + y ik,t, (b) i, k, k, k ϕ ik k k =, t Constraints () ensures that each CS i is assigned to a cell

5 that can be reached at time slice t, given its assignment y ik,t and y ik,t at times t and t, respectively. The use of constraints () allow us to approximate a Dubins vehicle ([9]) by considering, not only the platform s last location but the turning radius to reach it. ) Potential Information Gain Constraints: f rkt is the potential information gain for collection requirement r from cell k at time slice t. It consists of three components: f rkt = f rk,t }} potential information gain at t + d }} rkt temporal g }} rkt geospatial This relationship is shown in Figure. The locations of two information UxVs and a CS are represented by circles and a star, respectively, in the figure. It is assumed that each UxV collects some information from the cells they are assigned at each time steps (g rkt > 0; d rkt = 0) so the potential information decreases. Cells with no UxV assigned to them increased its potential of information gain due to the temporal component (g rkt = 0; d rkt > 0). t = t = t = Low IG High IG Fig. : Potential Information Gain Update Concept In (7), d rkt represents a decay on the value of the information on cell k and g rkt represents the gain of information on collection requirement r from cell k at time slice t. g rkt can be represented as g rkt = e rk (x t ) (f rk,t + d rkt ) where e rk (x t ) [0, ] represents the effectiveness of the team of UxVs gaining information on collection requirement r from cell k, as a function of the assignment x t. x t = x ikt } i,k vector of cell assignments at time slice t, for all UxVs For consistency, e rk (x t ) will be represented by e rkt. Using the Attenuated Disk Model to characterize each sensor ([0]), we can define e rkt by e rkt = e jrkk t x jk t, r, k, t (8) j k g rkt can then be represented as g rkt = e irkk t θ irkk t + i k i (7) k e irkk t γ irkk t, r, k, t (9) where θ irkk t = x ik t f rk,t and γ irkk t = x ik t d rkt. 5) Communication Constraints: For communication objectives, consider ijt = k k j i η kk y ikt y jk t, i, j Decision variable c ijt is defined by if ijt mincr c ijt = i CR j }, t, i, j, t (0) j i It is assumed that data is received at the CSs with no delays. ) Information Sharing Constraints: Let Π jrt = e jrkk t θ jrkk t () k k represents the contribution of UxV i to collection requirement r at time slice t. Then Πjrt if c Ω ijrt = ijt =, i, j, r, t () j i The nonlinear mathematical formulation above can be linearized by standard techniques from operations research. When a centralized framework is assumed, the set I includes all available UxVs to be assigned in the area of interest; when a decentralized framework is assumed, each CS will solve the programming model only considering the other CSs within their communication range. While analyzing the effects of decentralization on solution quality, constraints (9) to () are not enforced: different configurations of UxVs are evaluated (i.e., c ijt = for some i, j and t) without considering the CS communication range limitations. IV. PRELIMINARY RESULTS Based on the concepts described in Sections II - III, a simulation was implemented to show the applicability and potential of our approach. We considered the assignment of UAVs to surveil the littoral of an area represented by a grid of 0 x 0 cells. Both UAVs are assumed to be controlled by stationary ground control stations: the control station of UAV is located in cell k = 8 (or cell (, 9)), control station of UAV is located at cell k = (or cell (, 7)). Figure 5 shows the selected area of operation and the location of the ground control stations. Note that on this description we are only interested in evaluating the routes defined by the two control stations and not the actual location of the control stations on the area under consideration. α and β in equation () are set to 0.5 and 0, respectively. The littoral surveillance mission consists of two () collection requirements: () detecting incoming maritime vessels and () detecting vehicles approaching the coastline, both suspected to be involved in drug-related activities. A low potential information gain region for collection requirement represents, for example, a body of water while looking for a car. Tracking results from the sensing system (e.g., detection of the maritime vessels) may update the priority of any of these collection requirements. The initial information gain map for each collection requirement is

6 High UAV and CS (0,0) Potential Information Gain UAV and CS (,) Low Fig. 5: Area of operation and initial location of CSs and UAVs UAV UAV Collection Requirement Collection Requirement TABLE I: Discretized effectiveness for the sensor suite on each UAV for each Collecting Requirement shown in Figure and Figure 7, for collection requirements and respectively. On-board sensors, on both UAVs, are assumed to have a discretized effectiveness of collecting information only on the assigned cell. Discretized effectiveness is captured in Table I. Moreover, UAVs can only move to horizontally or vertically adjacent cells; no diagonal movement is allowed. The communication range between each UAV and its respective CS is distance units. High Fig. 7: Initial Potential Information Gain Map for Collection Requirement received by the on-board sensors in the UAV, and any information received from neighboring CS. The UAVs have the same initial potential information gain map and their altitude was assumed to be fixed. The routes defined for each UAV on two situations regarding littoral surveillance are compared. The two cases considered differ on the priorities assigned to each collection requirement. In the first case, the priority of surveilling the littoral for incoming vessels is higher than detecting vehicles in land. In the mathematical programming model this is represented by setting wt = 0.80 and wt = 0.0, t in the objective function. We solved the linearized formulation, equations () - (), using CPLEX.. The routes defined for both UAVs locate them closer to the littoral, keeping both UAVs always within communication range of its CS but maximizing the coverage area (i.e., disjoint sensors coverage area). This is shown in Figure 8. In the second case, both objectives were assumed to be equally important (wt = 0.50 and wt = 0.50, t). For this case, UAV, having the best sensor suite to detect maritime vessels is assigned to cover most of the littoral and UAV is assigned the inland surveillance (see Figure 9). Potential Information Gain High 5 5 Poten>al Informa>on Gain Low Fig. : Initial Potential Information Gain Map for Collection Requirement We considered a decentralized framework in which each UAV is operating independently, with coordination occurring only when the respective control stations are within communication distance of each other. Each unmanned vehicle system is solving the mathematical programing model considering only its perceived environment, derived from the information Low Fig. 8: Defined Routes for UAVs in Case (wt = 0.80 and wt = 0.0, t in the objective function)

7 5 5 High Low Poten>al Informa>on Gain Fig. 9: Defined Routes for UAVs in Case (w t = 0.50 and w t = 0.50, t in the objective function) V. CONCLUSION A mathematical programming model for the cooperative control of multiple autonomous UAVs involved in ISR operations, in particular littoral surveillance, was described. Our model assumes the existence of data fusion applications creating and maintaining a representation of the objects of interest in the area. A decentralized framework in which each UAV is operating independently, with coordination occurring only when the respective control stations are within communication distance of each other is considered. Each unmanned vehicle system solves the mathematical programing model considering only its perceived environment, derived from the information received by the on-board sensors, and any information received from neighboring CS. Using a small, simulated scenario, the applicability of the mathematical programming model for this type of operations is presented. Future work will include our development of heuristics that will allow us to solve the proposed mathematical model in feasible operational timelines. The dynamics of targets and the rate and requirements of new tasks on different missions might require contrasting levels of resource coordination. Having this type of analysis will be extremely beneficial to researchers developing new algorithms for autonomous unmanned vehicle systems and network infrastructures. A comparison of the performance of the proposed method with other resource management procedures will also be conducted. ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their helpful feedback on this document. [] L. Bakule, decentralized control: An overview, Annual Reviews in Control, vol., no., pp , 008. [5] T. Shima, S. J. Rasmussen, and P. 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