Asymptotic constant-factor approximation algorithm for the Traveling Salesperson Problem for Dubins' vehicle

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 $n^{2/3}$

Dynamic Vehicle Routing for Robotic Systems

Recent years have witnessed great advancements in the science and technology of autonomy, robotics, and networking. This paper surveys recent concepts and algorithms for dynamic vehicle routing (DVR), that is, for the automatic planning of optimal multivehicle routes to perform tasks that are generated over time by an exogenous process. We consider a rich variety of scenarios relevant for robotic applications. We begin by reviewing the basic DVR problem: demands for service arrive at random locations at random times and a vehicle travels to provide on-site service while minimizing the expected wait time of the demands. Next, we treat different multivehicle scenarios based on different models for demands (e.g., demands with different priority levels and impatient demands), vehicles (e.g., motion constraints, communication, and sensing capabilities), and tasks. The performance criterion used in these scenarios is either the expected wait time of the demands or the fraction of demands serviced successfully. In each specific DVR scenario, we adopt a rigorous technical approach that relies upon methods from queueing theory, combinatorial optimization, and stochastic geometry. First, we establish fundamental limits on the achievable performance, including limits on stability and quality of service. Second, we design algorithms, and provide provable guarantees on their performance with respect to the fundamental limits.United States. Air Force Office of Scientific Research (Award FA 8650-07-2-3744)United States. Army Research Office. Multidisciplinary University Research Initiative (Award W911NF-05-1-0219)National Science Foundation (U.S.) (Award ECCS-0705451)National Science Foundation (U.S.) (Award CMMI-0705453)United States. Army Research Office (Award W911NF-11-1-0092

Dynamic systems and subadditive functionals

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 125-131).Consider a problem where a number of dynamic systems are required to travel between points in minimum time. The study of this problem is traditionally divided into two parts: A combinatorial part that assigns points to every dynamic system and assigns the order of the traversal of the points, and a path planning part that produces the appropriate control for the dynamic systems to allow them to travel between the points. The first part of the problem is usually studied without consideration for the dynamic constraints of the systems, and this is usually compensated for in the second part. Ignoring the dynamics of the system in the combinatorial part of the problem can significantly compromise performance. In this work, we introduce a framework that allows us to tackle both of these parts at the same time. To that order, we introduce a class of functionals we call the Quasi-Euclidean functionals, and use them to study such problems for dynamic systems. We determine the asymptotic behavior of the costs of these problems, when the points are randomly distributed and their number tends to infinity. We show the applicability of our framework by producing results for the Traveling Salesperson Problem (TSP) and Minimum Bipartite Matching Problem (MBMP) for dynamic systems.by Sleiman M. Itani.Ph.D

Combinatorial Path Planning for a System of Multiple Unmanned Vehicles

In this dissertation, the problem of planning the motion of m Unmanned Vehicles (UVs) (or simply vehicles) through n points in a plane is considered. A motion plan for a vehicle is given by the sequence of points and the corresponding angles at which each point must be visited by the vehicle. We require that each vehicle return to the same initial location(depot) at the same heading after visiting the points. The objective of the motion planning problem is to choose at most q(≤ m) UVs and find their motion plans so that all the points are visited and the total cost of the tours of the chosen vehicles is a minimum amongst all the possible choices of vehicles and their tours. This problem is a generalization of the wellknown Traveling Salesman Problem (TSP) in many ways: (1) each UV takes the role of salesman (2) motion constraints of the UVs play an important role in determining the cost of travel between any two locations; in fact, the cost of the travel between any two locations depends on direction of travel along with the heading at the origin and destination, and (3) there is an additional combinatorial complexity stemming from the need to partition the points to be visited by each UV and the set of UVs that must be employed by the mission. In this dissertation, a sub-optimal, two-step approach to motion planning is presented to solve this problem:(1) the combinatorial problem of choosing the vehicles and their associated tours is based on Euclidean distances between points and (2) once the sequence of points to be visited is specified, the heading at each point is determined based on a Dynamic Programming scheme. The solution to the first step is based on a generalization of Held-Karp’s method. We modify the Lagrangian heuristics for finding a close sub-optimal solution. In the later chapters of the dissertation, we relax the assumption that all vehicles are homogenous. The motivation of heterogenous variant of Multi-depot, Multiple Traveling Salesmen Problem (MDMTSP) derives form applications involving Unmanned Aerial Vehicles (UAVs) or ground robots requiring multiple vehicles with different capabilities to visit a set of locations

Performance optimization for unmanned vehicle systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2008.Includes bibliographical references (p. 149-157).Technological advances in the area of unmanned vehicles are opening new possibilities for creating teams of vehicles performing complex missions with some degree of autonomy. Perhaps the most spectacular example of these advances concerns the increasing deployment of unmanned aerial vehicles (UAVs) in military operations. Unmanned Vehicle Systems (UVS) are mainly used in Information, Surveillance and Reconnaissance missions (ISR). In this context, the vehicles typically move about a low-threat environment which is sufficiently simple to be modeled successfully. This thesis develops tools for optimizing the performance of UVS performing ISR missions, assuming such a model.First, in a static environment, the UVS operator typically requires that a vehicle visit a set of waypoints once or repetitively, with no a priori specified order. Minimizing the length of the tour traveled by the vehicle through these waypoints requires solving a Traveling Salesman Problem (TSP). We study the TSP for the Dubins' vehicle, which models the limited turning radius of fixed wing UAVs. In contrast to previously proposed approaches, our algorithms determine an ordering of the waypoints that depends on the model of the vehicle dynamics. We evaluate the performance gains obtained by incorporating such a model in the mission planner.With a dynamic model of the environment the decision making level of the UVS also needs to solve a sensor scheduling problem. We consider M UAVs monitoring N > M sites with independent Markovian dynamics, and treat two important examples arising in this and other contexts, such as wireless channel or radar waveform selection. In the first example, the sensors must detect events arising at sites modeled as two-state Markov chains. In the second example, the sites are assumed to be Gaussian linear time invariant (LTI) systems and the sensors must keep the best possible estimate of the state of each site.(cont.) We first present a bound on the achievable performance which can be computed efficiently by a convex program, involving linear matrix inequalities in the LTI case. We give closed-form formulas for a feedback index policy proposed by Whittle. Comparing the performance of this policy to the bound, it is seen to perform very well in simulations. For the LTI example, we propose new open-loop periodic switching policies whose performance matches the bound.Ultimately, we need to solve the task scheduling and motion planning problems simultaneously. We first extend the approach developed for the sensor scheduling problems to the case where switching penalties model the path planning component. Finally, we propose a new modeling approach, based on fluid models for stochastic networks, to obtain insight into more complex spatiotemporal resource allocation problems. In particular, we give a necessary and sufficient stabilizability condition for the fluid approximation of the problem of harvesting data from a set of spatially distributed queues with spatially varying transmission rates using a mobile server.by Jerome Le Ny.Ph.D

Path Planning For Persistent Surveillance Applications Using Fixed-Wing Unmanned Aerial Vehicles

This thesis addresses coordinated path planning for fixed-wing Unmanned Aerial Vehicles (UAVs) engaged in persistent surveillance missions. While uniquely suited to this mission, fixed wing vehicles have maneuver constraints that can limit their performance in this role. Current technology vehicles are capable of long duration flight with a minimal acoustic footprint while carrying an array of cameras and sensors. Both military tactical and civilian safety applications can benefit from this technology. We make three main contributions: C1 A sequential path planner that generates a C2 flight plan to persistently acquire a covering set of data over a user designated area of interest. The planner features the following innovations: • A path length abstraction that embeds kino-dynamic motion constraints to estimate feasible path length • A Traveling Salesman-type planner to generate a covering set route based on the path length abstraction • A smooth path generator that provides C2 routes that satisfy user specified curvature constraints C2 A set of algorithms to coordinate multiple UAVs, including mission commencement from arbitrary locations to the start of a coordinated mission and de-confliction of paths to avoid collisions with other vehicles and fixed obstacles iv C3 A numerically robust toolbox of spline-based algorithms tailored for vehicle routing validated through flight test experiments on multiple platforms. A variety of tests and platforms are discussed. The algorithms presented are based on a technical approach with approximately equal emphasis on analysis, computation, dynamic simulation, and flight test experimentation. Our planner (C1) directly takes into account vehicle maneuverability and agility constraints that could otherwise render simple solutions infeasible. This is especially important when surveillance objectives elevate the importance of optimized paths. Researchers have devel oped a diverse range of solutions for persistent surveillance applications but few directly address dynamic maneuver constraints. The key feature of C1 is a two stage sequential solution that discretizes the problem so that graph search techniques can be combined with parametric polynomial curve generation. A method to abstract the kino-dynamics of the aerial platforms is then presented so that a graph search solution can be adapted for this application. An A* Traveling Salesman Problem (TSP) algorithm is developed to search the discretized space using the abstract distance metric to acquire more data or avoid obstacles. Results of the graph search are then transcribed into smooth paths based on vehicle maneuver constraints. A complete solution for a single vehicle periodic tour of the area is developed using the results of the graph search algorithm. To execute the mission, we present a simultaneous arrival algorithm (C2) to coordinate execution by multiple vehicles to satisfy data refresh requirements and to ensure there are no collisions at any of the path intersections. We present a toolbox of spline-based algorithms (C3) to streamline the development of C2 continuous paths with numerical stability. These tools are applied to an aerial persistent surveillance application to illustrate their utility. Comparisons with other parametric poly nomial approaches are highlighted to underscore the benefits of the B-spline framework. Performance limits with respect to feasibility constraints are documented

Optimal Control of Two-Wheeled Mobile Robots for Patrolling Operations

Optimal Control of Two-Wheeled Mobile Robots for Patrolling Operations Walaaeldin Ahmed Ghadiry, Concordia University, 2015 This work studies the use of the two-wheeled mobile robots in patrolling operations, and provides the most distance-e�cient as well as time-e�cient trajectories to patrol a given area. Novel formulations in the context of constrained optimization are introduced which can be solved using existing software. The main concept of the problem is directly related to the well-known Traveling Salesman Problem (TSP) and its variants, where a salesman starts from a base city and visits a number of other cities with minimum travel distance while satisfying the constraint that each city has to be visited only once. Finally, the salesman returns back to the starting base city after completing the mission. Two di�erent patrolling con�gurations that are related to the TSP and its variants, namely the Single Depot multiple Traveling Salesman Problem (mTSP) and the Multidepot multiple Traveling Salesman Problem (MmTSP) are investigated. Novel algorithms are introduced for the trajectory planning of multiple two-wheeled mobile robots, either with two di�erential motors (which can turn on the spot) or with Dubins-like vehicles. The output trajectories for both types of wheeled robots are investigated by using a model predictive control scheme to ensure their kinematic feasibility for the best monitoring performance. The proposed formulations and algorithms are veri�ed by a series of simulations using e�cient programming and optimization software as well as experimental tests in the lab environment

Exploration autonome et efficiente de chantiers miniers souterrains inconnus avec un drone filaire

Abstract: Underground mining stopes are often mapped using a sensor located at the end of a pole that the operator introduces into the stope from a secure area. The sensor emits laser beams that provide the distance to a detected wall, thus creating a 3D map. This produces shadow zones and a low point density on the distant walls. To address these challenges, a research team from the Université de Sherbrooke is designing a tethered drone equipped with a rotating LiDAR for this mission, thus benefiting from several points of view. The wired transmission allows for unlimited flight time, shared computing, and real-time communication. For compatibility with the movement of the drone after tether entanglements, the excess length is integrated into an onboard spool, contributing to the drone payload. During manual piloting, the human factor causes problems in the perception and comprehension of a virtual 3D environment, as well as the execution of an optimal mission. This thesis focuses on autonomous navigation in two aspects: path planning and exploration. The system must compute a trajectory that maps the entire environment, minimizing the mission time and respecting the maximum onboard tether length. Path planning using a Rapidly-exploring Random Tree (RRT) quickly finds a feasible path, but the optimization is computationally expensive and the performance is variable and unpredictable. Exploration by the frontier method is representative of the space to be explored and the path can be optimized by solving a Traveling Salesman Problem (TSP) but existing techniques for a tethered drone only consider the 2D case and do not optimize the global path. To meet these challenges, this thesis presents two new algorithms. The first one, RRT-Rope, produces an equal or shorter path than existing algorithms in a significantly shorter computation time, up to 70% faster than the next best algorithm in a representative environment. A modified version of RRT-connect computes a feasible path, shortened with a deterministic technique that takes advantage of previously added intermediate nodes. The second algorithm, TAPE, is the first 3D cavity exploration method that focuses on minimizing mission time and unwound tether length. On average, the overall path is 4% longer than the method that solves the TSP, but the tether remains under the allowed length in 100% of the simulated cases, compared to 53% with the initial method. The approach uses a 2-level hierarchical architecture: global planning solves a TSP after frontier extraction, and local planning minimizes the path cost and tether length via a decision function. The integration of these two tools in the NetherDrone produces an intelligent system for autonomous exploration, with semi-autonomous features for operator interaction. This work opens the door to new navigation approaches in the field of inspection, mapping, and Search and Rescue missions.La cartographie des chantiers miniers souterrains est souvent réalisée à l’aide d’un capteur situé au bout d’une perche que l’opérateur introduit dans le chantier, depuis une zone sécurisée. Le capteur émet des faisceaux laser qui fournissent la distance à un mur détecté, créant ainsi une carte en 3D. Ceci produit des zones d’ombres et une faible densité de points sur les parois éloignées. Pour relever ces défis, une équipe de recherche de l’Université de Sherbrooke conçoit un drone filaire équipé d’un LiDAR rotatif pour cette mission, bénéficiant ainsi de plusieurs points de vue. La transmission filaire permet un temps de vol illimité, un partage de calcul et une communication en temps réel. Pour une compatibilité avec le mouvement du drone lors des coincements du fil, la longueur excédante est intégrée dans une bobine embarquée, qui contribue à la charge utile du drone. Lors d’un pilotage manuel, le facteur humain entraîne des problèmes de perception et compréhension d’un environnement 3D virtuel, et d’exécution d’une mission optimale. Cette thèse se concentre sur la navigation autonome sous deux aspects : la planification de trajectoire et l’exploration. Le système doit calculer une trajectoire qui cartographie l’environnement complet, en minimisant le temps de mission et en respectant la longueur maximale de fil embarquée. La planification de trajectoire à l’aide d’un Rapidly-exploring Random Tree (RRT) trouve rapidement un chemin réalisable, mais l’optimisation est coûteuse en calcul et la performance est variable et imprévisible. L’exploration par la méthode des frontières est représentative de l’espace à explorer et le chemin peut être optimisé en résolvant un Traveling Salesman Problem (TSP), mais les techniques existantes pour un drone filaire ne considèrent que le cas 2D et n’optimisent pas le chemin global. Pour relever ces défis, cette thèse présente deux nouveaux algorithmes. Le premier, RRT-Rope, produit un chemin égal ou plus court que les algorithmes existants en un temps de calcul jusqu’à 70% plus court que le deuxième meilleur algorithme dans un environnement représentatif. Une version modifiée de RRT-connect calcule un chemin réalisable, raccourci avec une technique déterministe qui tire profit des noeuds intermédiaires préalablement ajoutés. Le deuxième algorithme, TAPE, est la première méthode d’exploration de cavités en 3D qui minimise le temps de mission et la longueur du fil déroulé. En moyenne, le trajet global est 4% plus long que la méthode qui résout le TSP, mais le fil reste sous la longueur autorisée dans 100% des cas simulés, contre 53% avec la méthode initiale. L’approche utilise une architecture hiérarchique à 2 niveaux : la planification globale résout un TSP après extraction des frontières, et la planification locale minimise le coût du chemin et la longueur de fil via une fonction de décision. L’intégration de ces deux outils dans le NetherDrone produit un système intelligent pour l’exploration autonome, doté de fonctionnalités semi-autonomes pour une interaction avec l’opérateur. Les travaux réalisés ouvrent la porte à de nouvelles approches de navigation dans le domaine des missions d’inspection, de cartographie et de recherche et sauvetage