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14
On the point-to-point and traveling salesperson problems for Dubins’ vehicle,”
- in American Control Conference,
, 2005
"... Abstract-In this paper we propose some novel planning and routing strategies for Dubins' vehicle, i.e., for a nonholonomic vehicle moving along paths with bounded curvature, without reversing direction. First, we study a stochastic version of the Traveling Salesperson Problem (TSP): given n ta ..."
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Cited by 73 (18 self)
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Abstract-In this paper we propose some novel planning and routing strategies for Dubins' vehicle, i.e., for a nonholonomic vehicle moving along paths with bounded curvature, without reversing direction. First, we study a stochastic version of the Traveling Salesperson Problem (TSP): given n targets randomly sampled from a uniform distribution in a rectangle, what is the shortest Dubins' tour through the targets and what is its length? We show that the expected length of such a tour is Ω(n 2/3 ) and we propose a novel algorithm that generates a tour of length O(n 2/3 log(n) 1/3 ) with high probability. Second, we study a dynamic version of the TSP (known as "Dynamic Traveling Repairperson Problem" in the Operations Research literature): given a stochastic process that generates targets, is there a policy that allows a Dubins vehicle to stabilize the system, in the sense that the number of unvisited targets does not diverge over time? If such policies exist, what is the minimum expected waiting period between the time a target is generated and the time it is visited? We propose a novel receding-horizon algorithm whose performance is almost within a constant factor from the optimum.
On Multiple UAV Routing with Stochastic Targets: Performance Bounds and Algorithms
- Proc. of the AIAA Conf. on Guidance, Navigation, and Control
, 2005
"... In this paper we consider the following problem. A number of Uninhabited Aerial Vehicles (UAVs), modeled as vehicles moving at constant speed along paths of bounded curvature, must visit stochastically-generated targets in a convex, compact region of the plane. Targets are generated according to a s ..."
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Cited by 16 (6 self)
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In this paper we consider the following problem. A number of Uninhabited Aerial Vehicles (UAVs), modeled as vehicles moving at constant speed along paths of bounded curvature, must visit stochastically-generated targets in a convex, compact region of the plane. Targets are generated according to a spatio-temporal Poisson process, uniformly in the region. It is desired to minimize the expected waiting time between the appearance of a target, and the time it is visited. We present partially centralized algorithms for UAV routing, assigning regions of responsibility to each vehicle, and compare their performance with respect to asymptotic performance bounds, in the light and heavy load limits. Simulation results are presented and discussed. I.
The Curvature-Constrained Traveling Salesman Problem For High Point Densities
"... We consider algorithms for the curvature-constrained traveling salesman problem, when the nonholonomic constraint is described by Dubins’ model. We indicate a proof of the NP-hardness of this problem. In the case of low point densities, i.e., when the Euclidean distances between the points are lar ..."
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Cited by 7 (1 self)
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We consider algorithms for the curvature-constrained traveling salesman problem, when the nonholonomic constraint is described by Dubins’ model. We indicate a proof of the NP-hardness of this problem. In the case of low point densities, i.e., when the Euclidean distances between the points are larger than the turning radius of the vehicle, various heuristics based on the Euclidean Traveling salesman problem are expected to perform well. In this paper we do not put a constraint on the minimum Euclidean distance. We show that any algorithm that computes a tour for the Dubins ’ vehicle following an ordering of points optimal for the Euclidean TSP cannot have an approximation ratio better than Ω(n), where n is the number of points. We then propose an algorithm that is not based on the Euclidean solution and seems to behave differently. For�this �algorithm, we obtain an approximation �1 ρ � � ρ � �� 2 guarantee of O min + ε logn, 1 + ε, where ρ is the minimum turning radius, and ε is the minimum Euclidean distance between any two points.
On the Dubins Traveling Salesperson Problems: novel approximation algorithms
"... In this paper we study minimum-time motion planning and routing problems for the Dubins vehicle, i.e., a nonholonomic vehicle that is constrained to move along planar paths of bounded curvature, without reversing direction. Motivated by autonomous aerial vehicle applications, we consider the Traveli ..."
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Cited by 3 (1 self)
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In this paper we study minimum-time motion planning and routing problems for the Dubins vehicle, i.e., a nonholonomic vehicle that is constrained to move along planar paths of bounded curvature, without reversing direction. Motivated by autonomous aerial vehicle applications, we consider the Traveling Salesperson Problem for the Dubins vehicle (DTSP): given n points on a plane, what is the shortest Dubins tour through these points and what is its length? Specifically, we study a stochastic version of the DTSP where the n targets are randomly sampled from a uniform distribution. We show that the expected length of such a tour is of order at least n 2/3 and we propose a novel algorithm yielding a solution with length of order n 2/3 with high probability. Additionally, we study a dynamic version of the DTSP: given a stochastic process that generates target points, is there a policy which guarantees that the number of unvisited points does not diverge over time? If such stable policies exist, what is the minimum expected time that a newly generated target waits before being visited by the vehicle? We propose a novel stabilizing algorithm such that the expected wait time is provably within a constant factor from the optimum.
Cooperative path planning for a class of carrier-vehicle systems
- IEEE Conf. on Decision and Control
, 2004
"... Abstract — In this work we concentrate on the problem of path planning in a scenario in which two different vehicles with complementary capabilities are employed cooperatively to perform a desired task in an optimal way. In particular we consider the case in which a vehicle carrier, typically slow b ..."
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Cited by 2 (1 self)
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Abstract — In this work we concentrate on the problem of path planning in a scenario in which two different vehicles with complementary capabilities are employed cooperatively to perform a desired task in an optimal way. In particular we consider the case in which a vehicle carrier, typically slow but with virtually infinite operativity range, and a carried vehicle, which on the contrary is typically fast but with a shorter operative range, can be controlled together to pursuit a certain mission while minimizing a pre-defined cost function. In particular we will concentrate on a particular scenario, which we denoted as “fast-rescue ” problem, providing optimal and heuristic solutions to various cases. I.
Bounded-curvature shortest paths through a sequence of points USING CONVEX OPTIMIZATION
, 2013
"... We consider the problem of computing shortest paths having curvature at most one almost everywhere and visiting a sequence of n points in the plane in a given order. This problem is a subproblem of the Dubins traveling salesman problem and also arises naturally in path planning for point car-like ro ..."
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Cited by 1 (1 self)
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We consider the problem of computing shortest paths having curvature at most one almost everywhere and visiting a sequence of n points in the plane in a given order. This problem is a subproblem of the Dubins traveling salesman problem and also arises naturally in path planning for point car-like robots in the presence of polygonal obstacles. We show that when consecutive waypoints are a distance of at least four apart, this question reduces to a family of convex optimization problems over polyhedra in Rn.
2009), Specification and planning of interactive UAV missions in adversarial environments
- in AIAA Guidance, Navigation, and Control Conference
"... In this paper, specification and planning of UAV missions, in which interaction with the operators, adversaries, and the environment plays a crucial role, are studied. A novel specification method is introduced to model interactive tasks in UAV missions and process algebra framework is used to model ..."
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Cited by 1 (0 self)
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In this paper, specification and planning of UAV missions, in which interaction with the operators, adversaries, and the environment plays a crucial role, are studied. A novel specification method is introduced to model interactive tasks in UAV missions and process algebra framework is used to model complex interactive tasks from relatively simple ones. An anytime state-space search algorithm is proposed. The algorithm effectively searches for a feasible solution and improves on such solution over time, eventually terminating with an optimal solution. I.
