The Moving Target Traveling Salesman Problem (MT-TSP) seeks a trajectory that intercepts several moving targets, within a particular time window for each target. When generic nonlinear target trajectories or kinematic constraints on the agent are present, no prior algorithm guarantees convergence to an optimal MT-TSP solution. Therefore, we introduce the Iterated Random Generalized (IRG) TSP framework. The idea behind IRG is to alternate between randomly sampling a set of agent configuration-time points, corresponding to interceptions of targets, and finding a sequence of interception points by solving a generalized TSP (GTSP). This alternation asymptotically converges to the optimum. We introduce two parallel algorithms within the IRG framework. The first algorithm, IRG-PGLNS, solves GTSPs using PGLNS, our parallelized extension of state-of-the-art solver GLNS. The second algorithm, Parallel Communicating GTSPs (PCG), solves GTSPs for several sets of points simultaneously. We present numerical results for three MT-TSP variants: one where intercepting a target only requires coming within a particular distance, another where the agent is a variable-speed Dubins car, and a third where the agent is a robot arm. We show that IRG-PGLNS and PCG converge faster than a baseline based on prior work. We further validate our framework with physical robot experiments.

We present a novel algorithm that fuses the existing convex-programming based approach with heuristic information to find optimality guarantees and near-optimal paths for the Shortest Path Problem in the Graph of Convex Sets (SPP-GCS). Our method, inspired by A* initiates a best-first-like procedure from a designated subset of vertices and iteratively expands it until further growth is neither possible nor beneficial. Traditionally, obtaining solutions with bounds for an optimization problem involves solving a relaxation, modifying the relaxed solution to a feasible one, and then comparing the two solutions to establish bounds. However, for SPP-GCS, we demonstrate that reversing this process can be more advantageous, especially with Euclidean travel costs. In other words, we initially employ A* to find a feasible solution for SPP-GCS, then solve a convex relaxation restricted to the vertices explored by A* to obtain a relaxed solution, and finally, compare the solutions to derive bounds. We present numerical results to highlight the advantages of our algorithm over the existing approach in terms of the sizes of the convex programs solved and computation time.

The moving target traveling salesman problem with obstacles (MT-TSP-O) seeks an obstacle-free trajectory for an agent that intercepts a given set of moving targets, each within specified time windows, and returns to the agent's starting position. Each target moves with a constant velocity within its time windows, and the agent has a speed limit no smaller than any target's speed. We present FMC*-TSP, the first complete and bounded-suboptimal algorithm for the MT-TSP-O, and results for an agent whose configuration space is$\mathbb{R}^{3}$. Our algorithm interleaves a high-level search and a lowlevel search, where the high-level search solves a generalized traveling salesman problem with time windows (GTSP-TW) to find a sequence of targets and corresponding time windows for the agent to visit. Given such a sequence, the low-level search then finds an associated agent trajectory. To solve the low-level planning problem, we develop a new algorithm called FMC*, which finds a shortest path on a graph of convex sets (GCS) via implicit graph search and pruning techniques specialized for problems with moving targets. We test FMC*-TSP on 280 problem instances with up to 40 targets and demonstrate its smaller median runtime than a baseline based on prior work.

Multi-Agent Path Finding (MAPF) seeks collision-free paths for multiple agents from start to goal locations. This paper considers a generalization of MAPF called Multi-Agent Combinatorial Path Finding (MCPF) where agents must collectively visit a set of intermediate target locations before reaching their goals. MCPF is challenging as it involves both planning collision-free paths for multiple agents and target sequencing, i.e., assigning targets to and computing the visiting order for each agent. A recent method Conflict-Based Steiner Search (CBSS) is developed to solve MCPF to optimality, which, however, does not scale well when the number of agents or targets is large (e.g. 50 targets). While MAPF research has developed methods to plan bounded sub-optimality paths for many agents, it remains unknown how to find bounded sub-optimal solutions in the presence of many targets. This paper fills this gap by developing a methodAK*for target sequencing (A for Approximation and K* for K-best), which leverages approximation algorithms for traveling salesman problems.AK*is motivated by MCPF, but is a standalone method that can solve K-best routing problems in general. We prove thatAK*has worst-case polynomial runtime complexity and finds bounded sub-optimal solutions. WithAK*, we develop twoCBSSvariants that find bounded sub-optimal paths for MCPF. Our results verify the fast running speeds of our methods with up to 200 targets. Note to Practitioners—The motivation of this paper originates from the need to plan conflict-free paths for multiple mobile robots in cluttered environment in warehouse logistics, manufacturing and inspection. While existing methods for multi-agent planning typically consider finding paths from starts to goals, this paper investigates the case, where agents must collectively visit a set of intermediate target locations before reaching their goals, for the purpose of inspection, picking or placing parts, etc. To solve the problem, this paper first develops an algorithm to find K-best solutions for traveling salesman problems with bounded sub-optimality, which then leads to two multi-agent planners that can handle hundreds of targets and tens of agents. We provide a Gazebo simulation to showcase the usage of the planner in a warehouse like environment.

We introduce a new bounding approach called Continuity* (C$^{*}$), which provides optimality guarantees for the Moving-Target Traveling Salesman Problem (MT-TSP). Our approach relaxes the continuity constraints on the agent's tour by partitioning the targets' trajectories into smaller segments. This allows the agent to arrive at any point within a segment and depart from any point in the same segment when visiting each target. This formulation enables us to pose the bounding problem as a Generalized Traveling Salesman Problem (GTSP) on a graph, where the cost of traveling along an edge requires solving a new problem called the Shortest Feasible Travel (SFT). We present various methods for computing bounds for the SFT problem, leading to several variants of C$^{*}$. We first prove that the proposed algorithms provide valid lower-bounds for the MT-TSP. Additionally, we provide computational results to validate the performance of all C$^{*}$variants on instances with up to 15 targets. For the special case where targets move along straight lines, we compare our C$^{*}$variants with a mixed-integer Second Order Conic Program (SOCP) based method, the current state-of-the-art solver for the MT-TSP. While the SOCP-based method performs well on instances with 5 and 10 targets, C$^{*}$outperforms it on instances with 15 targets. For the general case, on average, our approaches find feasible solutions within approximately 4.5$\%$of the lower-bounds for the tested instances.

This paper introduces a new formulation that finds the optimum for the Moving-Target Traveling Salesman Problem (MT-TSP), which seeks to find a shortest path for an agent, that starts at a depot, visits a set of moving targets exactly once within their assigned time-windows, and returns to the depot. The formulation relies on the key idea that when the targets move along lines, their trajectories become convex sets within the space-time coordinate system. The problem then reduces to finding the shortest path within a graph of convex sets, subject to some speed constraints. We compare our formulation with the current state-of-the-art Mixed Integer Conic Program (MICP) formulation for the MT-TSP. The experimental results show that our formulation outperforms the MICP for instances with up to 20 targets, with up to two orders of magnitude reduction in runtime, and up to a 60% tighter optimality gap. We also show that the solution cost from the convex relaxation of our formulation provides significantly tighter lower-bounds for the MT-TSP than the ones from the MICP.

In this article, we consider a multi-agent path planning problem in a partially impeded environment. The impeded environment is represented by a graph with select road segments (edges) in disrepair impeding vehicular movement in the road network. A primary vehicle, which we refer to as a convoy, wishes to travel from a starting location to a destination while minimizing some accumulated cost. The convoy may traverse an impeded edge for an additional cost (associated with repairing the edge) than if it were unimpeded. A support vehicle, which we refer to as a service vehicle, is simultaneously deployed to assist the convoy by repairing edges, reducing the cost for the convoy to traverse those edges. The convoy is permitted to wait at any vertex to allow the service vehicle to complete repairing an edge. The service vehicle is permitted to terminate its path at any vertex. The goal is then to find a pair of paths so the convoy reaches its destination while minimizing the total time (cost) the two vehicles are active, including any time the convoy waits. We refer to this problem as the Assisted Shortest Path Problem (ASPP). We present a generalized permanent labeling algorithm (GPLA) to find an optimal solution for the ASPP. We also introduce additional modifications to the labeling algorithm to significantly improve the computation time and refer to the modified labeling algorithm as GPLA*. Computational results are presented to illustrate the effectiveness of GPLA* in solving the ASPP.Note to Practitioners—One motivation for this work is to improve the efficiency of autonomous warehouse operations, where multiple robots need to coordinate their plans. Take for example two robots operating in a warehouse where one robot is moving goods and the second robot is making repairs or clearing obstructions (fallen goods, objects left by workers, etc.) along the way. The presented algorithm’s underlying structure is relatively simple and the algorithm itself does not require special software or solvers. The algorithm generates sub-optimal solutions as it progresses and terminates with the optimal solution. A large class of problems involving asynchronous actions between two or more agents can be handled using the presented algorithm or an extension of it. In this paper we restrict ourselves to two agents. A limitation of the presented algorithm and its possible extensions is the memory required as the graph representing the problem grows in size. We compare our work against an algorithm with similar approach (centralized$A^*$) and show that the presented algorithm is superior in both memory and computational time. We also present results on relatively large graphs to show the algorithm has practical value. This work can also be applied to rescue missions for people to escape wildfires, flooding or other natural disasters. A robotic agent can scout ahead for impacted pathways and assist victim(s) find the best path to escape to safety.

We interleave sampling based motion planning methods with pruning ideas from minimum spanning tree algorithms to develop a new approach for solving a Multi-Goal Path Finding (MGPF) problem in high dimensional spaces. The approach alternates between sampling points from selected regions in the search space and de-emphasizing regions that may not lead to good solutions for MGPF. Our approach provides an asymptotic, 2-approximation guarantee for MGPF. We also present extensive numerical results to illustrate the advantages of our proposed approach over uniform sampling in terms of the quality of the solutions found and computation speed. Note to Practitioners—MGPF is concerned with finding a collision-free, near-optimal path for a robot visiting a set of target configurations. This problem arises in applications that use robotic manipulators such as advanced manufacturing, surface inspection, package sorting, and in other logistical applications where the cost of the traveling between any two configurations of a robot cannot be readily determined a-priori. As robots are expected to perform a large number of tasks, the sequencing of these tasks become important specifically when the travel costs are challenging to estimate. This paper provides an approach to handle this problem in higher dimensions with theoretical guarantees as well as provides simulation results on a broad class of environments to corroborate its performance with respect to the state of the art.

Multi-Agent Path Finding (MA-PF) computes a set of collision-free paths for multiple agents from their respective starting locations to destinations. This paper considers a generalization of MA-PF called Multi-Agent Teamwise Cooperative Path Finding (MA-TC-PF), where agents are grouped as multiple teams and each team has its own objective to be minimized. For example, an objective can be the sum or max of individual arrival times of the agents. In general, there is more than one team, and MA-TC-PF is thus a multi-objective planning problem with the goal of finding the entire Pareto-optimal front that represents all possible trade-offs among the objectives of the teams. To solve MA-TC-PF, we propose two algorithms TC-CBS and TC-M*, which leverage the existing CBS and M* for conventional MA-PF. We discuss the conditions under which the proposed algorithms are complete and are guaranteed to find the Pareto-optimal front. We present numerical results for several types of MA-TC-PF problems.

Multi-Agent Path Finding (MA-PF) finds collision-free paths for multiple agents from their respective start to goal locations. This paper investigates a generalization of MA-PF called Multi-Agent Teamwise Cooperative Path Finding (MA-TC-PF), where agents are grouped as multiple teams and each team has its own objective to minimize. In general, there is more than one team, and MA-TC-PF is thus a multi-objective planning problem with the goal of finding the entire Pareto-optimal front that represents all possible trade-offs among the objectives of the teams. We show that the existing CBS and M* for MA-PF can be modified to solve MA-TC-PF, which is verified with tests. We discuss the conditions under which the proposed algorithms are complete and are guaranteed to find the Pareto-optimal front for MA-TC-PF.

Conventional multi-agent path planners typically compute an ensemble of paths while optimizing a single objective, such as path length. However, many applications may require multiple objectives, say fuel consumption and completion time, to be simultaneously optimized during planning and these criteria may not be readily compared and sometimes lie in competition with each other. The goal of the problem is thus to find a Pareto-optimal set of solutions instead of a single optimal solution. Naively applying existing multi-objective search algorithms, such as multi-objective A* (MOA*), to multi-agent path finding may prove to be inefficient as the dimensionality of the search space grows exponentially with the number of agents. This article presents an approach named Multi-Objective Conflict-Based Search (MO-CBS) that attempts to address this so-called curse of dimensionality by leveraging prior Conflict-Based Search (CBS), a well-known algorithm for single-objective multi-agent path finding, and principles of dominance from multi-objective optimization literature. We also develop several variants of MO-CBS to improve its performance. We prove that MO-CBS and its variants can compute the entire Pareto-optimal set. Numerical results show that MO-CBS outperforms MOM*, a recently developed state-of-the-art multi-objective multi-agent planner. Note to Practitioners—The motivation of this article originates from the need to optimize multiple path criteria when planning conflict-free paths for multiple mobile robots in applications such as warehouse logistics, surveillance, construction site routing, and hazardous material transportation. Existing methods for multi-agent planning typically consider optimizing a single path criteria. This article develops a novel multi-objective multi-agent planner as well as its variants that are guaranteed to find all Pareto-optimal solutions for the problem. We also provide an illustrative example of the algorithm to plan paths for multiple agents that transport materials in a construction site while optimizing both path length and risk. In this example, computing and visualizing a set of Pareto-optimal solutions makes it intuitive for the practitioner to understand the underlying trade-off between conflicting objectives and to choose the most preferred solution for execution based on their domain knowledge.

The Resource Constrained Shortest Path Problem (RCSPP) seeks to determine a minimum-cost path between a start and a goal location while ensuring that one or multiple types of resource consumed along the path do not exceed their limits. This problem is often solved on a graph where a path is incrementally built from the start towards the goal during the search. RCSPP is computationally challenging as comparing these partial solution paths is based on multiple criteria (i.e., the accumulated cost and resource along the path), and in general, there does not exist a single path that optimizes all criteria simultaneously. Consequently, the search needs to maintain and explore a large number of partial paths in order to find an optimal solution. While a variety of algorithms have been developed to solve RCSPP, they either have little consideration about efficiently comparing and maintaining the partial paths, which reduces their overall runtime efficiency, or are restricted to handle only one resource constraint as opposed to multiple resource constraints. This paper develops Enhanced Resource Constrained A* (ERCA*), a fast A*-based algorithm that can find an optimal solution while satisfying multiple resource constraints. ERCA* leverages both the recent advances in multi-objective path planning to efficiently compare and maintain partial paths, and techniques from the existing RCSPP literature. Furthermore, ERCA* has a functional parameter to broker a trade-off between solution quality and runtime efficiency. The results show ERCA* often runs several orders of magnitude faster than an existing leading algorithm for RCSPP.

Persistent monitoring missions require an up-to-date knowledge of the changing state of the underlying environment. Unmannned aerial vehicles (UAVs) can be gainfully employed to continually visit a set of targets representing tasks (and locations) in the environment and collect data therein for long time periods. The enduring nature of these missions requires the UAV to be regularly recharged at a service station. In this article, we consider the case in which the service station is not colocated with any of the targets. An efficient monitoring requires the revisit time, defined as the maximum of the time elapsed between successive revisits to targets, to be minimized. Here, we consider the problem of determining UAV routes that lead to the minimum revisit time. The problem is NP-hard, and its computational difficulty increases with the fuel capacity of the UAV. We develop an algorithm to construct near-optimal solutions to the problem quickly when the fuel capacity exceeds a threshold. We also develop lower bounds to the optimal revisit time and use these bounds to demonstrate (through numerical simulations) that the constructed solutions are, on an average, at most 0.01% away from the optimum.

Conventional multiagent path finding (MAPF) problems aim to compute an ensemble of collision-free paths for multiple agents from their respective starting locations to preallocated destinations. This article considers a generalized version of MAPF called multiagent combinatorial path finding, where agents must collectively visit a large number of intermediate target locations along their paths before arriving at destinations. This problem involves not only planning collision-free paths for multiple agents but also assigning targets and specifying the visiting order for each agent (i.e., target sequencing). To solve the problem, we leverage conflict-based search (CBS) for MAPF and propose a novel approach called conflict-based Steiner search (CBSS). CBSS interleaves 1) the collision resolution strategy in CBS to bypass the curse of dimensionality in MAPF and 2) multiple traveling salesman algorithms to handle the combinatorics in target sequencing, to compute optimal or bounded suboptimal paths for agents while visiting all the targets. We also develop two variants of CBSS that trade off runtime against solution optimality. Our test results verify the advantage of CBSS over the baselines in terms of computing cheaper paths and improving success rates within a runtime limit for up to 20 agents and 50 targets. Finally, we run both Gazebo simulation and physical robot tests to validate that the planned paths are executable.

We interleave sampling based motion planning methods with pruning ideas from minimum spanning tree algorithms to develop a new approach for solving a Multi-Goal Path Finding (MGPF) problem in high dimensional spaces. The approach alternates between sampling points from selected regions in the search space and de-emphasizing regions that may not lead to good solutions for MGPF. Our approach provides an asymptotic, 2-approximation guarantee for MGPF. We also present extensive numerical results to illustrate the advantages of our proposed approach over uniform sampling in terms of the quality of the solutions found and computation speed.

This work addresses a Multi-Objective Shortest Path Problem (MO-SPP) on a graph where the goal is to find a set of Pareto-optimal solutions from a start node to a destination in the graph. A family of approaches based on MOA* have been developed to solve MO-SPP in the literature. Typically, these approaches maintain a "frontier" set at each node during the search process to keep track of the non-dominated, partial paths to reach that node. This search process becomes computationally expensive when the number of objectives increases as the number of Pareto-optimal solutions becomes large. In this work, we introduce a new method to efficiently maintain these frontiers for multiple objectives by incrementally constructing balanced binary search trees within the MOA* search framework. We first show that our approach correctly finds the Pareto-optimal front, and then provide extensive simulation results for problems with three, four and five objectives to show that our method runs faster than existing techniques by up to an order of magnitude.

Recent advances in vehicle connectivity have allowed formation of autonomous vehicle platoons for improved mobility and traffic throughput. In order to avoid a pile-up in such platoons, it is important to ensure platoon (string) stability, which is the focus of this work. As per conventional definition of string stability, the power (2-norm) of the spacing error signals should not amplify downstream in a platoon. But in practice, it is the infinity-norm of the spacing error signal that dictates whether a collision occurs. We address this discrepancy in the first part of our work, where we reconsider string stability from a safety perspective and develop an upper limit on the maximum spacing error in a homogeneous platoon as a function of the acceleration maneuver of the lead vehicle. In the second part of this paper, we extend our previous results by providing the minimum achievable time headway for platoons with two-predecessor lookup schemes experiencing burst-noise packet losses. Finally, we utilize throttle and brake maps to develop a longitudinal vehicle model and validate it against a Lincoln MKZ which is then used for numerical corroboration of the proposed time headway selection algorithms.

In this article, we introduce a cooperative path planning algorithm for a cardinal and a support robot where the cardinal robot is unable to traverse a subset of edges in a network until the support robot has first traversed them. This subset of edges represent paths in an environment that are initially unavailable to the cardinal robot and require the assistance of the support robot. A (2 + α)-approximation algorithm (where α is the supremum of the ratio of the travel time of the support robot versus the travel time of the cardinal robot) is presented for this problem and is applied to various types of networks in order to examine the quality of the solutions it produces. We then conclude by discussing some potential future work concerning variations of this problem.

Conventional multi-agent path planners typically compute an ensemble of paths while optimizing a single objective, such as path length. However, many applications may require multiple objectives, say fuel consumption and completion time, to be simultaneously optimized during planning and these criteria may not be readily compared and sometimes lie in competition with each other. Naively applying existing multi-objective search algorithms to multi-agent path finding may prove to be inefficient as the size of the space of possible solutions, i.e., the Pareto-optimal set, can grow exponentially with the number of agents (the dimension of the search space). This article presents an approach named Multi-objective Conflict-based Search (MO-CBS) that bypasses this so-called curse of dimensionality by leveraging prior Conflict-based Search (CBS), a well-known algorithm for single-objective multi-agent path finding, and principles of dominance from multi-objective optimization literature. We prove that MO-CBS is able to compute the entire Pareto-optimal set. Our results show that MO-CBS can solve problem instances with hundreds of Pareto-optimal solutions which the standard multi-objective A* algorithms could not find within a bounded time.

In multi-agent applications such as surveillance and logistics, fleets of mobile agents are often expected to coordinate and safely visit a large number of goal locations as efficiently as possible. The multi-agent planning problem in these applications involves allocating and sequencing goals for each agent while simultaneously producing conflict-free paths for the agents. In this article, we introduce a new algorithm called MS* which computes an optimal solution for this multi-agent problem by fusing and advancing state of the art solvers for multi-agent path finding (MAPF) and multiple travelling salesman problem (mTSP). MS* leverages our prior subdimensional expansion approach for MAPF and embeds the mTSP solvers to optimally allocate and sequence goals for agents. Numerical results show that our new algorithm can solve the multi-agent problem with 20 agents and 50 goals in a minute of CPU time on a standard laptop.

Multi-agent path finding (MAPF) determines an ensemble of collision-free paths for multiple agents between their respective start and goal locations. Among the available MAPF planners for workspace modeled as a graph, A*-based approaches have been widely investigated due to their guarantees on completeness and solution optimality, and have demonstrated their efficiency in many scenarios. However, almost all of these A*-based methods assume that each agent executes an action concurrently in that all agents start and stop together. This article presents a natural generalization of MAPF with asynchronous actions (MAPF-AA) where agents do not necessarily start and stop concurrently. The main contribution of the work is a proposed approach called Loosely Synchronized Search (LSS) that extends A*-based MAPF planners to handle asynchronous actions. We show LSS is complete and finds an optimal solution if one exists. We also combine LSS with other existing MAPF methods that aims to trade-off optimality for computational efficiency. Numerical results are presented to corroborate the performance of LSS and the applicability of the proposed method is verified in the Robotarium, a remotely accessible swarm robotics research platform.

This article addresses a persistent monitoring problem (PMP) that requires an unmanned aerial vehicle (UAV) to repeatedly visit n targets of equal priority. The UAV has limited onboard fuel/charge and must be regularly serviced at a depot. Given a fixed number of visits, k, for the UAV to the targets between successive services, the objective of the PMP is to determine an optimal sequence of visits such that the maximum time elapsed between successive visits to any target is minimized. This planning problem is a generalization of the traveling salesman problem and is NP-hard. We characterize the optimal solutions to this problem for different values of k and develop algorithms that can compute the optimal solutions relatively fast. Numerical results are also presented to corroborate the performance of the proposed approach.

Multiple studies have illustrated the potential for dramatic societal, environmental and economic benefits from significant penetration of autonomous driving. However, all the current approaches to autonomous driving require the automotive manufacturers to shoulder the primary responsibility and liability associated with replacing human perception and decision making with automation, potentially slowing the penetration of autonomous vehicles, and consequently slowing the realization of the societal benefits of autonomous vehicles. We propose here a new approach to autonomous driving that will re-balance the responsibility and liabilities associated with autonomous driving between traditional automotive manufacturers, private infrastructure players, and third-party players. Our proposed distributed intelligence architecture leverages the significant advancements in connectivity and edge computing in the recent decades to partition the driving functions between the vehicle, edge computers on the road side, and specialized third-party computers that reside in the vehicle. Infrastructure becomes a critical enabler for autonomy. With this Infrastructure Enabled Autonomy (IEA) concept, the traditional automotive manufacturers will only need to shoulder responsibility and liability comparable to what they already do today, and the infrastructure and third-party players will share the added responsibility and liabilities associated with autonomous functionalities. We propose a Bayesian Network Model based framework for assessing the risk benefits of such a distributed intelligence architecture. An additional benefit of the proposed architecture is that it enables “autonomy as a service” while still allowing for private ownership of automobiles.

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.

At busy airports, air traffic controllers seek to find schedules for aircraft at the runway that aim to minimize delays of the aircraft while maximizing runway throughput. In reality, finding optimal schedules by a human controller is hard to accomplish since the number of feasible schedules available for the scheduling problem is quite large. In this paper, we pose this problem as a multiobjective optimization problem, with respect to total aircraft delay and runway throughput. Using principles of multiobjective dynamic programming, we develop an algorithm to find a set of Pareto-optimal solutions that completely specify the nondominated frontier. In addition to finding these solutions, this paper provides a proof of the algorithm's correctness and gives an analysis of its performance against a baseline algorithm using the operational data for a model of the Dallas/Fort Worth International Airport.

This paper is about the allocation of tours of m targets to n vehicles. The motion of the vehicles satisfies a nonholonomic constraint (i.e., the yaw rate of the vehicle is bounded). Each target is to be visited by one and only one vehicle. Given a set of targets and the yaw rate constraints on the vehicles, the problem addressed in this paper is 1) to assign each vehicle a sequence of targets to visit, and 2) to find a feasible path for each vehicle that passes through the assigned targets with a requirement that the vehicle returns to its initial position. The heading angle at each target location may not be specified. The objective function is to minimize the sum of the distances traveled by all vehicles. A constant factor approximation algorithm is presented for the above resource allocation problem for both the single and the multiple vehicle case. Note to Practitioners-The motivation for this paper stems from the need to develop resource allocation algorithms for unmanned aerial vehicles (UAVs). Small autonomous UAVs are seen as ideal platforms for many applications, such as searching for targets, mapping a given area, traffic surveillance, fire monitoring, etc. The main advantage of using these small autonomous vehicles is that they can be used in situations where a manned mission is dangerous or not possible. Resource allocation problems naturally arise in these applications where one would want to optimally assign a given set of vehicles to the tasks at hand. The feature that differentiates these resource allocation problems from similar problems previously studied in the literature is that there are constraints on the motion of the vehicle. This paper addresses the constraint that captures the inability of a fixed wing aircraft to turn at any arbitrary yaw rate. The basic problem addressed in this paper is as follows: Given n vehicles and m targets, find a path for each vehicle satisfying yaw rate contraints such that each target is visited exactly once by a vehicle and the total distance traveled by all vehicles is minimized. We assume that the targets are at least 2r apart, where r is the minimum turning radius of the vehicle. This is a reasonable assumption because the sensors on these vehicles can map or see an area whose width is at least 2r. We give an algorithm to solve this problem by combining ideas from the traveling salesman problem and the path planning literature. We also show how these algorithms perform in the worst-case scenario