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.

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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.

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.

We consider the problem of computing shortest paths, whose curvature is constrained to be at most one almost everywhere, and that visit a sequence of n points in the plane in a given order. This problem arises naturally in path planning for point car-like robots in the presence of polygonal obstacles, and is also a sub-problem of the Dubins Traveling Salesman Problem. We show that, under some hypotheses on the relative positions of the points, the shortest bounded-curvature path through a sequence of points is unique and can be computed by convex optimization. In particular, we show that this problem reduces, in O(n) time, to minimizing a strictly convex function over a convex domain of Rn defined by O(n) linear constraints. This convex function is the length, in terms of θ1,..., θn, of a shortest curvature-constrained path that goes through the points p1,..., pn in order and whose tangent vector at pi has polar angle θi. This result reveals a fundamental property of curvature-constrained paths among polygonal obstacles. Moreover, it improves the previously known algorithms for solving this problem which were (i) a linear-time approximation algorithm for computing a path that is at most 5.03 times longer than the optimal one [19], (ii) the trivial approximation algorithm based on a discretization of the set of polar angles at each point pi, and a search in the graph of all induced curvature-constrained paths, and (iii) an unpractical algebraic approach based on the isolation of the roots of 2n algebraic systems of O(n) equations of bounded degree [8].

servers bundle for uncertain bioreactors, ” Automatica, vol. 45, no. 1,

Motivated by applications in which a nonholonomic robotic vehicle should sequentially hit a series of waypoints in the pres-ence of stochastic drift, we formulate a new version of the Dubins vehicle traveling salesperson problem. In our approach, we first compute the minimum expected time feedback control to hit one waypoint based on the Hamilton-Jacobi-Bellman equation. Next, minimum expected times associated with the control are used to construct a traveling salesperson problem based on a waypoint hitting angle discretization. We provide numerical results illus-trating our solution and analyze how the stochastic drift affects the solution. NOMENCLATURE v Speed of Dubins vehicle ∆xi x component of distance from Dubins vehicle to way-point i ∆yi y component of distance from Dubins vehicle to way-point i θ Heading angle of Dubins vehicle u Feedback-controlled turning rate N Number of waypoints K Number of possible final heading angles θ fk Discrete final heading angle at which the Dubins vehi-cle should hit the waypoint, k = 1,...K T (·) Minimum expected time to hit the waypoint µ(n) Index in 1,...,N of the nth waypoint to be visited c(·) Edge length between two nodes ∗Address correspondence to this author.

This article proposes the first known algorithm that achieves a constant-factor approximation of the minimum length tour for a Dubins’ vehicle through n points on the plane. By Dubins’ vehicle, we mean a vehicle constrained to move at constant speed along paths with bounded curvature without reversing direction. For this version of the classic Traveling Salesperson Problem, our algorithm closes the gap between previously established lower and upper bounds; the achievable performance is of order n2/3.

Abstract — We consider algorithms for the curvatureconstrained 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. I.

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