Distributed Scheduling Using Constraint Optimization and Multiagent Path Planning Christopher T. Cannon 1 , Robert N. Lass 1 , Evan A. Sultanik 1 , William C. Regli 1 , David Šišlák 2 , and Michal Pěchouček 2 1 Department of Computer Science, College of Engineering Drexel University, Philadelphia, PA, USA 2 Agent Technology Center, Faculty of Electrical Engineering Czech Technical University in Prague, Prague, CZ 12th International Workshop on Distributed Constraint Reasoning 11 May 2010 Department of Science Computer Cannon et al. (DU & CTU) Distributed Scheduling DCR 2010 05-11 1 / 26
Problem Statement Problem? Solutions to the distributed scheduling problem (assigning n workers to m tasks at time points) only consider worker-task assignment or space deconfliction. Why? Distributed scheduling problems often occur in three-dimensional continuous environments where workers must be assigned tasks and then must physically travel to that task. Solution? An approach which first uses distributed constraint optimization to assign workers to tasks and then uses a distributed multiagent path planner to create a path from the worker to its tasks. Department of Science Computer Cannon et al. (DU & CTU) Distributed Scheduling DCR 2010 05-11 2 / 26
Outline Motivating Example 1 Technical Approach 2 Experiments 3 Conclusions & Future Work 4 Department of Science Computer Cannon et al. (DU & CTU) Distributed Scheduling DCR 2010 05-11 3 / 26
Outline Motivating Example 1 Technical Approach 2 Experiments 3 Conclusions & Future Work 4 Department of Science Computer Cannon et al. (DU & CTU) Distributed Scheduling DCR 2010 05-11 3 / 26
Outline Motivating Example 1 Technical Approach 2 Experiments 3 Conclusions & Future Work 4 Department of Science Computer Cannon et al. (DU & CTU) Distributed Scheduling DCR 2010 05-11 3 / 26
Outline Motivating Example 1 Technical Approach 2 Experiments 3 Conclusions & Future Work 4 Department of Science Computer Cannon et al. (DU & CTU) Distributed Scheduling DCR 2010 05-11 3 / 26
Outline Motivating Example 1 Technical Approach 2 Experiments 3 Conclusions & Future Work 4 Department of Science Computer Cannon et al. (DU & CTU) Distributed Scheduling DCR 2010 05-11 4 / 26
Classical Example: Distributed Sensor Networks 1 2 The problem consists of: 3 A set of agents; 1 each equipped with Doppler radar sensors; each sensor has three sectors; allowed one active sector at any given time; a 1 a 2 communicating over an ad-hoc start t network; end tracking moving targets; and a 3 a 4 target must lie within at least three sensors for accurate tracking. Department of Science 1Example from DARPA’s Autonomous Negotiating Teams (ANT) Program. Computer Cannon et al. (DU & CTU) Distributed Scheduling DCR 2010 05-11 5 / 26
Motivating Example: Unmanned Aerial Vehicle Surveillance The problem consists of: A set of UAVs (agents); each equipped with a camera sensor; assigned to monitor a subset of the enemy targets; communicating over a wireless network; and the goal is to minimize the amount of time between a UAV surveilling a target. Department of Science Computer Cannon et al. (DU & CTU) Distributed Scheduling DCR 2010 05-11 6 / 26
Motivating Example: Unmanned Aerial Vehicle Surveillance The problem consists of: A set of UAVs (agents); each equipped with a camera t 3 a 1 a 2 sensor; t 2 assigned to monitor a subset of the enemy targets; t 1 communicating over a wireless network; and the goal is to minimize the amount of time between a UAV surveilling a target. Department of Science Computer Cannon et al. (DU & CTU) Distributed Scheduling DCR 2010 05-11 6 / 26
Motivating Example: Unmanned Aerial Vehicle Surveillance The problem consists of: A set of UAVs (agents); each equipped with a camera sensor; t 3 a 1 a 2 assigned to monitor a subset of t 2 the enemy targets; t 1 communicating over a wireless network; and the goal is to minimize the amount of time between a UAV surveilling a target. Department of Science Computer Cannon et al. (DU & CTU) Distributed Scheduling DCR 2010 05-11 6 / 26
Motivating Example: Unmanned Aerial Vehicle Surveillance The problem consists of: A set of UAVs (agents); each equipped with a camera sensor; t 3 a 1 a 2 assigned to monitor a subset of t 2 the enemy targets; t 1 communicating over a wireless network; and the goal is to minimize the amount of time between a UAV surveilling a target. Department of Science Computer Cannon et al. (DU & CTU) Distributed Scheduling DCR 2010 05-11 6 / 26
Motivating Example: Unmanned Aerial Vehicle Surveillance The problem consists of: A set of UAVs (agents); gap each equipped with a camera { sensor; t 1 assigned to monitor a subset of t 2 the enemy targets; t 3 communicating over a wireless network; and time a 1 a 2 the goal is to minimize the amount of time between a UAV surveilling a target. Department of Science Computer Cannon et al. (DU & CTU) Distributed Scheduling DCR 2010 05-11 6 / 26
Motivating Example: Unmanned Aerial Vehicle Surveillance The problem consists of: A set of UAVs (agents); gap each equipped with a camera { sensor; t 1 assigned to monitor a subset of t 2 the enemy targets; t 3 communicating over a wireless network; and time a 1 a 2 the goal is to minimize the amount of time between a UAV surveilling a target. Traditional Approach Traditionally, a DisCOP approach focuses on selection (ignoring path creation) and a multiagent planning approach focuses on path creation (ignoring selection). Department of Science Computer Cannon et al. (DU & CTU) Distributed Scheduling DCR 2010 05-11 6 / 26
Outline Motivating Example 1 Technical Approach 2 Experiments 3 Conclusions & Future Work 4 Department of Science Computer Cannon et al. (DU & CTU) Distributed Scheduling DCR 2010 05-11 7 / 26
Technical Approach Overview The algorithm consists of four steps: 1 The DisCOP agent selects the Selected target assignments; DisCOP TSP Targets 2 the TSP approximation Agent Approx. algorithm orders the selected targets based upon the current Ordered Re-solve Sequence position; 3 the AA* path planner creates a Path conflict-free flight plan; and Planner 4 after the UAV completes its flight path, the algorithm restarts. Flight Plan Department of Science Computer Cannon et al. (DU & CTU) Distributed Scheduling DCR 2010 05-11 8 / 26
Step 1: DisCOP Agent Selected DisCOP TSP Targets Agent Approx. Ordered Re-solve Sequence Path Planner Flight Plan Department of Science Computer Cannon et al. (DU & CTU) Distributed Scheduling DCR 2010 05-11 9 / 26
Distributed Constraint Optimization Problem (DisCOP) There are four components to a DisCOP: 1 A set of agents A = { a 1 , a 2 , . . . , a n } ; 2 a set of variables V = { v 1 , v 2 , . . . , v | V | } ; 3 a set of domains that contain the values that may be assigned to said variables D = { D 1 , D 2 , . . . , D | V | } ; and 4 a set of constraints over the variable’s assignments. The objective is to have the agents assign values to their variables such that some metric over the resulting contraints’ vallues is either minimized or maximized. Department of Science Computer Cannon et al. (DU & CTU) Distributed Scheduling DCR 2010 05-11 10 / 26
Distributed Stohastic Search (DSA) The DSA family of algorithms generally ∆ > 0 Conflict No Conflict follows these steps: DSA-A v with p – – Selects random values for the agents 1 DSA-B v with p v with p – own variables; DSA-C v with p v with p v with p DSA-D v with p – v enters a loop which checks for new 2 DSA-E v with p v with p v neighbor messages; stochastically decides whether to 3 An incomplete algorithm ( e.g. , DSA-B) was update its values based on the chosen over a complete algorithm ( e.g. , received messages; ADOPT, DPOP) because of its: sends the updated values to its 4 Computational and memory cost; 1 neighbors; and any-time properties; and 2 ends when a solution is requested or a 5 fault tolerance. 3 terminating condition is met. W. Zhang, et al. Distributed Stochastic Search and Distributed Breakout: Properties, Comparison and Applications to Constraint Optimization Problems in Sensor Networks. Artificial Intelligence , 161:55–87, January 2005. Department of Science Computer Cannon et al. (DU & CTU) Distributed Scheduling DCR 2010 05-11 11 / 26
DisCOP to UAV Surveillance Assignment Mapping The mapping is as follows: Agents: Each UAV agent corresponds to a DisCOP agent; Variables: each agent has a set of variables which contains a single variable for each constrained target; t 3 a 1 a 2 Domain: the domain for each variable is t 2 boolean (Covered, Not Covered); and t 1 Constraints: the cost for each target is as follows: Low Cost (more than one agent): the number of agents constrained with the target; High Cost (no agents): twice the number of agents; and No Cost (one agent): zero. Department of Science Computer Cannon et al. (DU & CTU) Distributed Scheduling DCR 2010 05-11 12 / 26
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