Path planning is important for the autonomy of Unmanned Aerial Vehicle (UAV), especially for scheduling UAV delivery. However, the operating environment of UAVs is usually uncertain and dynamic. Without proper planning, collisions may happen where multiple UAVs are congested. Besides, there may also be temporary no-fly zone setup by authorities that makes airspace unusable. Thus, proper pre-departure planning that avoids such places is needed. In this paper, we formulate this problem into a Constraint Satisfaction Problem to find a collision-free shortest path on a dynamic graph. We propose a collision-free path planning algorithm that is based on A* algorithm. The main novelty is that we invent a heuristic function that also considers waiting time. We later show that, with added waiting penalty, the proposed algorithm is optimal because the heuristic is admissible. Implementation of this algorithm simulates UAV delivery using Singapore's airspace structure. Our simulation exhibits desirable runtime performance. Using the proposed algorithm, the percentage of collision-free routes decreases as number of requests per unit area increases, and this percentage drops significantly at boundary value. Our empirical analysis could aid the decision-making of no-fly zone policy and infrastructure of UAV delivery.
Given we have global information regarding the the existing schedules of UAVs and their current locations, we can optimize the route through off-line planning. One natural way is using A* algorithm. A* algorithm @cite_4 is a best-first, efficient and optimal search algorithm. It uses heuristics to guide the search, and therefore, reduce the number of nodes needed to be explored. Another advantage for using A* is that it can apply on both 2D and 3D space as long as the graph is connected. @cite_1 proposed an offline improved A* algorithm to deal with realistic constraints in UAV movement, including maximum moving angle, minimum route leg length, minimum flight height and maximum route length. Their algorithm can avoid collision with terrain while minimize the flight height. However, it only handles static graph, and can be computationally expensive. proposed fixes by trimming some less-permissble nodes, or imposing some hard nodes that the route must follows, but doing so will lose some potentially optimal solutions, and thus lose its completeness and optimality.
@cite_1 @cite_4
2785555231 1969483458
UAV route planning is to plan a feasible route for the UAV considering the time of the UAV reaching the target, fuel consumption, mission requirements and the terrain and threat distribution in the flight area and other factors, in order to ensure the completion of the mission. We describe an improved algorithm of A∗ search approach which called sparse A∗ search approach in detail, including its content and process, and carried out a simulation experiment. And based on its disadvantages, we give an optimized method. This paper considers the problem of finding minimum-energy cooperative routes in a wireless network with variable wireless channels. We assume that each node in the network is equipped with a single omnidirectional antenna and, motivated by the large body of physical layer research indicating its potential utility, that multiple nodes are able to coordinate their transmissions at the physical layer in order to take advantage of spatial diversity. Such coordination, however, is intrinsically intertwined with routing decisions, thus motivating the work. We first formulate the energy cost of forming a cooperative link between two nodes based on a two-stage transmission strategy assuming that only statistical knowledge about channels is available. Utilizing the link cost formulation, we show that optimal static routes in a network can be computed by running Dijkstra's algorithm over an extended network graph created by cooperative links. However, due to the variability of wireless channels, we argue that a many-to-one cooperation model in static routing is suboptimal. Hence, we develop an opportunistic routing algorithm based on many-to-many cooperation, and show that optimal routes in a network can be computed by a stochastic version of the Bellman-Ford algorithm. We use static and opportunistic optimal algorithms as baselines to develop heuristic link selection algorithms that are energy efficient while being computationally simpler than the optimal algorithms. We simulate our algorithms and show that while optimal cooperation and link selection can reduce energy consumption by almost an order of magnitude compared to non-cooperative approaches, our simple heuristics achieve similar energy savings while being computationally efficient as well. We present a route planning technique solely based on the concept of node contraction. The nodes are first ordered by 'importance'. A hierarchy is then generated by iteratively contracting the least important node. Contracting a node υ means replacing shortest paths going through v by shortcuts. We obtain a hierarchical query algorithm using bidirectional shortest-path search. The forward search uses only edges leading to more important nodes and the backward search uses only edges coming from more important nodes. For fastest routes in road networks, the graph remains very sparse throughout the contraction process using rather simple heuristics for ordering the nodes. We have five times lower query times than the best previous hierarchical Dijkstra-based speedup techniques and a negative space overhead, i.e., the data structure for distance computation needs less space than the input graph. CHs can be combined with many other route planning techniques, leading to improved performance for many-to-many routing, transit-node routing, goal-directed routing or mobile and dynamic scenarios. Maximizing information gathered within a budget is a relevant problem for information gathering tasks for robots with cost or operating time constraints. This problem is also known as the informative path planning (IPP) problem or correlated orienteering. It can be formalized as that of finding budgeted routes in a graph such that the reward collected by the route is maximized, where the reward at nodes can be dependent. Unfortunately, the problem is NP-Hard and the state of the art methods are too slow to even present an approximate solution online. Here we present Randomized Anytime Orienteering (RAOr) algorithm that provides near optimal solutions while demonstrably converging to an efficient solution in runtimes that allows the solver to be run online. The key idea of our approach is to pose orienteering as a combination of a Constraint Satisfaction Problem and a Traveling Salesman Problem. This formulation allows us to restrict the search space to routes that incur minimum distance to visit a set of selected nodes, and rapidly search this space using random sampling. The paper provides the analysis of asymptotic near-optimality, convergence rates for RAOr algorithms, and present strategies to improve anytime performance of the algorithm. Our experimental results suggest an improvement by an order of magnitude over the state of the art methods in relevant simulation and in real world scenarios. Given a large city represented by nodes and arcs, with a subset of these nodes having people required to be evacuated in a disaster situation, and a subset of destination nodes where the people may be taken for safety, the evacuation route planner finds routes in this network to evacuate the people in minimum possible time. Evacuation route planning in pre-known disasters such as hurricanes is of utmost importance for civic authorities. Computing such evacuation routes in a large graph with road infrastructure constraints such as road capacities and travelling times can be challenging. The Capacity Constrained Route Planner (CCRP) is a well studied heuristic algorithm proposed by Lu, George and Shekhar for solving this problem. It uses shortest path computations as a basis for finding and scheduling possible evacuation paths in the graph. However, the algorithm fails to scale to very large graphs. Other algorithms based on CCRP like CCRP++ and Incremental Data Structure based CCRP have been proposed to scale them to larger graphs. In this paper, we analyze these algorithms from performance perspective and suggest a faster algorithm by extending the CCRP algorithm that avoids recomputing partial paths. We have carried out experiments on various graph structures which show a vast improvement in runtime without impacting the optimality of CCRP results. For instance, for the city of Oldenburg with 382285 people, 6105 nodes and 7034 edges, our algorithm produced an evacuation plan in 2.6 seconds as compared to 123.8 seconds by CCRP and 9.3 seconds by CCRP++. In a localized routing algorithm, each node currently holding a message makes forwarding decision solely based on the position information about itself, its neighbors and destination. In a unit graph, two nodes can communicate if and only if the distance between them is no more than the transmission radius, which is the same for each node. This paper proposes localized routing algorithms, aimed at minimizing total power for routing a message or maximizing the total number of routing tasks that a network can perform before a partition. The algorithms are combinations of known greedy power and or cost aware localized routing algorithms and an algorithm that guarantees delivery. A shortcut procedure is introduced in later algorithm to enhance its performance. Another improvement is to restrict the routing to nodes in a dominating set. These improvements require two-hop knowledge at each node. The efficiency of proposed algorithms is verified experimentally by comparing their power savings, and the number of routing tasks a network can perform before a node loses all its energy, with the corresponding shortest weighted path algorithms and localized algorithms that use fixed transmission power at each node. Significant energy savings are obtained, and feasibility of applying power and cost-aware localized schemes is demonstrated. Copyright © 2004 John Wiley & Sons, Ltd. Decentralized search by routing queries over a network is fast emerging as an important research problem, with potential applications in social search as well as peer-to-peer networks [17, 18]. In this paper, we introduce a novel Social Query Model (SQM) for decentralized search, which factors in realistic elements such as expertise levels and response rates of nodes, and has the Pagerank model and certain Markov Decision Processes as special cases. In the context of the model, we establish the existence of a query routing policy that is simultaneously optimal for all nodes, in that no subset of nodes will jointly have any incentive to use a different local routing policy. For computing the optimal policy, we present an efficient distributed approximation algorithm that is almost linear in the number of edges in the network. Extensive experiments on both simulated random graphs and real small-world networks demonstrate the potential of our model and the effectiveness of the proposed routing algorithm. We propose a new approach to edge bundling. At the first stage we route the edge paths so as to minimize a weighted sum of the total length of the paths together with their ink. As this problem is NP-hard, we provide an efficient heuristic that finds an approximate solution. The second stage then separates edges belonging to the same bundle. To achieve this, we provide a new and efficient algorithm that solves a variant of the metro-line crossing minimization problem. The method creates aesthetically pleasing edge routes that give an overview of the global graph structure, while still drawing each edge separately, without intersecting graph nodes, and with few crossings. In this paper, we study the problem of joint routing, link scheduling and power control to support high data rates for broadband wireless multihop networks. We first address the problem of finding an optimal link scheduling and power control policy that minimizes the total average transmission power in the wireless multihop network, subject to given constraints regarding the minimum average data rate per link, as well as peak transmission power constraints per node. Multiaccess signal interference is explicitly modeled. We use a duality approach whereby, as a byproduct of finding the optimal policy, we find the sensitivity of the minimal total average power with respect to the average data rate for each link. Since the minimal total average power is a convex function of the required minimum average data rates, shortest path algorithms with the link weights set to the link sensitivities can be used to guide the search for a globally optimum routing. We present a few simple examples that show our algorithm can find policies that support data rates that are not possible with conventional approaches. Moreover, we find that optimum allocations do not necessarily route traffic over minimum energy paths. Aiming at solving the problems of unsatisfactory routes planning that are suboptimal to optimal routes planning and dissatisfactory real time routes planning and routes planning of multiple unmanned aerial vehicles (UAVs) cooperation, a cost function of multiple UAVs routes planning is presented after modeling the primary factors influencing on multiple UAVs route planning. Then, Based on particle swarm optimization (PSO) algorithm, this paper presents the approaches of static three-dimensional routes planning and dynamic three-dimensional routes planning for multiple UAVs cooperation. The approaches can also be used to plan a single UAV route. Using these approaches, an emluator is designed and some experiments are made, and the results demonstrate that the approaches can satisfy the requests of the multiple UAVs routes planning. We propose optimal routing algorithms for Chord [1], a popular topology for routing in peer-to-peer networks. Chord is an undirected graph on 2b nodes arranged in a circle, with edges connecting pairs of nodes that are 2k positions apart for any k ≥ 0. The standard Chord routing algorithm uses edges in only one direction. Our algorithms exploit the bidirectionality of edges for optimality. At the heart of the new protocols lie algorithms for writing a positive integer d as the difference of two non-negative integers d′ and d″ such that the total number of 1-bits in the binary representation of d′ and d″ is minimized. Given that Chord is a variant of the hypercube, the optimal routes possess a surprising combinatorial structure. Load balanced routing in a network, i.e., minimizing the maximum traffic load any node carries for unsplittable flows, is a well known NP-hard problem. Finding practical algorithms remains a long standing challenge. In this paper we propose greedy routing using virtual coordinates that achieves both small path stretch ratio (compared to shortest path) and small load balancing ratio (compared to optimal load balanced routing), in a large scale wireless sensor network deployed densely inside a geometric domain with complex shape. We first provide a greedy routing scheme on a disk with a stretch ratio of at most 2, and under which the maximum load is a factor 4√2 smaller than the maximum load under shortest path routing. This is the first simple routing scheme with a small stretch that has been proven to outperform shortest path routing in terms of load balancing. Then we transform a network of arbitrary shape to a disk by an area preserving map φ. We show that both the path length and the maximum traffic load in the original network only increases by an additional factor of d2, where d is the maximum length stretch of φ. Combined with the result on a disk we again achieve both bounded stretch and bounded load balancing ratio. Our simulation results evaluated the practical performance on both quality measures. Compared to single-hop networks such as WiFi, multihop infrastructure wireless mesh networks (WMNs) can potentially embrace the broadcast benefits of a wireless medium in a more flexible manner. Rather than being point-to-point, links in the WMNs may originate from a single node and reach more than one other node. Nodes located farther than a one-hop distance and overhearing such transmissions may opportunistically help relay packets for previous hops. This phenomenon is called opportunistic overhearing listening. With multiple radios, a node can also improve its capacity by transmitting over multiple radios simultaneously using orthogonal channels. Capitalizing on these potential advantages requires effective routing and efficient mapping of channels to radios (channel assignment (CA)). While efficient channel assignment can greatly reduce interference from nearby transmitters, effective routing can potentially relieve congestion on paths to the infrastructure. Routing, however, requires that only packets pertaining to a particular connection be routed on a predetermined route. Random network coding (RNC) breaks this constraint by allowing nodes to randomly mix packets overheard so far before forwarding. A relay node thus only needs to know how many packets, and not which packets, it should send. We mathematically formulate the joint problem of random network coding, channel assignment, and broadcast link scheduling, taking into account opportunistic overhearing, the interference constraints, the coding constraints, the number of orthogonal channels, the number of radios per node, and fairness among unicast connections. Based on this formulation, we develop a suboptimal, auction-based solution for overall network throughput optimization. Performance evaluation results show that our algorithm can effectively exploit multiple radios and channels and can cope with fairness issues arising from auctions. Our algorithm also shows promising gains over traditional routing solutions in which various channel assignment strategies are used. Reducing power consumption and increasing battery life of nodes in an ad-hoc network requires an integrated power control and routing strategy. Power optimal routing selects the multi-hop links that require the minimum total power cost for data transmission under a constraint on the link quality. This paper studies optimal power routing under the constraint of a fixed end-to-end probability of error and compares the power optimal routes obtained with this criterion with those from the more commonly used fixed per hop error rate constraint. The comparison is carried out by looking at the properties of the power optimal graph, formed by the union of all the power optimal routes. The paper also provides algorithms to determine the power optimal routes. Geographic routing is one of the most widely-accepted techniques to route information in large-scale wireless sensor networks. It is based on a greedy forwarding strategy by which a sensor node selects as next hop relay the most promising neighbor (according to some metric) among those being closer to the destination than itself. This decision is based solely on the position of its neighbors and the destination. Given that sensor nodes are usually operated by batteries, energy-efficiency is a very important metric to be considered by the routing protocol. In this paper we present Locally-Optimal Source Routing (LOSR), a new localized and energy-efficient geographic routing algorithm for wireless sensor networks. Unlike existing energy-efficient geographic routing algorithms, in which current node routing the packet only considers nodes closer to destination than itself, LOSR uses all nodes in the neighborhood to compute a local energy-optimal path formed only by neighbors of the current node towards the selected next hop. Then, source routing is used to force data packets to follow that locally optimal path until next hop is reached. Our simulation results show that the proposed algorithm outperforms the best existing solution, over a variety of network densities and scenarios. In this paper, we revisit the problem of determining the minimum-length schedule that satisfies certain traffic demands in a wireless network. Traditional approaches for the determination of minimum-length schedules are based on a collision channel model, in which neighboring transmissions cause destructive interference if and only if they are within the "interference region" of the receiving nodes. By contrast, we adopt here a more realistic model for the physical layer by requiring that a threshold be exceeded by the signal-to-interference-plus-noise ratio (SINR) for a transmission to be successful. We present a novel formulation of the problem that incorporates various power and rate adaptation schemes while seamlessly integrating the generation of "matchings" (i.e., sets of links that can be activated simultaneously) by taking into consideration the SINR constraints at the receivers. For the formulated problem, we propose a column-generation-based solution method and show that it theoretically converges to a globally optimal solution, with a potential advantage of not having to enumerate all the feasible matchings a priori. We also discuss the influence of power control, spatial reuse, and variable transmission rates on network performance. Furthermore, we include aspects of the routing problem and provide computational results for our proposed column-generation-based solution procedure. Pathfinding for a single agent is the problem of planning a route from an initial location to a goal location in an environment, going around obstacles. Pathfinding for multiple agents also aims to plan such routes for each agent, subject to different constraints, such as restrictions on the length of each path or on the total length of paths, no self-intersecting paths, no intersection of paths plans, no crossing meeting each other. It also has variations for finding optimal solutions, e.g., with respect to the maximum path length, or the sum of plan lengths. These problems are important for many real-life applications, such as motion planning, vehicle routing, environmental monitoring, patrolling, computer games. Motivated by such applications, we introduce a formal framework that is general enough to address all these problems: we use the expressive high-level representation formalism and efficient solvers of the declarative programming paradigm Answer Set Programming. We also introduce heuristics to improve the computational efficiency and or solution quality. We show the applicability and usefulness of our framework by experiments, with randomly generated problem instances on a grid, on a real-world road network, and on a real computer game terrain. In this paper, we describe two heuristics for the Single Vehicle Loading Problem (SVLP), which can handle practical constraints that are frequently encountered in the freight transportation industry, such as the servicing order of clients; item fragility; and the stability of the goods. The two heuristics, Deepest-Bottom-Left-Fill and Maximum Touching Area, are 3D extensions of natural heuristics that have previously only been applied to 2D packing problems. We employ these heuristics as part of a two-phase tabu search algorithm for the Three-Dimensional Loading Capacitated Vehicle Routing Problem (3L-CVRP), where the task is to serve all customers using a homogeneous fleet of vehicles at minimum traveling cost. The resultant algorithm produces mostly superior solutions to existing approaches, and appears to scale better with problem size. Circular graph layout is a drawing scheme where all nodes are placed on the perimeter of a circle. An inherent issue with circular layouts is that the rigid restriction on node placement often gives rise to long edges and an overall dense drawing. We suggest here three independent, complementary techniques for lowering the density and improving the readability of circular layouts. First, a new algorithm is given for placing the nodes on the circle such that edge lengths are reduced. Second, we enhance the circular drawing style by allowing some of the edges to be routed around the exterior of the circle. This is accomplished with an algorithm for optimally selecting such a set of externally routed edges. The third technique reduces density by coupling groups of edges as bundled splines that share part of their route. Together, these techniques are able to reduce clutter, density and crossings compared with existing methods. We propose a novel localized routing protocol for wireless sensor networks (WSN) that is energy-efficient and guarantees delivery. We prove that it is constant factor of the optimum for dense networks. To forward a packet, a node s in graph G computes the cost of the energy weighted shortest path (SP) between s and each of its neighbors which are closer to the destination than itself. It then selects node x which minimizes the ratio of the cost of the SP to the progress towards the destination. It then sends the message to the first node on the SP from s to x: say node x'. Node x' restarts the same greedy routing process until the destination is reached or the routing fails. To recover from failure, our algorithm invokes face routing that guarantees delivery. This work is the first to optimize energy consumption of face routing. First, we build a connected dominating set from graph G, second we compute its Gabriel graph to obtain the planar graph G'. Face routing is applied on G' only to decide which edges to follow in the recovery process. On each edge, greedy routing is used. This two-phase (greedy-Face) end-to-end routing process (EtE) reiterates until the final destination is reached. Simulation results show that EtE outperforms several existing geographical routing on energy consumption metric.