Unmanned aerial vehicles (UAVs), or aerial drones, are an emerging technology with significant market potential. UAVs may lead to substantial cost savings in, for instance, monitoring of difficult-to-access infrastructure, spraying fields and performing surveillance in precision agriculture, as well as in deliveries of packages. In some applications, like disaster management, transport of medical supplies, or environmental monitoring, aerial drones may even help save lives. In this article, we provide a literature survey on optimization approaches to civil applications of UAVs. Our goal is to provide a fast point of entry into the topic for interested researchers and operations planning specialists. We describe the most promising aerial drone applications and outline characteristics of aerial drones relevant to operations planning. In this review of more than 200 articles, we provide insights into widespread and emerging modeling approaches. We conclude by suggesting promising directions for future research.

Optimization approaches for civil applications of unmanned aerial vehicles (UAVs) or aerial drones: A survey

Sense and avoid technologies with applications to unmanned aircraft systems: Review and prospects

This paper addresses the task scheduling and path planning problem for a team of cooperating vehicles performing autonomous deliveries in urban environments. The cooperating team comprises two vehicles with complementary capabilities, a truck restricted to travel along a street network, and a quadrotor micro-aerial vehicle of capacity one that can be deployed from the truck to perform deliveries. The problem is formulated as an optimal path planning problem on a graph and the goal is to find the shortest cooperative route enabling the quadrotor to deliver items at all requested locations. The problem is shown to be NP-hard. A solution is then proposed using a novel reduction to the Generalized Traveling Salesman Problem, for which well-established heuristic solvers exist. The heterogeneous delivery problem contains as a special case the problem of scheduling deliveries from multiple static warehouses. We propose two additional algorithms, based on enumeration and a reduction to the traveling salesman problem, for this special case. Simulation results compare the performance of the presented algorithms and demonstrate examples of delivery route computations over real urban street maps.

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Planning Paths for Package Delivery in Heterogeneous Multirobot Teams

We consider a single Unmanned Aerial Vehicle (UAV) routing problem where there are multiple depots and the vehicle is allowed to refuel at any depot. The objective of the problem is to find a path for the UAV such that each target is visited at least once by the vehicle, the fuel constraint is never violated along the path for the UAV, and the total fuel required by the UAV is a minimum. We develop an approximation algorithm for the problem, and propose fast construction and improvement heuristics to solve the same. Computational results show that solutions whose costs are on an average within 1.4% of the optimum can be obtained relatively fast for the problem involving five depots and 25 targets.

Algorithms for Routing an Unmanned Aerial Vehicle in the Presence of Refueling Depots

Dynamic path planning for autonomous driving on various roads with avoidance of static and moving obstacles

Heterogeneous unmanned aerial vehicles (UAVs) are being developed for several civil and military applications. These vehicles can differ either in their motion constraints or sensing/attack capabilities. This article uses methods from operations research to address a fundamental routing problem involving heterogeneous UAVs. The approach is to transform the routing problem into a relatively better understood single, asymmetric, traveling salesman problem (ATSP) and use the algorithms available for the ATSP to address the routing problem. To test the effectiveness of the transformation, the well-known Lin-Kernighan-Helsgaun heuristic was applied to the transformed ATSP. Computational results on the transformed ATSP show that solutions whose costs are within 16% of the optimum can be obtained relatively fast [within 40 s of central processing unit (CPU)] for the routing problem involving ten heterogeneous UAVs and 40 targets.

Today's Traveling Salesman Problem

Nomenclature jAj = cardinality of a set A A , A, @A = interior, closure, and boundary of a set A, respectively C = cost of an aircraft reconnaissance tour , m d x;x0 = length of shortest aircraft path from state x to state x0, m nsamples = actual number of samples to build a roadmap nsamples = estimated number of samples to build a roadmap rmin = Dubins aircraft minimum turn radius R = s-dimensional Euclidean space S = circle parameterized by angle radians ranging from 0 to 2 SE(2) = special Euclidean group R S T = set fT 1; T 2; . . . ; T ng of n targets to be photographed by aircraft V T i = visibility region of ith target Va = Dubins aircraft airspeed X = aircraft state space x = aircraft state vector x; y = Dubins aircraft Earth-fixed Cartesian coordinates, m = parameter controls ratio of translational vs rotational density of roadmap = Dubins aircraft azimuth angle, rad 2 = set of all subsets of a set A

Sampling-Based Path Planning for a Visual Reconnaissance Unmanned Air Vehicle

Unmanned aerial vehicles (UAVs) are being increasingly used for surveillance missions in civil and military applications. These vehicles can be heterogeneous in the sense that they can differ either in their motion constraints or sensing/attack capabilities. Given a surveillance mission that require a group of heterogeneous UAVs to visit a set of targets, this paper addresses a resource allocation problem of finding the optimal sequence of targets for each vehicle such that 1) each target is visited at least once by some vehicle, and 2) the total cost travelled by all the vehicles is minimized. This problem can be posed as a Heterogeneous, Multiple Depot, Multiple Traveling Salesman Problem (HMDMTSP). This paper presents a transformation of a Heterogeneous, Multiple Depot, Multiple Traveling Salesman Problem (HMDMTSP) into a single, Asymmetric, Traveling Salesman Problem (ATSP). As a result, algorithms available for the single salesman problem can be used to solve the HMDMTSP. To show the effectiveness of the transformation, the well known Lin-Kernighan-Helsgaun heuristic was applied to the transformed ATSP. Computational results show that good quality solutions can be obtained for the HMDMTSP relatively fast.

A transformation for a Heterogeneous, Multiple Depot, Multiple Traveling Salesman Problem

This article considers a path planning problem for a single fixed-wing aircraft performing a reconnaissance mission using EO (Electro-Optical) camera(s). A mathematical formulation of the general aircraft visual reconnaissance problem for static ground targets in terrain is given and it is shown, under simplifying assumptions, that it can be reduced to what we call the PVDTSP (Polygon-Visiting Dubins Traveling Salesman Problem), a variation of the famous TSP (Traveling Salesman Problem). Two algorithms are developed to solve the PVDTSP. They fall into the class of algorithms known as sampling-based roadmap methods because they operate by sampling a finite set of points from a continuous state space in order to reduce a continuous motion planning problem to planning on a finite discrete graph. The first method is resolution complete, which means it provably converges to a nonisolated global optimum as the number of samples grows. The second method achieves slightly shorter computation times by using approximate dynamic programming, but consequently is only guaranteed to converge to a nonisolated global optimum modulo target order. Numerical experiments indicate that, for up to about 20 targets, both methods deliver good solutions suitably quickly for online purposes. Additionally, both algorithms allow trade-off of computation time for solution quality and are shown extensible to handle wind, airspace constraints, any vehicle dynamics, and open-path (vs. closed-tour) problems.

Sampling-Based Roadmap Methods for a Visual Reconnaissance UAV ∗

In this paper, a Multiple Depot, Multiple Traveling Salesman Problem is transformed into a Single, Asymmetric Traveling Salesman Problem if the cost of the edges satisfy the triangle inequality. This improves on the previously known transformation for a 2-Depot, Multiple Traveling Salesman Problem in the literature. To test the effectiveness of the transformation, some computational results are presented by applying the well known LKH heuristic on the transformed problem for instances involving Dubins vehicles. Results show that the transformation is effective and high quality solutions can be found for large instances in a relatively short time.

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Paul Oberlin

Papers

Today's Traveling Salesman Problem

Sampling-Based Path Planning for a Visual Reconnaissance Unmanned Air Vehicle

A transformation for a Heterogeneous, Multiple Depot, Multiple Traveling Salesman Problem

Sampling-Based Roadmap Methods for a Visual Reconnaissance UAV ∗

A transformation for a Multiple Depot, Multiple Traveling Salesman Problem