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On the Time Complexity of ConflictFree Vehicle Routing
, 2005
"... In this paper, we study the following problem: given n vehicles and origindestination pairs in the plane, what is the minimum time needed to transfer each vehicle from its origin to its destination, avoiding conflicts with other vehicles? The environment is free of obstacles, and a conflict occurs ..."
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Cited by 16 (5 self)
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In this paper, we study the following problem: given n vehicles and origindestination pairs in the plane, what is the minimum time needed to transfer each vehicle from its origin to its destination, avoiding conflicts with other vehicles? The environment is free of obstacles, and a conflict occurs when the distance between any two vehicles is smaller than a velocitydependent safety distance. We derive lower and upper bounds on the time needed to complete the transfer, in the case in which the origin and destination points can be chosen arbitrarily, proving that the transfer takes Θ ( √ n ¯ L) time to complete, where ¯ L is the average distance between origins and destinations. We also analyze the case in which origin and destination points are generated randomly according to a uniform distribution, and present an algorithm providing a constructive upper bound on the time needed for complete the transfer, proving that in the random case the transfer requires O ( √ n log n) time.
Computing Pareto optimal coordinations on roadmaps
 Intl. J. Robotics Research
, 2005
"... ABSTRACT. We consider coordination of multiple robots in a common environment, each robot having its own (distinct) roadmap. Our primary contribution is a classification of and exact algorithm for computing vectorvalued — or Pareto — optima for collisionfree coordination. We indicate the utility o ..."
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Cited by 14 (3 self)
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ABSTRACT. We consider coordination of multiple robots in a common environment, each robot having its own (distinct) roadmap. Our primary contribution is a classification of and exact algorithm for computing vectorvalued — or Pareto — optima for collisionfree coordination. We indicate the utility of new geometric techniques from CAT(0) geometry and give an argument that curvature bounds are the key distinguishing feature between systems for which the classification is finite and for those in which it is not. 1.
Nonpositive curvature and Paretooptimal coordination of robots
 SIAM J. Control & Optimization
"... Abstract. Given a collection of robots sharing a common environment, assume that each possesses a graph (a 1d complex also known as a roadmap) approximating its configuration space and, furthermore, that each robot wishes to travel to a goal while optimizing elapsed time. We consider vectorvalued ..."
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Cited by 14 (1 self)
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Abstract. Given a collection of robots sharing a common environment, assume that each possesses a graph (a 1d complex also known as a roadmap) approximating its configuration space and, furthermore, that each robot wishes to travel to a goal while optimizing elapsed time. We consider vectorvalued (or Pareto) optima for collisionfree coordination on the product of these roadmaps with collisiontype obstacles. Such optima are by no means unique: in fact, continua of Pareto optimal coordinations are possible. We prove a finite bound on the number of optimal coordinations in the physically relevant case where all obstacles are cylindrical (i.e., defined by pairwise collisions). The proofs rely crucially on perspectives from geometric group theory and cat(0) geometry. In particular, the finiteness bound depends on the fact that the associated coordination space is devoid of positive curvature. We also demonstrate that the finiteness bounds holds for systems with moving obstacles following known trajectories. 1. Introduction. 1.1. Motivation. In numerous settings, the coordination of multiple robots remains a basic and challenging research issue. Autonomous guided vehicles (AGVs) are used in a
Time complexity of sensorbased vehicle routing
 in Robotics: Science and Systems
, 2005
"... Abstract — In this paper, we study the following motion coordination problem: given n vehicles and n origindestination pairs in the plane, what is the minimum time needed to transfer each vehicle from its origin to its destination, avoiding conflicts with other vehicles? The environment is free of ..."
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Cited by 10 (2 self)
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Abstract — In this paper, we study the following motion coordination problem: given n vehicles and n origindestination pairs in the plane, what is the minimum time needed to transfer each vehicle from its origin to its destination, avoiding conflicts with other vehicles? The environment is free of obstacles and a conflict occurs when distance between any two vehicles is smaller than a velocitydependent safety distance. In the case where the origin and destination points can be chosen arbitrarily, we show that the transfer takes Θ ( √ n ¯ L) time to complete, where ¯ L is the average distance between the origin and destination points. We also analyze the case in which origin and destination points are generated randomly according to a uniform distribution, and present an algorithm providing a constructive upper bound on the time needed to transfer vehicles from origins to their corresponding destination, proving that the transfer takes Θ ( √ n) time for this case. I.
Pareto optimal multirobot coordination with acceleration constraints
"... Abstract — We consider a collection of robots sharing a common environment, each robot constrained to move on a roadmap in its configuration space. To program optimal collisionfree motions requires a choice of the appropriate notion of optimality. We work in the case where each robot wishes to trav ..."
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Cited by 3 (0 self)
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Abstract — We consider a collection of robots sharing a common environment, each robot constrained to move on a roadmap in its configuration space. To program optimal collisionfree motions requires a choice of the appropriate notion of optimality. We work in the case where each robot wishes to travel to a goal while optimizing elapsed time and consider vectorvalued (Pareto) optima. Earlier work demonstrated a finite number of Paretooptimal classes of motion plans when the robots are subjected to velocity bounds but no acceleration bounds. This paper demonstrates that when velocity and acceleration are bounded, the finiteness result still holds for certain systems, e.g., two robots; however, in the general case, the acceleration bounds can lead to continua of Pareto optima. We give examples and explain the result in terms of the geometry of phase space. I.
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"... We consider the coordination of multiple robots in a common environment, each robot having its own (distinct) roadmap. Our primary contribution is a classification of and exact algorithm for computing vectorvalued (or Pareto) optima for collisionfree coordination. We indicate the utility of new ge ..."
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We consider the coordination of multiple robots in a common environment, each robot having its own (distinct) roadmap. Our primary contribution is a classification of and exact algorithm for computing vectorvalued (or Pareto) optima for collisionfree coordination. We indicate the utility of new geometric techniques from CAT(0) geometry and give an argument that curvature bounds are the key distinguishing feature between systems for which the classification is finite and for those in which it is not. KEY WORDS—motion planning, optimality, coordination spaces, roadmaps, multiple robots 1.
Ball Passing: Balancing Rewards, Risks, Costs, and RealTime Constraints
"... Abstract. We are looking a generic solution for the optimized ball passing problem in the robotic soccer which is applicable to different RoboCup leagues and other digital simulated sports games like basketball or ice hockey. In doing so, we show that previously published ball passing methods do not ..."
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Abstract. We are looking a generic solution for the optimized ball passing problem in the robotic soccer which is applicable to different RoboCup leagues and other digital simulated sports games like basketball or ice hockey. In doing so, we show that previously published ball passing methods do not properly address the necessary balance between the anticipated rewards, costs, and risks. The multicriteria nature of this optimization problem requires using the Pareto optimality approach. The problem itself is substantially inconvex, nothing else except the search of all available alternatives in the Pareto set appears to be applicable in this case. Realtime constraints are further complicating the problem. We propose a scalable and robust solution for decision making with multiple optimality criteria; is quality degrades in a graceful way once the real time constrains are kicking in. Our method is treating equally direct and leading passes to the partners and self passing while fast dribbling the ball. The new method also allows easily modeling the whole spectrum of risk aversive to risk talking attitudes; therefore it is generic indeed.