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Flocking for MultiAgent Dynamic Systems: Algorithms and Theory
, 2006
"... In this paper, we present a theoretical framework for design and analysis of distributed flocking algorithms. Two cases of flocking in freespace and presence of multiple obstacles are considered. We present three flocking algorithms: two for freeflocking and one for constrained flocking. A compre ..."
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Cited by 436 (2 self)
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In this paper, we present a theoretical framework for design and analysis of distributed flocking algorithms. Two cases of flocking in freespace and presence of multiple obstacles are considered. We present three flocking algorithms: two for freeflocking and one for constrained flocking. A comprehensive analysis of the first two algorithms is provided. We demonstrate the first algorithm embodies all three rules of Reynolds. This is a formal approach to extraction of interaction rules that lead to the emergence of collective behavior. We show that the first algorithm generically leads to regular fragmentation, whereas the second and third algorithms both lead to flocking. A systematic method is provided for construction of cost functions (or collective potentials) for flocking. These collective potentials penalize deviation from a class of latticeshape objects called αlattices. We use a multispecies framework for construction of collective potentials that consist of flockmembers, or αagents, and virtual agents associated with αagents called β and γagents. We show that migration of flocks can be performed using a peertopeer network of agents, i.e. “flocks need no leaders.” A “universal” definition of flocking for particle systems with similarities to Lyapunov stability is given. Several simulation results are provided that demonstrate performing 2D and 3D flocking, split/rejoin maneuver, and squeezing maneuver for hundreds of agents using the proposed algorithms.
Graphical models inference in optimal control of stochastic multiagent systems
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 2008
"... In this article we consider the issue of optimal control in collaborative multiagent systems with stochastic dynamics. The agents have a joint task in which they have to reach a number of target states. The dynamics of the agents contains additive control and additive noise, and the autonomous part ..."
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Cited by 20 (1 self)
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In this article we consider the issue of optimal control in collaborative multiagent systems with stochastic dynamics. The agents have a joint task in which they have to reach a number of target states. The dynamics of the agents contains additive control and additive noise, and the autonomous part factorizes over the agents. Full observation of the global state is assumed. The goal is to minimize the accumulated joint cost, which consists of integrated instantaneous costs and a joint end cost. The joint end cost expresses the joint task of the agents. The instantaneous costs are quadratic in the control and factorize over the agents. The optimal control is given as a weighted linear combination of singleagent to singletarget controls. The singleagent to singletarget controls are expressed in terms of diffusion processes. These controls, when not closed form expressions, are formulated in terms of path integrals, which are calculated approximately by MetropolisHastings sampling. The weights in the control are interpreted as marginals of a joint distribution over agent to target assignments. The structure of the latter is represented by a graphical model, and the marginals are obtained by graphical model inference. Exact inference of the graphical model will break down in large systems, and so approximate inference methods are needed. We use naive mean field approximation and belief propagation to approximate the optimal control in systems with linear dynamics. We compare the approximate inference methods with the exact solution, and we show that they can accurately compute the optimal control. Finally, we demonstrate the control method in multiagent systems with nonlinear dynamics consisting of up to 80 agents that have to reach an equal number of target states.
An approximation algorithm for scheduling aircraft with holding time
 In Proceedings of CDC’04, the 43rd IEEE Conference on Decision and Control
, 2004
"... AbstractWe consider the problem of scheduling arrival air traffic in the vicinity of large airports. The problem is posed as a single queue problem, from which aircraft can be pulled out and put "on hold", in holding loops, each loop taking a fixed amount of time to traverse, before they ..."
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Cited by 12 (1 self)
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AbstractWe consider the problem of scheduling arrival air traffic in the vicinity of large airports. The problem is posed as a single queue problem, from which aircraft can be pulled out and put "on hold", in holding loops, each loop taking a fixed amount of time to traverse, before they join the queue again. The difficulty of deriving efficient solutions to this problem (which is currently controlled non optimally by human Air Traffic Controllers) is the minimization of "idle time" generated by traversing an integer number of loops. We formulate this problem as a single machine scheduling problem where we are given N jobs characterized by release times and deadlines. We are given a processing time and and a holding time. In a feasible schedule, each job is assigned a starting time within a constraint set corresponding to an integer number of processing times and holding times. Our goal is to find feasible schedules to alternatively minimize two objectives: the sum of the starting times of all jobs and the makespan (the time at which all jobs are finished). We present approximation algorithms which can alternatively approximate two objectives with factors of 5 and 3, respectively. Our main algorithm consists of solving two subproblems, one of which is solved optimally using dynamic programming, while the other is solved approximately using linear programming relaxation and rounding.
Optimal leader allocation in UAV formation pairs under nocost switching,”
 in American Control Conference,
, 2012
"... AbstractWe study the leader allocation problem in UAV formation pairs when switching the lead incurs a fuel cost. While in formation, UAVs are assumed to adhere to a notion of cooperativeness. The problem is formulated as the combination of a nonconvex and a discrete optimization problem where t ..."
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AbstractWe study the leader allocation problem in UAV formation pairs when switching the lead incurs a fuel cost. While in formation, UAVs are assumed to adhere to a notion of cooperativeness. The problem is formulated as the combination of a nonconvex and a discrete optimization problem where the leader allocations are constrained to those that induce cooperation between UAVs. A equivalent formulation of the problem allows us to express the constraint set as a family of equality and inequality constraints. By restricting our search to solutions of a specific form, we replace the nonconvex problem with a convex one while preserving the optimal value of the original problem. A necessary and sufficient condition is obtained which is used to verify a solution to the discrete problem. The results are combined to design the OPTIMAL COST ALGORITHM, which efficiently solves the original problem. Our results are verified in simulation.
A Multiobjective Evolutionary Approach to Aircraft Landing Scheduling Problems
"... Abstract—Scheduling aircraft landings has been a complex and challenging problem in air traffic control for long time. In this paper, we propose to solve the aircraft landing scheduling problem (ALSP) using multiobjective evolutionary algorithms (MOEAs). Specifically, we consider simultaneously min ..."
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Abstract—Scheduling aircraft landings has been a complex and challenging problem in air traffic control for long time. In this paper, we propose to solve the aircraft landing scheduling problem (ALSP) using multiobjective evolutionary algorithms (MOEAs). Specifically, we consider simultaneously minimizing the total scheduled time of arrival and the total cost, and formulate the ALSP as a 2objective optimization problem. A MOEA named MultiObjective Neighborhood Search Differential Evolution (MONSDE) is applied to solve the 2objective ALSP. Besides, a ranking scheme named nondominated average ranking is also proposed to determine the optimal landing sequence. Advantages of our approaches are demonstrated on two example scenarios. I.
Formation Geometries and Route Optimization for Commercial Formation Flight
"... Formation flight provides an effective way to dramatically reduce fuel burn without fundamental changes to the aircraft flying today. A two aircraft echelon formation is investigated along with three different three aircraft formations. A three aircraft invertedV formation geometry is shown to hav ..."
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Formation flight provides an effective way to dramatically reduce fuel burn without fundamental changes to the aircraft flying today. A two aircraft echelon formation is investigated along with three different three aircraft formations. A three aircraft invertedV formation geometry is shown to have many favorable characteristics compared to other formation geometries. All of the aircraft in this formation need very small aileron deflections to trim in roll, for most spanwise spacings the formation is statically stable, and the total formation induced drag is insensitive to high levels of positioning uncertainty. A trade study was conducted to determine the fuel savings and difference in flight times that result from applying formation flight to missions of different stage length and different spacings between the origin cities. For a two aircraft echelon formation, the maximum fuel savings were 4 % with a tiptotip gap between the aircraft equal to 10 % of the span and 10% with a tip overlap equal to 10 % of the span. For the three aircraft invertedV formation, the maximum fuel savings were about 7 % with tiptotip gaps equal to 10 % of the span and about 16 % with tip overlaps equal to 10 % of the span. A case study examined the use of formation flight on five FedEx flights from the pacific