Robôs manipuladores vem desempenhando um importante papel em operações orbitais, e isso foi possível devido ao grande avanço da robótica espacial nas últimas décadas. Porém, o planejamento do movimento ainda é considerado um dos maiores desafios nesse campo, embora diversos métodos e considerações tenham sido propostas para resolver esse problema. As primeiras contribuições na área de planejamento de movimento dependiam de uma representação explícita do espaço de configuração do robô. Dessa forma, o planejamento de movimento para sistemas robóticos com muitos graus de liberdade era impraticável. Para lidar com esse problema, surgiram os métodos baseados em amostragem, dentre eles, o método de Árvore Aleatória de Exploração Rápida - RRT (do inglês, Rapidly- Exploring Random Tree). Estes métodos, ao invés da construção de todo o conjunto de configurações livre de colisões, requerem apenas a verificação de colisão com obstáculos para um conjunto discreto e finito de configurações do robô. Consequentemente, para este tipo de problema, são métodos mais vantajosos em termos computacionais. Com esta motivação, o presente trabalho tem como objetivo o desenvolvimento de um planejador de rota e de um planejador de trajetória para um robô manipulador espacial de base livre flutuante com dois braços, ambos planejadores com suporte a desvio de obstáculos estáticos. O conceito de manipulador dinamicamente equivalente é utilizado para modelar o manipulador espacial. Isso permite que o planejamento seja feito para um manipulador de base fixa subatuado dinamicamente equivalente ao manipulador de base livre flutuante. Os algoritmos baseados em amostragem RRT* e RRTControl disponibilizados na biblioteca OMPL (do inglês, Open Motion Planning Library) foram adaptados para resolver este problema de planejamento. O algoritmo RRT* é usado para o planejamento de rota, e o RRTControl para o planejamento de trajetória. Ambos planejadores utilizam o espaço de configuração das juntas do robô. Para possibilitar que a orientação e posição final dos dois efetuadores do robô pudessem ser especificadas no espaço da tarefa, um algoritmo de cinemática inversa baseado em algoritmo genético também foi desenvolvido para encontrar a solução da cinemática inversa do manipulador. / Robot manipulator has played an important role in orbital missions and this was possible due to the advance of space robotics in recent decades. However, motion planning is still considered one of the biggest challenges of the field though various methods and considerations were proposed by researchers to handle this problem. The first contributions in this field were dependent on an explicit representation of the free configuration space. Consequently, it was impractical to solve the motion planning problem for robotic systems with many degrees of freedom. In order to cope with this limitation, sampling-based methods were proposed, in particular, the Rapidly-Exploring Random Tree – RRT. Sampling-based methods only requires a procedure to verify collision with obstacles for a discrete amount of robot configuration during planning. Therefore, they are more advantageous in computational terms. In this work a path planner and a trajectory planner were developed for a free-floating planar manipulator with two arms with support for static obstacle avoidance. The Dynamically Equivalent Manipulator approach was used for modelling the robot. Thus, the planners were developed based on a fixed-base underactuated manipulator model which is dynamically equivalent to the free-floating manipulator. The sampling-based algorithms RRT* and RRTControl of the Open Motion Planning Library (OMPL) were adapted to solve this motion planning problem. The RRT* were used for path planning, and the RRTControl for trajectory planning, both carried out in the robot joint space. As the desired orientations and positions of the two end-effectors were specified in the task-space, a genetic algorithm was also developed to compute the inverse kinematics of the manipulator.

Como tópico de fundamental importância na robótica, o planejamento de rotas tem encontrado excelentes resultados nos últimos anos através da utilização de algoritmos baseados no conceito de árvore de exploração rápida, RRT. No entanto, a aplicação desses métodos em sistemas robóticos espaciais revela um cenário ainda a ser explorado. O comportamento não-holonômico e a presença de singularidades dinâmicas são alguns fatores que dificultam a consideração de obstáculos no planejamento de rotas desses sistemas. Além disso, os trabalhos relacionados ao planejamento de movimento para manipuladores espaciais mostram-se concentrados na estratégia ponto-a-ponto, com interesse especial nos aspectos particulares da dinâmica desses sistemas. De modo geral, para manipuladores espaciais, o planejamento de trajetória envolvendo o desvio de obstáculos depende de uma rota previamente computada. Contudo, essa tarefa carece de formulações ou técnicas solidificadas, sobretudo para manipuladores espaciais de base livre flutuante. Com esta motivação, o trabalho proposto nesta dissertação de mestrado cria um planejador de rotas com suporte a desvio de obstáculos para um manipulador espacial planar de base livre flutuante. O modelo dinâmico utilizado é baseado no conceito de manipulador dinamicamente equivalente e incorporado a um algoritmo baseado no conceito de RRT. / As major challenge in the field of robotics, path planning has experienced successful results in recent years by means of the RRT algorithm. However, the application of such algorithms in space manipulators reveals a scenario yet to be explored. The non-holonomic behavior, added to the presence of dynamic singularities are only a few factors that make collision-avoidance path planning of these systems such a hard task. Besides, works in the field of motion planning of space manipulators often concentrate in the strategy pointto- point, with particular interest in the complex dynamics of such systems. As a rule of thumb, collision-avoidance for space manipulators depends on a previous computed path. However, this task still lacks robust formulations, specially in the case of free-floating manipulators. With this motivation, the proposed work creates a collision-avoiding path planning for a free-floating planar manipulator. The dynamic model is based on the Dynamically Equivalent Manipulator and the concept of Rapidly-Exploring Random Trees serves as a frame for the developed algorithm.

A aplicação de técnicas baseadas em amostragem em algoritmos que envolvem o planejamento de trajetórias de robôs tem se tornado cada vez mais difundida. Deste grupo, um dos algoritmos mais utilizados é chamado Rapidly-exploring Random Tree (RRT), que se baseia na amostragem incremental para calcular de forma eficiente os planos de trajetória do robô evitando colisões com obstáculos. Vários esforços tem sido realizados a fim de reduzir o custo computacional do algoritmo RRT, visando aplicações que necessitem de respostas mais rápidas do algoritmo, como, por exemplo, em ambientes dinâmicos. Um dos dilemas relacionados ao RRT está na etapa de geração de primitivas de movimento. Se várias primitivas são geradas, permitindo o robô executar vários movimentos básicos diferentes, um grande custo computacional é gasto. Por outro lado, quando poucas primitivas são geradas e, consequentemente, poucos movimentos básicos são permitidos, o robô pode não ser capaz de encontrar uma solução para o problema, mesmo que esta exista. Motivados por este problema, um método de geração de primitivas de movimento foi proposto. Tal método é comparado com os métodos tradicional e aleatório de geração de primitivas, considerando não apenas o custo computacional de cada um, mas também a qualidade da solução obtida. O método proposto é aplicado ao algoritmo RRT, que depois é aplicado em um caso de estudo em um ambiente dinâmico. No estudo de caso, o algoritmo RRT otimizado é avaliado em termos de seus custos computacionais durante planejamentos e replanejamento de trajetória. As simulações são realizadas em dois simuladores: um desenvolvido em linguagem Python e outro em Matlab. / The application of sample-based techniques in path-planning algorithms has become year-by-year more widespread. In this group, one of the most widely used algorithms is the Rapidly-exploring Random Tree (RRT), which is based on an incremental sampling of configurations to efficiently compute the robot\'s path while avoiding obstacles. Many efforts have been made to reduce RRT computational costs, targeting, in particular, applications in which quick responses are required, e.g., in dynamic environments. One of the dilemmas posed by the RRT arises from its motion primitives generation. If many primitives are generated to enable the robot to perform a broad range of basic movements, a signicant computational cost is required. On the other hand, when only a few primitives are generated, thus, enabling a limited number of basic movements, the robot may be unable to find a solution to the problem, even if one exists. To address this quandary, an optimized method for primitive generation is proposed. This method is compared with the traditional and random primitive generation methods, considering not only computational cost, but also the quality of local and global solutions that may be attained. The optimized method is applied to the RRT algorithm, which is then used in a case study in dynamic environments. In the study, the modied RRT is evaluated in terms of the computational costs of its planning and replanning. The simulations were developed to access the effectiveness and efficiency of the proposed algorithm.

A aplicação de técnicas baseadas em amostragem em algoritmos que envolvem o planejamento de trajetórias de robôs tem se tornado cada vez mais difundida. Deste grupo, um dos algoritmos mais utilizados é chamado Rapidly-exploring Random Tree (RRT), que se baseia na amostragem incremental para calcular de forma eficiente os planos de trajetória do robô evitando colisões com obstáculos. Vários esforços tem sido realizados a fim de reduzir o custo computacional do algoritmo RRT, visando aplicações que necessitem de respostas mais rápidas do algoritmo, como, por exemplo, em ambientes dinâmicos. Um dos dilemas relacionados ao RRT está na etapa de geração de primitivas de movimento. Se várias primitivas são geradas, permitindo o robô executar vários movimentos básicos diferentes, um grande custo computacional é gasto. Por outro lado, quando poucas primitivas são geradas e, consequentemente, poucos movimentos básicos são permitidos, o robô pode não ser capaz de encontrar uma solução para o problema, mesmo que esta exista. Motivados por este problema, um método de geração de primitivas de movimento foi proposto. Tal método é comparado com os métodos tradicional e aleatório de geração de primitivas, considerando não apenas o custo computacional de cada um, mas também a qualidade da solução obtida. O método proposto é aplicado ao algoritmo RRT, que depois é aplicado em um caso de estudo em um ambiente dinâmico. No estudo de caso, o algoritmo RRT otimizado é avaliado em termos de seus custos computacionais durante planejamentos e replanejamento de trajetória. As simulações são realizadas em dois simuladores: um desenvolvido em linguagem Python e outro em Matlab. / The application of sample-based techniques in path-planning algorithms has become year-by-year more widespread. In this group, one of the most widely used algorithms is the Rapidly-exploring Random Tree (RRT), which is based on an incremental sampling of configurations to efficiently compute the robot\'s path while avoiding obstacles. Many efforts have been made to reduce RRT computational costs, targeting, in particular, applications in which quick responses are required, e.g., in dynamic environments. One of the dilemmas posed by the RRT arises from its motion primitives generation. If many primitives are generated to enable the robot to perform a broad range of basic movements, a signicant computational cost is required. On the other hand, when only a few primitives are generated, thus, enabling a limited number of basic movements, the robot may be unable to find a solution to the problem, even if one exists. To address this quandary, an optimized method for primitive generation is proposed. This method is compared with the traditional and random primitive generation methods, considering not only computational cost, but also the quality of local and global solutions that may be attained. The optimized method is applied to the RRT algorithm, which is then used in a case study in dynamic environments. In the study, the modied RRT is evaluated in terms of the computational costs of its planning and replanning. The simulations were developed to access the effectiveness and efficiency of the proposed algorithm.

Como tópico de fundamental importância na robótica, o planejamento de rotas tem encontrado excelentes resultados nos últimos anos através da utilização de algoritmos baseados no conceito de árvore de exploração rápida, RRT. No entanto, a aplicação desses métodos em sistemas robóticos espaciais revela um cenário ainda a ser explorado. O comportamento não-holonômico e a presença de singularidades dinâmicas são alguns fatores que dificultam a consideração de obstáculos no planejamento de rotas desses sistemas. Além disso, os trabalhos relacionados ao planejamento de movimento para manipuladores espaciais mostram-se concentrados na estratégia ponto-a-ponto, com interesse especial nos aspectos particulares da dinâmica desses sistemas. De modo geral, para manipuladores espaciais, o planejamento de trajetória envolvendo o desvio de obstáculos depende de uma rota previamente computada. Contudo, essa tarefa carece de formulações ou técnicas solidificadas, sobretudo para manipuladores espaciais de base livre flutuante. Com esta motivação, o trabalho proposto nesta dissertação de mestrado cria um planejador de rotas com suporte a desvio de obstáculos para um manipulador espacial planar de base livre flutuante. O modelo dinâmico utilizado é baseado no conceito de manipulador dinamicamente equivalente e incorporado a um algoritmo baseado no conceito de RRT. / As major challenge in the field of robotics, path planning has experienced successful results in recent years by means of the RRT algorithm. However, the application of such algorithms in space manipulators reveals a scenario yet to be explored. The non-holonomic behavior, added to the presence of dynamic singularities are only a few factors that make collision-avoidance path planning of these systems such a hard task. Besides, works in the field of motion planning of space manipulators often concentrate in the strategy pointto- point, with particular interest in the complex dynamics of such systems. As a rule of thumb, collision-avoidance for space manipulators depends on a previous computed path. However, this task still lacks robust formulations, specially in the case of free-floating manipulators. With this motivation, the proposed work creates a collision-avoiding path planning for a free-floating planar manipulator. The dynamic model is based on the Dynamically Equivalent Manipulator and the concept of Rapidly-Exploring Random Trees serves as a frame for the developed algorithm.

Motion planning problems are characterized by huge search spaces and complex obstacle structures with no concise mathematical expression. The fixed-wing airplane application considered in this thesis adds differential constraints and point-wise bounds, i. e. an infinite number of equality and inequality constraints. An optimal trajectory planning approach is presented, based on the randomized Rapidly-exploring Random Trees framework (RRT*). The local planner relies on differential flatness of the equations of motion to obtain tree branch candidates that automatically satisfy the differential constraints. Flat output trajectories, in this case equivalent to the airplane's flight path, are designed using Bézier curves. Segment feasibility in terms of point-wise inequality constraints is tested by an indicator integral, which is evaluated alongside the segment cost functional. Although the RRT* guarantees optimality in the limit of infinite planning time, it is argued by intuition and experimentation that convergence is not approached at a practically useful rate. Therefore, the randomized planner is augmented by a deterministic variational optimization technique. To this end, the optimal planning task is formulated as a semi-infinite optimization problem, using the intermediate result of the RRT(*) as an initial guess. The proposed optimization algorithm follows the feasible flavor of the primal-dual interior point paradigm. Discretization of functional (infinite) constraints is deferred to the linear subproblems, where it is realized implicitly by numeric quadrature. An inherent numerical ill-conditioning of the method is circumvented by a reduction-like approach, which tracks active constraint locations by introducing new problem variables. Obstacle avoidance is achieved by extending the line search procedure and dynamically adding obstacle-awareness constraints to the problem formulation. Experimental evaluation confirms that the hybrid approach is practically feasible and does indeed outperform RRT*'s built-in optimization mechanism, but the computational burden is still significant. / Bewegungsplanungsaufgaben sind typischerweise gekennzeichnet durch umfangreiche Suchräume, deren vollständige Exploration nicht praktikabel ist, sowie durch unstrukturierte Hindernisse, für die nur selten eine geschlossene mathematische Beschreibung existiert. Bei der in dieser Arbeit betrachteten Anwendung auf Flächenflugzeuge kommen differentielle Randbedingungen und beschränkte Systemgrößen erschwerend hinzu. Der vorgestellte Ansatz zur optimalen Trajektorienplanung basiert auf dem Rapidly-exploring Random Trees-Algorithmus (RRT*), welcher die Suchraumkomplexität durch Randomisierung beherrschbar macht. Der spezifische Beitrag ist eine Realisierung des lokalen Planers zur Generierung der Äste des Suchbaums. Dieser erfordert ein flaches Bewegungsmodell, sodass differentielle Randbedingungen automatisch erfüllt sind. Die Trajektorien des flachen Ausgangs, welche im betrachteten Beispiel der Flugbahn entsprechen, werden mittels Bézier-Kurven entworfen. Die Einhaltung der Ungleichungsnebenbedingungen wird durch ein Indikator-Integral überprüft, welches sich mit wenig Zusatzaufwand parallel zum Kostenfunktional berechnen lässt. Zwar konvergiert der RRT*-Algorithmus (im probabilistischen Sinne) zu einer optimalen Lösung, jedoch ist die Konvergenzrate aus praktischer Sicht unbrauchbar langsam. Es ist daher naheliegend, den Planer durch ein gradientenbasiertes lokales Optimierungsverfahren mit besseren Konvergenzeigenschaften zu unterstützen. Hierzu wird die aktuelle Zwischenlösung des Planers als Initialschätzung für ein kompatibles semi-infinites Optimierungsproblem verwendet. Der vorgeschlagene Optimierungsalgorithmus erweitert das verbreitete innere-Punkte-Konzept (primal dual interior point method) auf semi-infinite Probleme. Eine explizite Diskretisierung der funktionalen Ungleichungsnebenbedingungen ist nicht erforderlich, denn diese erfolgt implizit durch eine numerische Integralauswertung im Rahmen der linearen Teilprobleme. Da die Methode an Stellen aktiver Nebenbedingungen nicht wohldefiniert ist, kommt zusätzlich eine Variante des Reduktions-Ansatzes zum Einsatz, bei welcher der Vektor der Optimierungsvariablen um die (endliche) Menge der aktiven Indizes erweitert wird. Weiterhin wurde eine Kollisionsvermeidung integriert, die in den Teilschritt der Liniensuche eingreift und die Problemformulierung dynamisch um Randbedingungen zur lokalen Berücksichtigung von Hindernissen erweitert. Experimentelle Untersuchungen bestätigen, dass die Ergebnisse des hybriden Ansatzes aus RRT(*) und numerischem Optimierungsverfahren der klassischen RRT*-basierten Trajektorienoptimierung überlegen sind. Der erforderliche Rechenaufwand ist zwar beträchtlich, aber unter realistischen Bedingungen praktisch beherrschbar.

In this thesis, we consider the motion planning problem for an autonomous vehicle in an obstacle-cluttered environment approximated by zonotopes, and we propose an input sampling algorithm leveraging discrete-time control barrier function conditions (DCBF). Specifically, an optimization-based control barrier function that takes into account the geometric shapes of the vehicle and obstacles is constructed and verified. We then propose a discrete-time CBF that guarantees the safety during the inter-sampling intervals. It is worth noting that we do not need an explicit expression of the barrier function, but instead, an numerically efficient algorithm is proposed to evaluate and implement the CBF/DCBF conditions. Finally, an RRT algorithm is incorporated that draws the input sampling from the input space restricted to DCBF condition. Thanks to our proposed DCBF and input sampling method approach, our proposed method is less conservative, computationally efficient and guarantees the safety during the sampling intervals. Numerical simulation with unicycle model has been done to demonstrate the favorable properties of the algorithm. / I det här dokumentet tar vi upp problemet med rörelseplanering för ett autonomt fordon i en hinderfylld miljö som approximeras av zonotoper och föreslår en algoritm för insatsprovtagning som utnyttjar diskreta villkor för kontrollbarriärfunktioner (DCBF). Vi konstruerar och verifierar en optimeringsbaserad kontrollbarriärfunktion som tar hänsyn till fordonets och hindrens geometriska former. Vi föreslår sedan en diskret CBF i diskret tid som garanterar säkerheten under intervallerna mellan provtagningarna. Det är värt att notera att vi inte behöver ett explicit uttryck för barriärfunktionen, utan istället föreslås en numeriskt effektiv algoritm för att utvärdera och genomföra CBF/DCBF-villkoren. Slutligen införlivas en RRT-algoritm som drar inmatningsprovtagningen från inmatningsutrymmet som är begränsat till DCBF-villkoret. Tack vare vår föreslagna metod för DCBF och insatsprovtagning är vår föreslagna metod mindre konservativ, beräkningsmässigt effektiv och garanterar säkerheten under provtagningsintervallerna. Numerisk simulering med encykelmodell har gjorts för att verifiera algoritmen.

The Unmanned Aerial Vehicle (UAV) has over the last years become an increasingly prevalent technology in several sectors of modern society. Many UAVs are today used in a wide series of applications, from disaster relief to surveillance. A recent initiative by the Swedish Sea Rescue Society (SSRS) aims to implement UAVs in their emergency response. By quickly deploying drones to an area of interest, an assessment can be made, prior to personnel getting there, thus saving time and increasing the likelihood of a successful rescue operation. An aircraft like this, that will travel great distances, have to rely on a navigation system that does not require an operator to continuously see the vehicle. To travel to its goal, or search an area, the operator should be able to define a travel route that the UAV follows, by feeding it a series of waypoints. As an initial step towards that kind of system, this thesis has developed and tested the concept of waypoint navigation on a small and slow airship/blimp, in a simulated indoor environment. Mainly, two commonly used navigation algorithms were tested and compared. One is inspired by a sub-category of machine learning: reinforcement learning (RL), and the other one is based on the rapidly exploring random tree (RRT) algorithm. Four experiments were conducted to compare the two methods in terms of travel distance, average speed, energy efficiency, as well as robustness towards changes in the waypoint configurations. Results show that when the blimp was controlled by the best performing RL-based version, it generally travelled a more optimal (distance-wise) path than the RRT-based method. It also, in most cases, proved to be more robust against changes in the test tracks, and performed more consistently over different waypoint configurations. However, the RRT approach usually resulted in a higher average speed and energy efficiency. Also, the RL algorithm had some trouble navigating tracks where a physical obstacle was present. To sum up, the choice of algorithm depends on which parameters are prioritized by the blimp operator for a certain track. If a high velocity and energy efficiency is desirable, the RRT-based method is recommended. However, if it is important that the blimp travels as short a distance as possible between waypoints, and a higher degree of consistency in its performance is wanted, then the RL-method should be used. Moving forward from this report, toward the future implementation of both methods in rescue operations, it would be reasonable to analyze their performance under more realistic conditions. This can be done using a real indoor airship. Looking at how hardware that do not exceed the payload of the blimp can execute both methods and how the blimp will determine its position and orientation is recommended. It would also be interesting to see how different reward function affect the performance of the blimp. / Den obemannade luftfarkosten (UAV) har under de senaste åren blivit en teknik vars användning blivit allt vanligare i flera sektorer av det moderna samhället. Olika sorters UAV robotar associeras idag med en omfattande serie användningsområden, från katastrofhjälp till övervakning. Ett nyligen påbörjat initiativ från svenska sjöräddningssällskapet (SSRS) syftar till att implementera drönare i deras utryckningar. Genom att snabbt sända drönare till platsen i fråga, kan en bedömning göras innan personal kommer dit, vilket sparar tid och ökar sannolikheten för en framgångsrik räddningsaktion. En farkost som denna, som kommer att resa långa sträckor, måste förlita sig på ett navigationssystem som inte kräver att en operatör kontinuerligt ser farkosten. För att resa till sitt mål, eller söka av ett område, bör operatören kunna definiera en resväg som drönaren följer genom att ge den en serie vägpunkter. Som ett inledande steg mot den typen av system har denna uppsats utvecklat och testat begreppet vägpunktsnavigering på ett litet och långsamt luftskepp/blimp, i en simulerad inomhusmiljö. Huvudsakligen testades och jämfördes två vanligt förekommande navigationsalgoritmer. En inspirerad av en underkategori till maskininlärning: förstärkningsinlärning (RL), och den andra baserad på rapidly exploring random tree (RRT) algoritmen. Fyra experiment utfördes för jämföra båda metoderna med avseende på färdsträcka, medelhastighet, energieffektivitet samt robusthet gentemot ändringar i färdpunktskonfigurationerna. Resultaten visar att när blimpen kontrollerades av den bästa RL-baserade versionen åkte den generellt en mer avståndsmässigt optimal väg än när den RRT-baserade metoden användes. I de flesta fallen visade sig även RL-metoden vara mer robust mot förändringar i testbanorna, och presterade mer konsekvent över olika vägpunktskonfigurationer. RRT-metoden resulterade dock vanligtvis i en högre medelhastighet och energieffektivitet. RL-algoritmen hade också problem med att navigera banor där den behövde ta sig runt ett hinder. Sammanfattningsvis beror valet av algoritm på vilka parametrar som prioriteras av blimpoperatören för en viss bana. Om en hög hastighet och energieffektivitet är önskvärd rekommenderas den RRT-baserade metoden. Men om det är viktigt att blimpen reser så kort avstånd som möjligt mellan färdpunkterna, och har en jämnare prestanda, bör RL-metoden användas. För att ta nästa steg, mot en framtida implementering av båda metoder i räddningsoperationer, vore det rimligt att analysera deras prestanda under mer realistiska förhållanden. Detta skulle kunna göras inomhus med ett riktigt luftskepp. Författarna rekommenderar att undersöka om hårdvara som inte överstiger blimpens maxlast kan utföra båda metodernas beräkningar och hur blimpen bestämmer sin position och orientering. Det skulle också vara intressant att se hur olika belöningsfunktioner påverkar blimpens prestanda.

When attempting to follow ground-based moving objects (hereafter referred to as ``waldos'') using an unmanned air vehicle (UAV), occlusion can become a significant problem for computer vision algorithms designed to track the object. When a waldo is occluded, the computer vision algorithm loses the track and the UAV's ability to predict movement degrades. We propose a path-planning and replanning method that moves a UAV to a location that maximizes the important waldos that can be seen while accounting for occlusion, and attempts to maximize the area it can see during travel. The proposed work moves beyond state-of-the-art algorithms designed to follow a single waldo while accounting for occlusion to enable tracking multiple prioritized waldos.

Due to the conditions peculiar to underwater, distinctive approaches are required to solve the navigation and path planning problem of an unmanned underwater vehicle (UUV). In this study, first of all, a detailed 6 degrees-of-freedom (DOF) mathematical model is formed, including the coupled non-linear forces and moments acting on an underwater vehicle. The hydrodynamic coefficients which correspond to the geometry of the vehicle which the model is based on are calculated using the strip theory. After the mathematical model is obtained, by applying appropriate linearization on the model, &ldquo / Linear Quadratic Regulator (LQR)&rdquo / control method is implemented to govern the surge, heave, pitch and yaw motions of the underwater vehicle. Path planning algorithm of the vehicle is based on tracking the waypoints. Permutation of the waypoints is obtained by solving the &ldquo / Travelling Salesman Problem (TSP)&rdquo / via genetic algorithm. Linked with that, &ldquo / Rapidly-Exploring Random Trees (RRT)&rdquo / algorithm is introduced into the path planning algorithm to avoid collisions in environments with obstacles. Underwater navigation solution is based on the &ldquo / Inertial Navigation System (INS)&rdquo / outputs, located on the vehicle. To correct the long-term drift of the inertial solution, &ldquo / Kalman Filter&rdquo / based integration algorithm is used and external aids such as &ldquo / Global Navigation Satellite System (GNSS)&rdquo / , &ldquo / Ultra-Short Baseline (USBL)&rdquo / acoustic navigation system and attitude sensors have been utilized. The control method, path planning and navigation algorithms used in this study are verified by simulation results.