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Modelado, detección de colisiones y planificación de movimientos en sistemas robotizados mediante volúmenes esféricosMellado Arteche, Martín 28 October 2015 (has links)
[EN] The efficiency of free-collision motion planning results very sensible on robot and obstacle modelling
technique selected. In this way, many works have been oriented to define models with proper
throughput to speed up the collision detection proccess. This dissertation presents a new approach to
the problem, whose complexity is reduced notably by means of using enveloping models of real
objects, allowing security regions or distances. This objective is reached by means of the definition of
a spherical model, composed of infinite spheres, generated from the application of linear or
polynomial equations to a reduced number of control spheres, giving the so-called poly-spheres and
spheroids respectively. These models, with evident simplicity, present a high modelling power, adapt
easily to the requirements need in collision-detection and path planning applications for robotics
systems.
In order to represent a complete multi-robot cell, an extended hierarchical structure has been defined,
in form of an AND-OR graph, with different degrees of accuracy, according to the different
approximation model used. In order to generate automatically this structure, a procedure has been
developed to compute the minimum volume enveloping spherical model in an off-line process with
two levels based on Downhill Simplex method and Hough transform. This procedure can be greatly
speed up by using clustering techniques to obtain appropiate initial conditions, allowing an on-line
use. With a hierarchical structure computed in such a way, a fast procedure for collision detection in a
multi-robot cell is introduced, based on several algorithms for distance computation including polyspheres
and spheroids. This methodology presents a fast and anticipativa response, in the sense that
every movement of a system has been validated before its execution, implying that not necessarily
must be done in an off-line simulation.
The use of spherical models, in addition to their fast distance computation, results suitable for the
definition of artificial potential fields allowing a path planning in robotics systems with up to six
degrees of freedom, including three for translation and three for rotation. The definition of these new
potential fields and the study of new planning techniques based on classical optimisation methods
allow their application straight forward in Cartesian space, with all their advantages.
Last but not least, with the help of some systems for robot programming, simulation and control, the
correctness of these contributions have been validated in a set of prototype applications, covering
from robot-obstacle and multi-robot collision detection, to motion planning for a robot-arm or an
auto-guided vehicle. / [ES] La eficiencia de la planificación de movimientos libres de colisión resulta muy sensible al modelado
de los robots y obstáculos que se consideren, por lo que, frente al modelado tradicional con politopos,
muchos trabajos en robótica han estado orientados a la definición de unos modelos que presenten
buenas prestaciones de cara a acelerar el proceso de detección de colisiones. En esta Tesis se presenta
una nueva perspectiva del problema, cuya complejidad queda reducida notablemente al utilizar
envolventes de los objetos reales, lo que permite definir zonas o distancias de seguridad. Para ello se
han definido unos modelos esféricos, compuestos de infinitas esferas generadas a partir de la
aplicación de unas relaciones lineales o polinómicas a un número reducido de esferas de control,
dando lugar a las llamadas poli-esferas y esferoides respectivamente. Estos modelos, de sencillez
clara, presentan una potencia de modelado elevada, adaptándose fácilmente a los requisitos necesarios
en las aplicaciones de detección de colisiones y planificación de movimientos en sistemas
robotizados.
Para la representación de una célula multi-robot completa, se ha definido una estructura jerárquica
extendida, en forma de grafo AND-OR, con diferentes grados de precisión, mediante diferentes
modelos de aproximación. De cara a generar automáticamente esta estructura, se ha desarrollado un
procedimiento para generar el modelo esférico envolvente de mínimo volumen en un proceso off-line
con dos niveles, basados en el método de minimización Downhill Simplex y en la transformada de
Hough. Este procedimiento se acelera enormemente al utilizar técnicas de agrupamiento para obtener
condiciones iniciales apropiadas, permitiendo su uso on-line. Con una estructura jerárquica generada
de esta forma, se introduce un procedimiento rápido de detección de colisiones aplicable a una célula
multi-robot, basado en algoritmos básicos de cálculo de distancias que pueden considerar poli-esferas
y esferoides. Esta metodología presenta una respuesta rápida y anticipativa, entendiendo por tal que
todo movimiento de cualquier sistema ha sido validado antes de su ejecución, por lo que no
necesariamente debe realizarse en una simulación off-line.
La utilización de modelos esféricos, así como el rápido cálculo de distancias entre ellos, resulta idónea
para la definición de campos potenciales artificiales que permitan una planificación de movimientos
en sistemas robotizados con hasta seis grados de libertad, incluyendo tres de traslación y tres de
rotación. La definición de estos nuevos campos potenciales y el estudio de nuevas técnicas de
planificación basados en métodos clásicos de optimización permiten su aplicación directamente en el
espacio cartesiano, con las claras ventajas que esto conlleva.
Finalmente, con la ayuda de varios sistemas de programación, simulación y control de robots, se ha
demostrado la validez de estas aportaciones en una serie de aplicaciones prototipo que van desde la
detección de colisiones de un robot con un obstáculo o entre sistemas multi-robot, a la planificación
de movimientos de un brazo-robot o un vehículo autoguiado. / Mellado Arteche, M. (1996). Modelado, detección de colisiones y planificación de movimientos en sistemas robotizados mediante volúmenes esféricos [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/56621
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Aplikace Voronoiových diagramů v plánování dráhy robotu / Application of Voronoi Diagrams in Robot Motion PlanningPich, Václav January 2008 (has links)
This diploma project is focused on possible applications of computational geometry methods for robot motion planning among static and dynamic obstacles, particularly based on global robot motion planning by means of generalised Voronoi diagrams. The main effort was to convert this complex geometric and analytic problem to graph theory environment where the tasks of planning and searching paths between pairs of the graph vertices are effeciently solvable. The Voronoi diagram is created considering the whole searching space, while edges of this diagram satisfy that the distance from the surrounding obstacles is maximised and the path found along the Voronoi diagram edges is optimised from the point of view of its security (and it is collision-free).
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Robust Autonomous Landing of Fixed-Wing UAVs in WindFridén, Tobias January 2020 (has links)
Fixed-wing UAVs are today used in many different areas, from agriculture to search and rescue operations. Through various research efforts, they are becoming more and more autonomous. However, the procedure of landing a fixed-wing UAV remains a challenging task, which requires manual input from an experienced pilot. This work proposes a novel method which autonomously performs such landings. The main focus is on small and light-weight UAVs, for which the wind acts as a major disturbance and has to be taken into account. Robustness to other disturbances, such as variations in environmental factors or measurement errors, has also been prioritized during the development of this method.The main contribution of this work consists of a framework in which der\-iva\-tive-free optimization is used to calculate a set of waypoints, which are feasible to use in different wind speeds and directions, for a selected UAV model. These waypoints are then combined online using motion planning techniques, to create a trajectory which safely brings the UAV to a position where the landing descent can be initiated. To ensure a safe descent in a predefined area, another nonlinear optimization problem is formulated and solved. Finally, the proposed method is implemented on a real UAV platform. A number of simulations in different wind conditions are performed, and data from a real flight experiment is presented. The results indicate that the method successfully calculates feasible landing sequences in different scenarios, and that it is applicable in a real-world landing.
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Mission and Motion Planning for Multi-robot Systems in Constrained EnvironmentsJanuary 2019 (has links)
abstract: As robots become mechanically more capable, they are going to be more and more integrated into our daily lives. Over time, human’s expectation of what the robot capabilities are is getting higher. Therefore, it can be conjectured that often robots will not act as human commanders intended them to do. That is, the users of the robots may have a different point of view from the one the robots do.
The first part of this dissertation covers methods that resolve some instances of this mismatch when the mission requirements are expressed in Linear Temporal Logic (LTL) for handling coverage, sequencing, conditions and avoidance. That is, the following general questions are addressed:
* What cause of the given mission is unrealizable?
* Is there any other feasible mission that is close to the given one?
In order to answer these questions, the LTL Revision Problem is applied and it is formulated as a graph search problem. It is shown that in general the problem is NP-Complete. Hence, it is proved that the heuristic algorihtm has 2-approximation bound in some cases. This problem, then, is extended to two different versions: one is for the weighted transition system and another is for the specification under quantitative preference. Next, a follow up question is addressed:
* How can an LTL specified mission be scaled up to multiple robots operating in confined environments?
The Cooperative Multi-agent Planning Problem is addressed by borrowing a technique from cooperative pathfinding problems in discrete grid environments. Since centralized planning for multi-robot systems is computationally challenging and easily results in state space explosion, a distributed planning approach is provided through agent coupling and de-coupling.
In addition, in order to make such robot missions work in the real world, robots should take actions in the continuous physical world. Hence, in the second part of this thesis, the resulting motion planning problems is addressed for non-holonomic robots.
That is, it is devoted to autonomous vehicles’ motion planning in challenging environments such as rural, semi-structured roads. This planning problem is solved with an on-the-fly hierarchical approach, using a pre-computed lattice planner. It is also proved that the proposed algorithm guarantees resolution-completeness in such demanding environments. Finally, possible extensions are discussed. / Dissertation/Thesis / Doctoral Dissertation Computer Science 2019
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Methods in intelligent transportation systems exploiting vehicle connectivity, autonomy and roadway dataZhang, Yue 29 September 2019 (has links)
Intelligent transportation systems involve a variety of information and control systems methodologies, from cooperative systems which aim at traffic flow optimization by means of vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communication, to information fusion from multiple traffic sensing modalities. This thesis aims to address three problems in intelligent transportation systems, one in optimal control of connected automated vehicles, one in discrete-event and hybrid traffic simulation model, and one in sensing and classifying roadway obstacles in smart cities.
The first set of problems addressed relates to optimally controlling connected automated vehicles (CAVs) crossing an urban intersection without any explicit traffic signaling. A decentralized optimal control framework is established whereby, under proper coordination among CAVs, each CAV can jointly minimize its energy consumption and travel time subject to hard safety constraints. A closed-form analytical solution is derived while taking speed, control, and safety constraints into consideration. The analytical solution of each such problem, when it exists, yields the optimal CAV acceleration/deceleration. The framework is capable of accommodating for turns and ensures the absence of collisions. In the meantime, a measurement of passenger comfort is taken into account while the vehicles make turns. In addition to the first-in-first-out (FIFO) ordering structure, the concept of dynamic resequencing is introduced which aims at further increasing the traffic throughput. This thesis also studies the impact of CAVs and shows the benefit that can be achieved by incorporating CAVs to conventional traffic.
To validate the effectiveness of the proposed solution, a discrete-event and hybrid simulation framework based on SimEvents is proposed, which facilitates safety and performance evaluation of an intelligent transportation system. The traffic simulation model enables traffic study at the microscopic level, including new control algorithms for CAVs under different traffic scenarios, the event-driven aspects of transportation systems, and the effects of communication delays. The framework spans multiple toolboxes including MATLAB, Simulink, and SimEvents.
In another direction, an unsupervised anomaly detection system is developed based on data collected through the Street Bump smartphone application. The system, which is built based on signal processing techniques and the concept of information entropy, is capable of generating a prioritized list of roadway obstacles, such that the higher-ranked entries are most likely to be actionable bumps (e.g., potholes) requiring immediate attention, while those lower-ranked are most likely to be nonactionable bumps(e.g., flat castings, cobblestone streets, speed bumps) for which no immediate action is needed. This system enables the City to efficiently prioritize repairs. Results on an actual data set provided by the City of Boston illustrate the feasibility and effectiveness of the system in practice.
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Méthodes inspirées de la robotique pour la simulation des changements conformationnels des protéines / Robotics-Inspired Methods for the Simulation of Conformational Changes in ProteinsAl Bluwi, Ibrahim 25 September 2012 (has links)
Cette thèse présente une approche de modélisation inspirée par la robotique pour l'étude des changements conformationnels des protéines. Cette approche est basée sur une représentation mécanistique des protéines permettant l'application de méthodes efficaces provenant du domaine de la robotique. Elle fournit également une méthode appropriée pour le traitement « gros-grains » des protéines sans perte de détail au niveau atomique. L'approche présentée dans cette thèse est appliquée à deux types de problèmes de simulation moléculaire. Dans le premier, cette approche est utilisée pour améliorer l'échantillonnage de l'espace conformationnel des protéines. Plus précisément, cette approche de modélisation est utilisée pour implémenter des classes de mouvements pour l'échantillonnage, aussi bien connues que nouvelles, ainsi qu'une stratégie d'échantillonnage mixte, dans le contexte de la méthode de Monte Carlo. Les résultats des simulations effectuées sur des protéines ayant des topologies différentes montrent que cette stratégie améliore l'échantillonnage, sans toutefois nécessiter de ressources de calcul supplémentaires. Dans le deuxième type de problèmes abordés ici, l'approche de modélisation mécanistique est utilisée pour implémenter une méthode inspirée par la robotique et appliquée à la simulation de mouvements de grande amplitude dans les protéines. Cette méthode est basée sur la combinaison de l'algorithme RRT (Rapidly-exploring Random Tree) avec l'analyse en modes normaux, qui permet une exploration efficace des espaces de dimension élevée tels les espaces conformationnels des protéines. Les résultats de simulations effectuées sur un ensemble de protéines montrent l'efficacité de la méthode proposée pour l'étude des transitions conformationnelles / Proteins are biological macromolecules that play essential roles in living organisms. Un- derstanding the relationship between protein structure, dynamics and function is indis- pensable for advances in fields such as biology, pharmacology and biotechnology. Study- ing this relationship requires a combination of experimental and computational methods, whose development is the object of very active interdisciplinary research. In such a context, this thesis presents a robotics-inspired modeling approach for studying confor- mational changes in proteins. This approach is based on a mechanistic representation of proteins that enables the application of efficient methods originating from the field of robotics. It also provides an accurate method for coarse-grained treatment of proteins without loosing full-atom details.The presented approach is applied in this thesis to two different molecular simulation problems. First, the approach is used to enhance sampling of the conformational space of proteins using the Monte Carlo method. The modeling approach is used to implement new and known Monte Carlo trial move classes as well as a mixed sampling strategy. Results of simulations performed on proteins with different topologies show that this strategy enhances sampling without demanding higher computational resources. In the second problem tackled in this thesis, the mechanistic modeling approach is used to implement a robotics-inspired method for simulating large amplitude motions in proteins. This method is based on the combination of the Rapidly-exploring Random Tree (RRT) algorithm with Normal Mode Analysis (NMA), which allows efficient exploration of the high dimensional conformational spaces of proteins. Results of simulations performed on ten different proteins of different sizes and topologies show the effectiveness of the proposed method for studying conformational transitions
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Planification de mouvement pour la manipulation d'objets sous contraintes d'interaction homme-robot / Motion planning for object manipulation under human-robot interaction constraintsMainprice, Jim 17 December 2012 (has links)
Un robot agit sur son environnement par le mouvement, sa capacité à planifier ses mouvements est donc une composante essentielle de son autonomie. L'objectif de cette thèse est concevoir des méthodes algorithmiques performantes permettant le calcul automatique de trajectoires pour des systèmes robotiques complexes dans le cadre de la robotique d'assistance. Les systèmes considérés qui ont pour vocation de servir l'homme et de l'accompagner dans des tâches du quotidien doivent tenir compte de la sécurité et du bien-être de l'homme. Pour cela, les mouvements du robot doivent être générés en considérant explicitement le partenaire humain raisonant sur un modèle du comportement social de l'homme, de ses capacités et de ses limites afin de produire un comportement synergique optimal.Dans cette thèse nous étendons les travaux pionniers menés au LAAS dans ce domaine afin de produire des mouvements considérant l’homme de manière explicite dans des environnements encombrés. Des algorithmes d’exploration de l’espace des configurations par échantillonnage aléatoire sont combinés à des algorithmes d’optimisation de trajectoire afin de produire des mouvements sûrs et agréables. Nous proposons dans un deuxième temps un planificateur de tâche d’échange d’objet prenant en compte la mobilité du receveur humain permettant ainsi de partager l’effort lors du transfert. La pertinence de cette approche a été étudiée dans une étude utilisateur. Finalement, nous présentons une architecture logicielle qui permet de prendre en compte l’homme de manière dynamique lors de la réalisation de tâches de manipulation interactive / A robot act upon its environment through motion, the ability to plan its movements is therefore an essential component of its autonomy. The objective of this thesis is to design algorithmic methods to perform automatic trajectory computation for complex robotic systems in the context of assistive robotics. This emerging field of autonomous robotics applications brings new constraints and new challenges. Such systems that are designed to serve humans and to help in daily tasks must consider the safety and well-being of the surrounding humans. To do this, the robot's motions must be generated by considering the human partner explicitly. For comfort and efficiency, the robot must take into account a model of human social behavior, capabilities and limitations to produce an optimal synergistic behavior.In this thesis we extend to cluttered environments the pioneering work that has been conducted at LAAS in this field. Algorithms that explore the configuration space by random sampling are combined with trajectory optimization algorithms to produce safe and human aware motions. Secondly we propose a planner for object handover taking into account the mobility of the human recipient allowing to share the effort during the transfer. The relevance of this approach has been studied in a user study. Finally, we present a software architecture developed in collaboration with a partner of the European project Dexmart that allows to take dynamically into account humans during the execution of interactive manipulation tasks
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Planification de mouvement pour tiges élastiques / Motion planning for elastic rodsRoussel, Olivier 05 October 2015 (has links)
Le problème de la planification du mouvement a été largement étudié dans le cas de corps rigides articulés mais peu de travaux considèrent les corps déformables. En particulier, les tiges élastiques telles que cables électriques, flexibles hydrauliques et pneumatiques, apparaissent dans de nombreux contextes industriels. Du fait d'une modélisation complexe et d'un grand nombre de degrés de liberté, l'extension des méthodes de planification de mouvement à de tels corps est un problème particulièrement difficile. En se basant sur les propriétés des configurations à l'équilibre statique, cette thèse propose plusieurs approches au problème de planification de mouvement pour des tiges élastiques. / The motion planning problem has been broadly studied in the case of articulated rigid body systems but so far few work have considered deformable bodies. In particular, elastic rods such as electric cables, hydraulic or pneumatic hoses, appear in many industrial contexts. Due to complex models and high number of degrees of freedom, the extension of motion planning methods to such bodies is a difficult problem. By taking advantage of the properties of static equilibrium configurations, this thesis presents several approaches to the motion planning problem for elastic rods.
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Kinodynamic motion planning for quadrotor-like aerial robots / Planification kinodynamique de mouvements pour des systèmes aériens de type quadrirotorBoeuf, Alexandre 05 July 2017 (has links)
La planification de mouvement est le domaine de l’informatique qui a trait au développement de techniques algorithmiques permettant la génération automatique de trajectoires pour un système mécanique. La nature d’un tel système varie selon les champs d’application. En animation par ordinateur il peut s’agir d’un avatar humanoïde. En biologie moléculaire cela peut être une protéine. Le domaine d’application de ces travaux étant la robotique aérienne, le système est ici un UAV (Unmanned Aerial Vehicle: véhicule aérien sans pilote) à quatre hélices appelé quadrirotor. Le problème de planification de mouvements consiste à calculer une série de mouvements qui amène le système d’une configuration initiale donnée à une configuration finale souhaitée sans générer de collisions avec son environnement, la plupart du temps connu à l’avance. Les méthodes habituelles explorent l’espace des configurations du système sans tenir compte de sa dynamique. Cependant, la force de poussée qui permet à un quadrirotor de voler est par construction parallèle aux axes de rotation des hélices, ce qui implique que certains mouvements ne peuvent pas être effectués. De plus, l’intensité de cette force de poussée, et donc l’accélération linéaire du centre de masse, sont limitées par les capacités physiques du robot. Pour toutes ces raisons, non seulement la position et l’orientation doivent être planifiées, mais les dérivées plus élevées doivent l’être également si l’on veut que le système physique soit en mesure de réellement exécuter le mouvement. Lorsque c’est le cas, on parle de planification kinodynamique de mouvements. Une distinction est faite entre le planificateur local et le planificateur global. Le premier est chargé de produire une trajectoire valide entre deux états du système sans nécessairement tenir compte des collisions. Le second est l’algorithme principal qui est chargé de résoudre le problème de planification de mouvement en explorant l’espace d’état du système. Il fait appel au planificateur local. Nous présentons un planificateur local qui interpole deux états comprenant un nombre arbitraire de degrés de liberté ainsi que leurs dérivées premières et secondes. Compte tenu d’un ensemble de limites sur les dérivées des degrés de liberté jusqu’au quatrième ordre (snap), il produit rapidement une trajectoire en temps minimal quasi optimale qui respecte ces limites. Dans la plupart des algorithmes modernes de planification de mouvements, l’exploration est guidée par une fonction de distance (ou métrique). Le meilleur choix pour celle-ci est le cost-to-go, c.a.d. le coût associé à la méthode locale. Dans le contexte de la planification kinodynamique de mouvements, il correspond à la durée de la trajectoire en temps minimal. Le problème dans ce cas est que calculer le cost-to-go est aussi difficile (et donc aussi coûteux) que de calculer la trajectoire optimale elle-même. Nous présentons une métrique qui est une bonne approximation du cost-to-go, mais dont le calcul est beaucoup moins coûteux. Le paradigme dominant en planification de mouvements aujourd’hui est l’échantillonnage aléatoire. Cette classe d’algorithmes repose sur un échantillonnage aléatoire de l’espace d’état afin de l’explorer rapidement. Une stratégie commune est l’échantillonnage uniforme. Il semble toutefois que, dans notre contexte, ce soit un choix assez médiocre. En effet, une grande majorité des états uniformément échantillonnés ne peuvent pas être interpolés. Nous présentons une stratégie d’échantillonnage incrémentale qui diminue considérablement la probabilité que cela ne se produise. / Motion planning is the field of computer science that aims at developing algorithmic techniques allowing the automatic computation of trajecto- ries for a mechanical system. The nature of such a system vary according to the fields of application. In computer animation it could be a humanoid avatar. In molecular biology it could be a protein. The field of application of this work being aerial robotics, the system is here a four-rotor UAV (Unmanned Aerial Vehicle) called quadrotor. The motion planning problem consists in computing a series of motions that brings the system from a given initial configuration to a desired final configuration without generating collisions with its environment, most of the time known in advance. Usual methods explore the system’s configuration space regardless of its dynamics. By construction the thrust force that allows a quadrotor to fly is tangential to its attitude which implies that not every motion can be performed. Furthermore, the magnitude of this thrust force and hence the linear acceleration of the center of mass are limited by the physical capabilities of the robot. For all these reasons, not only position and orientation must be planned, higher derivatives must be planned also if the motion is to be executed. When this is the case we talk of kinodynamic motion planning. A distinction is made between the local planner and the global planner. The former is in charge of producing a valid trajectory between two states of the system without necessarily taking collisions into account. The later is the overall algorithmic process that is in charge of solving the motion planning problem by exploring the state space of the system. It relies on multiple calls to the local planner. We present a local planner that interpolates two states consisting of an arbitrary number of degrees of freedom (dof) and their first and second derivatives. Given a set of bounds on the dof derivatives up to the fourth order (snap), it quickly produces a near-optimal minimum time trajectory that respects those bounds. In most of modern global motion planning algorithms, the exploration is guided by a distance function (or metric). The best choice is the cost-to-go, i.e. the cost associated to the local method. In the context of kinodynamic motion planning, it is the duration of the minimal-time trajectory. The problem in this case is that computing the cost-to-go is as hard (and thus as costly) as computing the optimal trajectory itself. We present a metric that is a good approximation of the cost-to-go but which computation is far less time consuming. The dominant paradigm nowadays is sampling-based motion planning. This class of algorithms relies on random sampling of the state space in order to quickly explore it. A common strategy is uniform sampling. It however appears that, in our context, it is a rather poor choice. Indeed, a great majority of uniformly sampled states cannot be interpolated. We present an incremental sampling strategy that significantly decreases the probability of this happening.
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Sampling-based Path Planning for an Autonomous HelicopterPettersson, Per Olof January 2006 (has links)
Many of the applications that have been proposed for future small unmanned aerial vehicles (UAVs) are at low altitude in areas with many obstacles. A vital component for successful navigation in such environments is a path planner that can find collision free paths for the UAV. Two popular path planning algorithms are the probabilistic roadmap algorithm (PRM) and the rapidly-exploring random tree algorithm (RRT). Adaptations of these algorithms to an unmanned autonomous helicopter are presented in this thesis, together with a number of extensions for handling constraints at different stages of the planning process. The result of this work is twofold: First, the described planners and extensions have been implemented and integrated into the software architecture of a UAV. A number of flight tests with these algorithms have been performed on a physical helicopter and the results from some of them are presented in this thesis. Second, an empirical study has been conducted, comparing the performance of the different algorithms and extensions in this planning domain. It is shown that with the environment known in advance, the PRM algorithm generally performs better than the RRT algorithm due to its precompiled roadmaps, but that the latter is also usable as long as the environment is not too complex. The study also shows that simple geometric constraints can be added in the runtime phase of the PRM algorithm, without a big impact on performance. It is also shown that postponing the motion constraints to the runtime phase can improve the performance of the planner in some cases. / <p>Report code: LiU–Tek–Lic–2006:10.</p>
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