Auction-based Multi-Robot Task Allocation in COMSTAR - CiteSeerX

Auction-based Multi-Robot Task Allocation in COMSTAR Matthew Hoeing1 , Prithviraj Dasgupta1 , Plamen Petrov2 , Stephen O’Hara1,2 1 Computer Science Department University of Nebraska, Omaha, NE 68182 2 21st Century Systems Inc. 6825 Pine Street, Suite 141, Omaha, NE 68127. E-mail: {mhoeing, pdasgupta}@mail.unomaha.edu, {plamen,sohara}@21csi.com ABSTRACT Over the past few years, swarm based systems have emerged as an attractive paradigm for building large scale distributed systems composed of numerous independent but coordinating units. In our previous work, we have developed a protoype system called COMSTAR (Cooperative Multi-agent Systems for automatic TArget Recognition) using a swarm of unmanned aerial vehicles(UAVs) that is capable of identifying targets in software simulations of reconnaissance operations. Experimental results from the simulations of the COMSTAR system show that task selection among the UAVs is a crucial operation that determines the overall efficiency of the system. Previously described techniques for task selection among swarm units use a centralized server such as a ground control station to coordinate the activities of the swarm units. However, such systems are not truly distributed since the behavior of the swarm units is predominantly directed by the centralized server’s task allocation algorithm. In this paper we focus on the problem of distributed task selection in a swarmed system where each swarm unit decides on the tasks it will execute by sharing information and coordinating its actions with other swarm units without the intervention of a centralized ground control station supervising its activities. Specifically, we build our task selection algorithm on an auction-based algorithm for task selection in robotic swarms described by Kalra et al. We report experimental results in a simulated environment with 18 robots and 20 tasks and compare the performance of our auction-based algorithm with other heuristic-based task selection strategies in multi-agent swarms. Our simulation results show that the auction-based algorithm improves the task completion times by 30 − 60% and reduces the communication overhead by as much as 90% with respect to other heuristic-based strategies maintaining similar performance in load balancing. 1 1 The COMSTAR project is supported by a Small-business Technology Transfer Research (STTR) grant from DoDNavAir made available through 21st Century Systems Inc.

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Categories & Subject Descriptors: I.2.11 Distributed Artificial Intelligence: Multi-agent systems General Terms: Management, Design, Experimentation. Keywords: Multi-agent swarming, multi-robot task allocation(MRTA), auction, defense applications.

1. INTRODUCTION Automatic Target Recognition(ATR) is becoming an increasingly valuable image analysis tool that can greatly reduce manpower requirements. Currently, most airborne ATR is conducted with single Unmanned Aerial Vehicles (UAVs) that are controlled by human operators from a Ground Control Station (GCS). The UAV captures video data using its image sensors while flying over an area of interest(AOI) and communicates it to the ground control station over a wireless channel. The video data is then analysed by humans at the ground control station for identifying possible hostile entities in the AOI. Current UAV-based systems for aerial reconnaissance involve limited, if any, autonomy by the UAVs. A emerging direction in improving the capability of systems capable of peforming ATR has been to increase the on-board computation capabilities of UAVs to enable them to peform basic operations for ATR. However, the cost for operating and maintaining a single highpeformance UAV with sophisticated sensors and considerable on-board computing power is prohibitively expensive. Therefore, the overarching need in fieldable systems for ATR is to design a system comprising multiple lightweight, inexpensive UAVs with moderate on-board compuation power and limited capability sensors, which are capable of performing ATR tasks autonomously by coordinating their actions with each other while having minimal interactions with the centralized base station. Swarm-based systems provide an attractive paradigm to construct such systems using the combined power of behaviorally simple UAVs as swarm units. Over the past few years, swarm based systems have emerged as an attractive paradigm for building large scale distributed systems composed of numerous independent but coordinating units. The technique of swarming involves movement of entities (for e.g. insects, humans or combat vehicles) individually or in small-sized units to search and act upon objects of interest such as food, prey, or enemy within a search space. The advantage of swarm-based systems is that complex global behavior of the system can be manifested through relatively simple behavior patterns at the level of individual swarm units. This improves the scalability and robustness of the system. However, in the absence of the

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central coordinating mechanism, it becomes challenging to extract suitable behaviors from the swarm units to ensure efficient global performance of the swarmed system. In our previous work we have described a protoype system called COMSTAR (Cooperative Multi-agent Systems for automatic TArget Recognition) using unmanned aerial vehicles(UAVs)[7]. COMSTAR uses a swarming inspired coordination mechanism among UAVs to aid humans, located at a ground control station, in identifying targets in reconnaissance-like operations. In COMSTAR, algorithms embedded on software agents on-board UAVs are used to implement the different operations in swarming. COMSTAR has been tested using empirical simulations of target recognition scenarios and has been shown to be capable of performing ATR using a swarm of 20 − 50 UAVS, scalable to 100-s. UAVs in the COMSTAR system can operate with little or no directives and communication from the ground control station. Because of the swarmed nature of the system, the system is also robust against losses of individual or a small number of UAVs. In this paper we focus on the problem of distributed task selection by the UAVs in the COMSTAR system. The major contribution of this paper is an auction-based algorithm for task selection between UAVs that performs between 30 − 60% better in terms of task completion times over prior heuristic-based task selection strategies while achieving significant reduction (90%) in total communication bandwidth used by the UAVs. The rest of the paper is structured as follows: In Section 2, we provide an overview of the COMSTAR system. Section 3 describes the task selection problem in COMSTAR and describes our auction-based task selection algorithm. In Section 4, we compare the results of empirical simulations of the auction-based algorithm for task selection with other task selection strategies in COMSTAR. Section 5 discusses related work in the area on multi-robot task allocation and swarming, and, finally we conclude.

2.

THE COMSTAR SYSTEM

We consider a scenario where UAV operators at the ground control station are interested in detecting potential targets within a reconnaissance area. To achieve this, individual swarm units(mini UAVs) are deployed from the ground control station into the area of interest(AOI). A mini-UAV is a lightweight unmanned aircraft capable of carrying moderate payload including image sensors, avionics, and communication equipment, and, equipped with a lightweight processor for performing moderate computation. To model the limited computational capability of a UAV, we assume a single UAV is not capable of definitively identifying the image of an object obtained through its image sensors as a target. Nevertheless, we assume a single UAV to be capable of identifying an object as a target with a certain, albeit low, degree of certainty. To confirm an object as a target, we postulate that a certain minimum number of UAVs must concur that an object, observed by each of them independently and possibly at different times, is a target. This can be achieved by directing multiple UAVs towards a recently discovered unconfirmed object to congregate around it and possibly confirm it as a target. In the COMSTAR system, we achieve the coordination among UAVs by using a swarming algorithm inspired by insect stigmergy. Following are some of the key features of the COMSTAR

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system: 1. The AOI is a two-dimensional environment and the boundaries of the AOI is known a priori by the UAVs. 2. Targets are distributed randomly within the AOI. The spatial distribution of targets is not known a priori by the UAVs and must be discovered by the UAVS in real-time. In this paper, we consider stationary targets only. 3. The set of actions required to be performed on an object within the AOI to confirm it as a target is referred to as a task in our environment. 4. A single UAV is only capable of discovering and partially performing tasks but lacks the computational resources required to complete a task on its own. 5. A task can be completed only if multiple UAVs share their computational resources towards executing the task. 6. To enlist the cooperation of other UAVs required to complete a task, a UAV that discovers a task communicates the task’s information to other UAVs. In contrast to some recent swarm-based systems[10], this communication has to be done in a distributed manner without using a central location or shared memory to facilitate information exchange among UAVs. 7. A UAV requires to move to the vicinity of a task discovered by another UAV to execute it. Each UAV executes the tasks independently and on completing its portion of execution on the task, communicates the progress of its execution (fraction of task still incomplete) to other UAVs within its communication range. To realize the swarming behavior in our system, we use the stigmergetic activity of social insects such as ants [5]. Stigmergy is a coordiantion mechanism that enables swarm units to exchange information about the environment with each other. For example, ants searching for food use a chemical substance called pheromone to mark the routes followed by them. Pheromone provides positive reinforcement to future ants, and, ants searching for the food later on get attracted to the pheromone to locate and possibly consume the food. In our system, when a UAV encounters a task, it deposits a certain amount of synthetic pheromone to mark the location and priority of the task. Pheromone decays over time. The set of tasks and the corresponding pheromones that each UAV is aware of is stored in a local data structure called the pheromone landscape within the UAV and corresponds to the UAV’s task list. A UAV communicates its task list to other UAVs within its communication range to disseminate task information across the swarm. The operations performed by a UAV to manifest swarming can be divided into the following phases: • Deployment: UAVs are deployed by a central manager into the environment. Once the UAVs are deployed, the manager does not supervise the UAVs. The UAVs revert to the manager only when their lifetime expires. For better overall coverage, the manager might choose to divide the environment into smaller sub-areas and deploy a subset of UAVs into each subarea[13].

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Figure 1: State transitions of a UAV performing distributed ATR using a swarmed model.

• Search and Discovery. In this phase, individual UAVs perform a blind or uninformed search within the search space to discover objects of interest. We assume that each UAV is provided with appropriate sensors, algorithms and information to enable it to identify objects of interest. When a UAV discovers an object of interest, it associates a certain amount of pheromone with the object to indicate the urgency with which other UAVs should arrive at the object to complete the task associated with that object. • Communication.: After a UAV discovers a task, it has to inform other UAVs about the parameters of the task including the task’s location and pheromone. To achieve this in a distributed manner, a UAV uses a point-to-point communication model to disseminate information about tasks it is aware of to other UAVs within its communication range. • Task Selection. A UAV stores information about incomplete tasks in the search space that it receives from other UAVs in a task list. A UAV must select a subset of tasks from its task list it wants to execute partially and the order in which it to visit the selected tasks to plan its path. • Task Execution. On arriving at the location corresponding to a task/object, a UAV performs the actions required on the object to complete its share of task. After completing its portion of execution for all the tasks on its task list, a UAV reverts to searching. The state transition diagram for a UAV in the COMSTAR system is shown in Figure 1. In the rest of the paper, we focus on the task selection problem in COMSTAR. Algorithms

for deployment, search and discovery, communication and task execution for COMSTAR are described in [7].

3. TASK SELECTION IN COMSTAR Task selection is one of the most crucial phases of the swarming mechanism as it determines the efficiency with which tasks are completed in the system. A suitable task selection mechanism ensures controlled swarming towards tasks to ensure appropriate commitment of resources to tasks, ability of the swarm to separate adaptively into sub-swarms and reduction in communication overhead. In this paper, we have used an auction based task selection algorithm for UAVs inspired by the market-based task selection algorithm for swarming agents described by Kalra and Martinoli in [15]. The major extension in our algorithm over the algorithm reported in [15] are the follwing: • [15] considers a scenario where a task requires only one robot for completion. In contrast, in COMSTAR, a task must be executed partially by multiple UAVs to be completed. • The robots in [15] accept only one task at a time. However, in COMSTAR, because each task requires multiple UAVs to be completed, therefore, it is more efficient for each UAV to maintain a list of tasks that it is capable of executing. • The coordination model among the robots in [15] is synchronous. In contrast, in COMSTAR, we consider an aynchronous model of task execution where each UAV can execute its portion of the task without any temporal constraints imposed by the actions of other UAVs on the same task.

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3.1 Auction algorithm for Task Selection 1. A UAV that discovers a task commences an auction by announcing the task’s location and requesting bids from other UAVs. 2. Every UAV that is within communication range of the auctioneer UAV receives the information about the task being auctioned. 3. A UAV that receives information about the task being auctioned can respond with a bid if only if it has at most one existing task in its task list. The value of the bid is given by the sum of straight line distances from the UAV’s current location to the auctioned task’s location, via the location of the task, if any, on the UAV’s task list. 4. The auctioneer continues to receive bids till the time for that auction expires. The auctioneer UAV then selects the top n bidders (n of the closest robots to the task) as the auction’s winners. If the auctioneer receives m bids, where 1 ≤ m < n, it selects only m winners. If the auctioneer does not receive any bids it restarts the auction. 5. The auctioneer informs the winning UAVs that they were selected to perform the task, while the UAVs that lost the auction are informed that they were not selected to perform the task. The winning bidder with the lowest valued bid (UAV furthest from the auctioneer) is informed by the auctioneer that it is going to be the last UAV to visit the task for the current auction. 6. Each selected UAV visits the task to partially complete it and deposits pheromone at the location corresponding to the task. The updated pheromone value is communicated to other UAVs that have been selected to perform the task, but have not yet performed the task. 7. A task is considered complete when the amount of pheromone associated with it reaches a threshold value of πT hr . 8. If the last UAV visiting the task observes that the pheromone value of the task is < πT hr after it has executed the task, it starts another round of auction for the same task. On the other hand, if the last UAV observes the pheromone value of the task is >= πT hr , it considers the task to be completed. The UAV then communicates the task completion information for the task at that location to other UAVs within its communication range. This prevents UAVs from rediscovering the same task and initiating another auction for the task later on.

4.

EXPERIMENTAL RESULTS

4.1 Experimental Setup We have simulated our algorithm on the Webots robotic simulation platform using robots to model UAVs. All our experiments were run with 18 robots and 20 targets placed randomly inside a 50 × 50 environment. Each robot is modeled as a generic DifferentialWheels model whose speed and

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direction are controlled by changing the relative rotation speed between the two wheels. The maximum speed of each wheel was set to 40. Each robot has the following sensors: (1) GPS: x, z location and heading, (2)Downward looking IR sensor for target detection with a measurement range between 0 and 2048, (3) Short-range radio transmitter and receiver for sending and receiving ping messages over channel 1 with a range of 1.5 units, and, (4) Long-range radio transmitter and receiver for sending and receiving gossip messages over channel 0 with a range of 7.5 units. Target Detection: The floor of the environment is black and corresponds to a zero intensity value on a robot’s downwardlooking IR sensor. Targets are placed on the floor of the environment and are given a random color different from black. When the IR sensor on a robot encounters a target, it returns a non-zero intensity value determined by the color of the target. The robot then associates 20 units of pheromone with the target. Pheromone decays at a rate of 0.01% per simulator tick. A target is considered identified when the pheromone associated with it reaches a threshold value of πT hr = 61.0. For the auction algorithm, the auctioneer robot selects n = 3 robots from the bidders to execute the task. 2 Robot Communication:When a target is found by a robot, it starts an auction for the target by sending a message containing the location of the target and the time at which the target was found to other robots within communication range of its long-range transmitter. Obstacle and Collision Avoidance: To prevent collision between robots, each robot uses a potential field based object avoidance technique described in [7]. Collision avoidance takes precedence over all other actions. Comparison Strategies: For comparing the performance of the auction based task selection algorithm, we have used two heuristic task selection strategies described in [20] and two market-based task selection strategies described in [12]. In the preference based heuristic, each robot selects a task that has the minimum number of other robots in its vicinity and is also closest to completion. In the proximity based heuristic, each robot selects a task that satisfies the criteria for the preference based heuristic, and, additionally, is closest to the robot doing the selection. For the marketbased strategies, the number of UAVs selecting a task for execution and the pheromone level at each task are dynamically updated based on the task’s current status. In the first market-based strategy called derivative following, the amplitude of the updates is drawn for a fixed distribution. In the second market-based strategy, called adaptive derivative following, the amplitude of the updates is dynamically adjusted to ensure rapid convergence to equilibria. In all of these strategies, agents broadcast information about a recently discovered task using a probabilistic flooding mechanism called gossiping[7].

4.2 Simulation Results Our objective in the first set of experiments is to compare the completion time for all tasks using the auction based task selection strategy with the task completion times using the different comparison strategies. For this set of exper2 The value of n = 3 was determined experimentally as the average number of UAVs, excluding the auctioneer itself, which are required to complete execution of a task, based on the value of πT hr = 61.0.

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Figure 2: Time required to identify all targets using different task selection strategies using 18 robots.

iments, the number of targets in the environment is kept fixed at 20. Figure 2 shows the time required to identify all targets within an environment using the different strategies. We observe that the auction based strategy performs better than all the other strategies by a margin of 30 − 60%. The superior performance of the auction-based strategy can be attributed to the fact that the auctioneer UAV only selects n = 3 bidders to execute the task, while in the other strategies, the UAV discovering a task gossips it, in the worst case, to all other UAVs. The overhead incurred by the UAVs to decide whether to move towards a task to execute it degrades the performance of the comparison strategies. Figure 3 measures the distribution of robots over tasks by comparing the number of times each task is visited by different robots before it was completed for the different strategies. We observe in the auction algorithm, an average of 5 robots visit each task before it is completed. The distribution of robots over tasks is relatively easy to control in the auction algorithm as the auctioneer selects n = 3 bidders in addition to itself to complete the task. However, in the market-based strategies, it is difficult to control the exact number of robots visiting each task. Therefore, we observe that the number of times each task is visited by a robot has a significant variance for the market based strategies. Figure 4 shows the variation in the number of tasks visited by a robot for the different strategies. For our setting of 20 tasks(targets), 18 robots and 5 robots required to complete a task, the average number of tasks that each robot should visit is given by 20×5 = 5.5. This value is obtained both 18 by the auction algorithm and the heuristic strategies. In the market-based strategies, we observe that some robots visited more than the average number of tasks while other robots visited far less than average. The variations observed in the graphs around the optimum value can be attributed to two things: 1. Inadequate dispersion of robots across the environment: In certain scenarios, where there are no robots within communication range of the auctioneer, the auctioneer robot might have to continue the auction for a considerable time before it gets at least one bid and is able

Figure 3: Number of times each target is visited by different robot using different task selection strategies.

to close the auction at the auction-timeout following the bid. During the time period the auctioneer waits to receive at least one bid, the pheromone value at the task can decay significantly. As a result, more than 4 robots have to visit the task and deposit pheromone at it to enable the task’s pheromone level reach the threshold value of πT hr . 2. Communication Inefficiency: Depending on the dispersion of robots in the environment, some robots encounter a significant delay while receiving information about a task until the auctioneer reaches within communication range of the robots. Figure 5 shows the number of bytes received and sent by each robot using the auction algorithm. As expected, the number of bytes received is almost double the number of bytes sent by each robot. This can be explained by the fact that whenever a robot behaves as an auctioneer, it has to receive messages from all bidders, while the bidders only receive one auction message from the auctioneer. Finally, Figure 6 compares the total number of bytes communicated (sent+received) by each robot using the auction algorithm and the market based derivative follower strategy.3 The auction algorithm shows a significant reduction in communication overhead by a factor of almost 90%. This can be attributed to the fact that in the market based strategy, robots use a point-to-point broadcast mechanism to disseminate information across the entire swarm. In contrast, in the auction algorithm, the information dissemination is limited only to robots within the communication range of the auctioneer robot. In conclusion, we observe that the auction based algorithm appears to be the most suitable task selection strategy in comparison to the other comparison strategies as it simultaneously achieves significant improvement in task completion time and significant reduction in communication overhead across the swarm. 3 The heuristic strategies use 37.5% more communication overhead than the market based strategy.

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Figure 4: Number of targets visited by each robot using different task selection strategies.

5.

RELATED WORK

Swarming-based systems have been abundant in nature and human history[9]. In the recent past, several computational systems using swarming have been developed for different applications including vehicle routing[22], self-repairing formation control for mobile agents [29], adaptive control in overlay networks[3, 14] in overlay networks. A seminal work in the field of UAV swarms for military applications is described in [28]. Most of these approaches use techniques such as greedy algorithms within a centralized shared memory setting [10, 25] to facilitates rapid information exchange between the swarm units. In contrast, in this paper we describe a a completely distributed, auction-based algorithm for task selection in swarming. In [1], distributed heuristic based strategies for capturing the collective aggregation dynamics in multi-agent swarms for gathering and clustering tasks are described. [17] describes heuristic-based stratgies for task constraints and signal reinforcement to analyze the effects of diversity and specialization on multi-agent swarms. These studies are complementary to the work described in this paper. Also complementary to our work is the model of distributed factory coordination described in [4, 6]. The auction-based algorithm described in this paper is inspired by the market-based algorithm for task allocation in robot swarms described by Kalra and Martinoli[15]. In their setting, each task requires only one robot for completion. Each robot also accepts only one task at a time and executes it. Consequently, the robots in their setting use a synchronous model for coordination. When a robot discovers a task it commences an auction. Other robots that receive the information of the task being auctioned respond with bids. The value of the bid corresponds to the distance of the bidding robot from the task being auctioned. The auctioneer robot selects the bidder that offers the highest bid (least distance from auctioneer). Because their model is synchronous, an auction for a task is considered to be completed instantaneously. In contrast, in our algorithm, multiple robots are determined as winners and the auction for a task is considered complete only when the desired number of robots for completing the task have been selected as

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Figure 5: Number of bytes of data sent and received by each robot using the auction algorithm for task allocation.

winners by the auctioneer, or, the auctioneer reaches a timeout for the auction without receiving the required number of bids. Independent of swarming, the problem of multi-robot task allocation(MRTA) has been investigated using different techqniues such as physical modeling[24], distributed planning[23] and market-based techniques[8]. One of the first algorithms for market based solutions for the MRTA problem was described in the MURDOCH system developed by Gerkey[11]. MURDOCH uses an auction mechanism inspired by the contract-net protocol[27] to allocate dynamically arriving tasks among multiple heterogenous robots. Gerkey also provides different classifications of the MRTA problem based on single and multiple combinations of robots and tasks. Task allocation in a multi-robot distributed system using a contract-net based protocol for the COMETS-UAV system has been described in [16]. The mechanism relies on one robot being elected as a leader(auctioneer) using a tokenring technique. In addition, the task allocation mechanism requires the leader to have knowledge about all the tasks it allocates to other robots(contractors). In contrast, the task selection strategies used in this paper do not require leader election and the information about tasks is maintained locally on each UAV in a distributed manner. Other approaches to multi-agent cooperation algorithms include the Martha system[2] that focuses on planning and distributed cooperation schemes, the ADOPT algorithm[21] and mediation protocol[19] that address coordination between agent teams using distributed constraint optimization techniques, and [18, 26] that uses agent-based distributed task allocation strategies using negotiation techniques. Most of these approaches are complementary to our work and consider scenarios where an agent has to allocate shared resources across multiple tasks.

6. CONCLUSION AND FUTURE DIRECTIONS In this paper, we have described an auction-based task selection algorithm for a swarming based prototype system

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[4]

[5]

[6]

[7]

Figure 6: Comparison between the number of bytes of data sent and received by each robot using the auction and market-based algorithms for task allocation.

[8]

[9] of UAVs called COMSTAR. The work reported here is our first step in the direction of auction-based algorithms in the context of swarming. One of the issues we are currently investigating is extending our algorithm to include targets with different priorities with different amounts of pheromone deposit. In our current algorithm, the number of targets that a robot may keep track of is currently limited to 2. Currently, we are investigating the system dynamics when a robot is allowed to maintain multiple tasks on its task list. Increasing the number of tasks on a robot’s task list is likely to improve system-wide performance by increasing overall robot awareness, thereby reducing the number of auctions and time needed to identify a target. Extending this idea, we can consider the possibility of allowing robots to dynamically adjust how many winners are selected in an auction depending on the amount of pheromone required to reach the threshold πT hr . If a target has been mostly identified, and needs only one more visit from a nearby robot, there is a waste of resources by allocating more than one winner in the subsequent auction. This would minimize the number of robots in use to confirm a target. Lastly, building on the above ideas, robots could optimize their routes through currently pursued targets with respect to target location, seeking a shortest path between the targets, as well as optimize with respect to target priority, giving preference to identifying high priority targets over low priority ones.

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The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)