Market-based Dynamic Task Allocation in Mobile Surveillance Systems By: Ahmed Elmogy Alaa Khamis Fakhri Karray

Outline Introduction Related work Proposed task allocation approach Simulations and results Conclusions and future work

Introduction Autonomous multi-robot systems have become an active research area and are highly seen in several new application areas in the recent years Advanced surveillance systems include a vast array of cooperative (static and mobile) sensors with varying sensing modalities that can sense continuously the volume of interest Mobile sensor coordination is one of the essential requirements for allocation of tasks to the robot team in the surveillance systems Ideally robots in the mobile sensor network will coordinate to distribute the tasks amongst themselves in a way that enables them to accomplish their mission efficiently and reliably In order to address the issue of task allocation, the fundamental question: which robot should execute which task should be encountered

Introduction (cont.) Multi-robot task allocation is a twofold problem First it addresses how to assign a set of tasks to a set of robots Second it considers how to coordinate the behavior of the robot team in order to do the cooperative tasks efficiently Important aspects have, to date been given little attention Allocation of complex tasks Dynamic task allocation Constrained task allocation Market based approaches have received significant attention and are growing very fast in the last few decades especially in multi-agent domains

Related work

Problem definition DEFINITION 1: Simple Task Allocation Given a set of robots R each looking for one task, and a set of tasks T each requires one robot. The simple task allocation can be defined by a function A: T→ R, mapping each task to a robot in order to be executed. Similarly, RT is the set of all allocations of tasks T to the team of robots R. DEFINITION 2: Complex Task Allocation Given a set of robots R, and a set of tasks T. let S T is a set or a bundle of tasks that is decomposable into other tasks M S. The complex task allocation can be defined by a function B: M → R, mapping each subtask to a robot to be responsible of completing it. Equivalently, RM is the set of all allocations of subtasks M to the team of robots R.

Problem formulation For single robot task, the problem is to find the optimal allocation of robots to tasks, which will be a set of robots and tasks pair : For the general case, the problem is to find the optimal allocation of a set of tasks to a subset of robots, which will be responsible for accomplishing it Each mobile sensor can express its ability to execute a task , or a bundle of tasks through bids or . The cost of a bundle of tasks can be simply computed as the sum of costs of the individual tasks:

Problem formulation (2) The group’s assignment determines the bundle of tasks that each mobile sensor receives. These bundles can be characterized as follows: The most common global objective is to minimize the sum of the team member costs which can be described mathematically as follows:

Proposed approach: Auction-based Task Allocation The crucial component of the proposed framework is the market-based architecture Market-based task allocation is an economically inspired approach that provides a way to coordinate the activities of a number of competitive agents The approach imitates the auction process of buying and selling services through bidding The context auctioning can be classified into Single-shot auction with static bids Single auction with dynamic bids Multiple simultaneous combinatorial auctions Centralized and decentralized simultaneous combinatorial auction mechanisms are implemented for task allocation

Proposed approach: Task Trees The task allocation algorithms are highly affected by the type of description of tasks to be allocated Most of task allocation approaches treated tasks as atomic units Allowing only static description for each task and so the only degree of freedom is determining to which robot the task will be assigned Task description using tree structures within the market framework The robot team members are permitted to bid on nodes representing varying levels of task abstraction. Enabling distributed planning, task allocation, and optimization among the robot team members

AND/OR task tree example Task Trees (Cont.) AND/OR task tree example

Proposed Approach Fixed Tree Task Allocation The proposed approach can be framed as iterated instances of ST-SR-TA (Single-Task Single-Robot Time-extended Assignment) An iterated market based complex task allocation approach is developed to allocate tasks to the robot team members through contract negotiation The proposed fixed task tree allocation could be seen as an instance of decompose-then-allocate approach The whole auction mechanism is based only on one task tree, which is proposed by the operator or the auctioneer Our approach is tested in a distributed surveillance problem in a simulated interior environment Use a developed version of a TSP algorithm as path planning algorithm to decide the order of visiting nodes

Proposed Approach Dynamic Tree Task Allocation The main drawback of fixed tree task allocation is that the cost of the final plan cannot be fully considered because the complex task is decomposed by the auctioneer without knowledge of the eventual task allocation A hybrid approach that combines both decompose-then-allocate and allocate-then- decompose methods is proposed The basic idea of the proposed dynamic tree allocation is to allow backtracking in order to recover the bad plans made by the auctioneers The proposed algorithm allows auctioning on all levels of abstraction of the mission task implemented by the task tree from the top to the bottom by allowing breadth first search

Dynamic tree task Allocation(cont.) Each robot evaluates its ability to execute the required task based on its plan not on the plan of auctioneer Most of the literature do not allow the robots to come with their plans unless the auctioneer found that it could not sell its proposed plan The auctioneer might sell its plan because of the profit it gains while the whole team can get more profit because one of the robots has a better plan Our proposed dynamic algorithm is either executed by allowing only one auctioneer (centralized allocation) or allowing different auctioneers (distributed allocation) The input tree structure is developed from AND/OR done by auctioneer and the whole team respectively to that is only done by the auctioneer

Surveillance scenario

Surveillance scenario (cont.)

Simulations and results

Conclusions A distributed market based architecture for complex task allocation is presented in this paper The proposed architecture integrates low-level motion control with high-level task allocation for mobile sensor network In order to reach the low-level motion control design, a TSP path planning technique is used Fixed and dynamic task trees are used as implementations of tasks, which are allocated to robots using auctioning A mission surveillance task is considered in this paper to test the developed algorithms The AND/OR tree is constructed by decomposing the surveillance mission into a set of areas which in turn decomposed to a set of monitoring points

Future work