FusionPlanner: A Multi-task Motion Planner for Mining Trucks using Multi-sensor Fusion Method

In recent years, significant achievements have been made in motion planning for intelligent vehicles. However, as a typical unstructured environment, open-pit mining attracts limited attention due to its complex operational conditions and adverse environmental factors. A comprehensive paradigm for unmanned transportation in open-pit mines is proposed in this research, including a simulation platform, a testing benchmark, and a trustworthy and robust motion planner. \textcolor{red}{Firstly, we propose a multi-task motion planning algorithm, called FusionPlanner, for autonomous mining trucks by the Multi-sensor fusion method to adapt both lateral and longitudinal control tasks for unmanned transportation. Then, we develop a novel benchmark called MiningNav, which offers three validation approaches to evaluate the trustworthiness and robustness of well-trained algorithms in transportation roads of open-pit mines. Finally, we introduce the Parallel Mining Simulator (PMS), a new high-fidelity simulator specifically designed for open-pit mining scenarios. PMS enables the users to manage and control open-pit mine transportation from both the single-truck control and multi-truck scheduling perspectives.} \textcolor{red}{The performance of FusionPlanner is tested by MiningNav in PMS, and the empirical results demonstrate a significant reduction in the number of collisions and takeovers of our planner. We anticipate our unmanned transportation paradigm will bring mining trucks one step closer to trustworthiness and robustness in continuous round-the-clock unmanned transportation.Comment: 2Pages, 10 figure

Motion Planning

Motion planning is a fundamental function in robotics and numerous intelligent machines. The global concept of planning involves multiple capabilities, such as path generation, dynamic planning, optimization, tracking, and control. This book has organized different planning topics into three general perspectives that are classified by the type of robotic applications. The chapters are a selection of recent developments in a) planning and tracking methods for unmanned aerial vehicles, b) heuristically based methods for navigation planning and routes optimization, and c) control techniques developed for path planning of autonomous wheeled platforms

A Systematic Survey of Control Techniques and Applications: From Autonomous Vehicles to Connected and Automated Vehicles

Vehicle control is one of the most critical challenges in autonomous vehicles (AVs) and connected and automated vehicles (CAVs), and it is paramount in vehicle safety, passenger comfort, transportation efficiency, and energy saving. This survey attempts to provide a comprehensive and thorough overview of the current state of vehicle control technology, focusing on the evolution from vehicle state estimation and trajectory tracking control in AVs at the microscopic level to collaborative control in CAVs at the macroscopic level. First, this review starts with vehicle key state estimation, specifically vehicle sideslip angle, which is the most pivotal state for vehicle trajectory control, to discuss representative approaches. Then, we present symbolic vehicle trajectory tracking control approaches for AVs. On top of that, we further review the collaborative control frameworks for CAVs and corresponding applications. Finally, this survey concludes with a discussion of future research directions and the challenges. This survey aims to provide a contextualized and in-depth look at state of the art in vehicle control for AVs and CAVs, identifying critical areas of focus and pointing out the potential areas for further exploration

Combining Sensors and Multibody Models for Applications in Vehicles, Machines, Robots and Humans

The combination of physical sensors and computational models to provide additional information about system states, inputs and/or parameters, in what is known as virtual sensing, is becoming increasingly popular in many sectors, such as the automotive, aeronautics, aerospatial, railway, machinery, robotics and human biomechanics sectors. While, in many cases, control-oriented models, which are generally simple, are the best choice, multibody models, which can be much more detailed, may be better suited to some applications, such as during the design stage of a new product

Contributions to improve the technologies supporting unmanned aircraft operations

Mención Internacional en el título de doctorUnmanned Aerial Vehicles (UAVs), in their smaller versions known as drones, are becoming increasingly important in today's societies. The systems that make them up present a multitude of challenges, of which error can be considered the common denominator. The perception of the environment is measured by sensors that have errors, the models that interpret the information and/or define behaviors are approximations of the world and therefore also have errors. Explaining error allows extending the limits of deterministic models to address real-world problems. The performance of the technologies embedded in drones depends on our ability to understand, model, and control the error of the systems that integrate them, as well as new technologies that may emerge. Flight controllers integrate various subsystems that are generally dependent on other systems. One example is the guidance systems. These systems provide the engine's propulsion controller with the necessary information to accomplish a desired mission. For this purpose, the flight controller is made up of a control law for the guidance system that reacts to the information perceived by the perception and navigation systems. The error of any of the subsystems propagates through the ecosystem of the controller, so the study of each of them is essential. On the other hand, among the strategies for error control are state-space estimators, where the Kalman filter has been a great ally of engineers since its appearance in the 1960s. Kalman filters are at the heart of information fusion systems, minimizing the error covariance of the system and allowing the measured states to be filtered and estimated in the absence of observations. State Space Models (SSM) are developed based on a set of hypotheses for modeling the world. Among the assumptions are that the models of the world must be linear, Markovian, and that the error of their models must be Gaussian. In general, systems are not linear, so linearization are performed on models that are already approximations of the world. In other cases, the noise to be controlled is not Gaussian, but it is approximated to that distribution in order to be able to deal with it. On the other hand, many systems are not Markovian, i.e., their states do not depend only on the previous state, but there are other dependencies that state space models cannot handle. This thesis deals a collection of studies in which error is formulated and reduced. First, the error in a computer vision-based precision landing system is studied, then estimation and filtering problems from the deep learning approach are addressed. Finally, classification concepts with deep learning over trajectories are studied. The first case of the collection xviiistudies the consequences of error propagation in a machine vision-based precision landing system. This paper proposes a set of strategies to reduce the impact on the guidance system, and ultimately reduce the error. The next two studies approach the estimation and filtering problem from the deep learning approach, where error is a function to be minimized by learning. The last case of the collection deals with a trajectory classification problem with real data. This work completes the two main fields in deep learning, regression and classification, where the error is considered as a probability function of class membership.Los vehículos aéreos no tripulados (UAV) en sus versiones de pequeño tamaño conocidos como drones, van tomando protagonismo en las sociedades actuales. Los sistemas que los componen presentan multitud de retos entre los cuales el error se puede considerar como el denominador común. La percepción del entorno se mide mediante sensores que tienen error, los modelos que interpretan la información y/o definen comportamientos son aproximaciones del mundo y por consiguiente también presentan error. Explicar el error permite extender los límites de los modelos deterministas para abordar problemas del mundo real. El rendimiento de las tecnologías embarcadas en los drones, dependen de nuestra capacidad de comprender, modelar y controlar el error de los sistemas que los integran, así como de las nuevas tecnologías que puedan surgir. Los controladores de vuelo integran diferentes subsistemas los cuales generalmente son dependientes de otros sistemas. Un caso de esta situación son los sistemas de guiado. Estos sistemas son los encargados de proporcionar al controlador de los motores información necesaria para cumplir con una misión deseada. Para ello se componen de una ley de control de guiado que reacciona a la información percibida por los sistemas de percepción y navegación. El error de cualquiera de estos sistemas se propaga por el ecosistema del controlador siendo vital su estudio. Por otro lado, entre las estrategias para abordar el control del error se encuentran los estimadores en espacios de estados, donde el filtro de Kalman desde su aparición en los años 60, ha sido y continúa siendo un gran aliado para los ingenieros. Los filtros de Kalman son el corazón de los sistemas de fusión de información, los cuales minimizan la covarianza del error del sistema, permitiendo filtrar los estados medidos y estimarlos cuando no se tienen observaciones. Los modelos de espacios de estados se desarrollan en base a un conjunto de hipótesis para modelar el mundo. Entre las hipótesis se encuentra que los modelos del mundo han de ser lineales, markovianos y que el error de sus modelos ha de ser gaussiano. Generalmente los sistemas no son lineales por lo que se realizan linealizaciones sobre modelos que a su vez ya son aproximaciones del mundo. En otros casos el ruido que se desea controlar no es gaussiano, pero se aproxima a esta distribución para poder abordarlo. Por otro lado, multitud de sistemas no son markovianos, es decir, sus estados no solo dependen del estado anterior, sino que existen otras dependencias que los modelos de espacio de estados no son capaces de abordar. Esta tesis aborda un compendio de estudios sobre los que se formula y reduce el error. En primer lugar, se estudia el error en un sistema de aterrizaje de precisión basado en visión por computador. Después se plantean problemas de estimación y filtrado desde la aproximación del aprendizaje profundo. Por último, se estudian los conceptos de clasificación con aprendizaje profundo sobre trayectorias. El primer caso del compendio estudia las consecuencias de la propagación del error de un sistema de aterrizaje de precisión basado en visión artificial. En este trabajo se propone un conjunto de estrategias para reducir el impacto sobre el sistema de guiado, y en última instancia reducir el error. Los siguientes dos estudios abordan el problema de estimación y filtrado desde la perspectiva del aprendizaje profundo, donde el error es una función que minimizar mediante aprendizaje. El último caso del compendio aborda un problema de clasificación de trayectorias con datos reales. Con este trabajo se completan los dos campos principales en aprendizaje profundo, regresión y clasificación, donde se plantea el error como una función de probabilidad de pertenencia a una clase.I would like to thank the Ministry of Science and Innovation for granting me the funding with reference PRE2018-086793, associated to the project TEC2017-88048-C2-2-R, which provide me the opportunity to carry out all my PhD. activities, including completing an international research internship.Programa de Doctorado en Ciencia y Tecnología Informática por la Universidad Carlos III de MadridPresidente: Antonio Berlanga de Jesús.- Secretario: Daniel Arias Medina.- Vocal: Alejandro Martínez Cav

Aerial Vehicles

This book contains 35 chapters written by experts in developing techniques for making aerial vehicles more intelligent, more reliable, more flexible in use, and safer in operation.It will also serve as an inspiration for further improvement of the design and application of aeral vehicles. The advanced techniques and research described here may also be applicable to other high-tech areas such as robotics, avionics, vetronics, and space

Locomotion system for ground mobile robots in uneven and unstructured environments

One of the technology domains with the greatest growth rates nowadays is service robots. The extensive use of ground mobile robots in environments that are unstructured or structured for humans is a promising challenge for the coming years, even though Automated Guided Vehicles (AGV) moving on flat and compact grounds are already commercially available and widely utilized to move components and products inside indoor industrial buildings. Agriculture, planetary exploration, military operations, demining, intervention in case of terrorist attacks, surveillance, and reconnaissance in hazardous conditions are important application domains. Due to the fact that it integrates the disciplines of locomotion, vision, cognition, and navigation, the design of a ground mobile robot is extremely interdisciplinary. In terms of mechanics, ground mobile robots, with the exception of those designed for particular surroundings and surfaces (such as slithering or sticky robots), can move on wheels (W), legs (L), tracks (T), or hybrids of these concepts (LW, LT, WT, LWT). In terms of maximum speed, obstacle crossing ability, step/stair climbing ability, slope climbing ability, walking capability on soft terrain, walking capability on uneven terrain, energy efficiency, mechanical complexity, control complexity, and technology readiness, a systematic comparison of these locomotion systems is provided in [1]. Based on the above-mentioned classification, in this thesis, we first introduce a small-scale hybrid locomotion robot for surveillance and inspection, WheTLHLoc, with two tracks, two revolving legs, two active wheels, and two passive omni wheels. The robot can move in several different ways, including using wheels on the flat, compact ground,[1] tracks on soft, yielding terrain, and a combination of tracks, legs, and wheels to navigate obstacles. In particular, static stability and non-slipping characteristics are considered while analyzing the process of climbing steps and stairs. The experimental test on the first prototype has proven the planned climbing maneuver’s efficacy and the WheTLHLoc robot's operational flexibility. Later we present another development of WheTLHLoc and introduce WheTLHLoc 2.0 with newly designed legs, enabling the robot to deal with bigger obstacles. Subsequently, a single-track bio-inspired ground mobile robot's conceptual and embodiment designs are presented. This robot is called SnakeTrack. It is designed for surveillance and inspection activities in unstructured environments with constrained areas. The vertebral column has two end modules and a variable number of vertebrae linked by compliant joints, and the surrounding track is its essential component. Four motors drive the robot: two control the track motion and two regulate the lateral flexion of the vertebral column for steering. The compliant joints enable limited passive torsion and retroflection of the vertebral column, which the robot can use to adapt to uneven terrain and increase traction. Eventually, the new version of SnakeTrack, called 'Porcospino', is introduced with the aim of allowing the robot to move in a wider variety of terrains. The novelty of this thesis lies in the development and presentation of three novel designs of small-scale mobile robots for surveillance and inspection in unstructured environments, and they employ hybrid locomotion systems that allow them to traverse a variety of terrains, including soft, yielding terrain and high obstacles. This thesis contributes to the field of mobile robotics by introducing new design concepts for hybrid locomotion systems that enable robots to navigate challenging environments. The robots presented in this thesis employ modular designs that allow their lengths to be adapted to suit specific tasks, and they are capable of restoring their correct position after falling over, making them highly adaptable and versatile. Furthermore, this thesis presents a detailed analysis of the robots' capabilities, including their step-climbing and motion planning abilities. In this thesis we also discuss possible refinements for the robots' designs to improve their performance and reliability. Overall, this thesis's contributions lie in the design and development of innovative mobile robots that address the challenges of surveillance and inspection in unstructured environments, and the analysis and evaluation of these robots' capabilities. The research presented in this thesis provides a foundation for further work in this field, and it may be of interest to researchers and practitioners in the areas of robotics, automation, and inspection. As a general note, the first robot, WheTLHLoc, is a hybrid locomotion robot capable of combining tracked locomotion on soft terrains, wheeled locomotion on flat and compact grounds, and high obstacle crossing capability. The second robot, SnakeTrack, is a small-size mono-track robot with a modular structure composed of a vertebral column and a single peripherical track revolving around it. The third robot, Porcospino, is an evolution of SnakeTrack and includes flexible spines on the track modules for improved traction on uneven but firm terrains, and refinements of the shape of the track guidance system. This thesis provides detailed descriptions of the design and prototyping of these robots and presents analytical and experimental results to verify their capabilities

Autonomous landing of fixed-wing aircraft on mobile platforms

E n esta tesis se propone un nuevo sistema que permite la operación de aeronaves autónomas sin tren de aterrizaje. El trabajo está motivado por el interés industrial en aeronaves con la capacidad de volar a gran altitud, con más capacidad de carga útil y capaces de aterrizar con viento cruzado. El enfoque seguido en este trabajo consiste en eliminar el sistema de aterrizaje de una aeronave de ala fija empleando una plataforma móvil de aterrizaje en tierra. La aeronave y la plataforma deben sincronizar su movimiento antes del aterrizaje, lo que se logra mediante la estimación del estado relativo entre ambas y el control cooperativo del movimiento. El objetivo principal de esta Tesis es el desarrollo de una solución práctica para el aterrizaje autónomo de una aeronave de ala fija en una plataforma móvil. En la tesis se combinan nuevos métodos con experimentos prácticos para los cuales se ha desarrollado un sistema de pruebas específico. Se desarrollan dos variantes diferentes del sistema de aterrizaje. El primero presta atención especial a la seguridad, es robusto ante retrasos en la comunicación entre vehículos y cumple procedimientos habituales de aterrizaje, al tiempo que reduce la complejidad del sistema. En el segundo se utilizan trayectorias optimizadas del vehículo y sincronización bilateral de posición para maximizar el rendimiento del aterrizaje en términos de requerimientos de longitud necesaria de pista, pero la estabilidad es dependiente del retraso de tiempo, con lo cual es necesario desarrollar un controlador estabilizador ampliado, basado en pasividad, que permite resolver este problema. Ambas estrategias imponen requisitos funcionales a los controladores de cada uno de los vehículos, lo que implica la capacidad de controlar el movimiento longitudinal sin afectar el control lateral o vertical, y viceversa. El control de vuelo basado en energía se utiliza para proporcionar dicha funcionalidad a la aeronave. Los sistemas de aterrizaje desarrollados se han analizado en simulación estableciéndose los límites de rendimiento mediante múltiples repeticiones aleatorias. Se llegó a la conclusión de que el controlador basado en seguridad proporciona un rendimiento de aterrizaje satisfactorio al tiempo que suministra una mayor seguridad operativa y un menor esfuerzo de implementación y certificación. El controlador basado en el rendimiento es prometedor para aplicaciones con una longitud de pista limitada. Se descubrió que los beneficios del controlador basado en el rendimiento son menos pronunciados para una dinámica de vehículos terrestres más lenta. Teniendo en cuenta la dinámica lenta de la configuración del demostrador, se eligió el enfoque basado en la seguridad para los primeros experimentos de aterrizaje. El sistema de aterrizaje se validó en diversas pruebas de aterrizaje exitosas, que, a juicio del autor, son las primeras en el mundo realizadas con aeronaves reales. En última instancia, el concepto propuesto ofrece importantes beneficios y constituye una estrategia prometedora para futuras soluciones de aterrizaje de aeronaves.In this thesis a new landing system is proposed, which allows for the operation of autonomous aircraft without landing gear. The work was motivated by the industrial need for more capable high altitude aircraft systems, which typically suffer from low payload capacity and high crosswind landing sensitivity. The approach followed in this work consists in removing the landing gear system from the aircraft and introducing a mobile ground-based landing platform. The vehicles must synchronize their motion prior to landing, which is achieved through relative state estimation and cooperative motion control. The development of a practical solution for the autonomous landing of an aircraft on a moving platform thus constitutes the main goal of this thesis. Therefore, theoretical investigations are combined with real experiments for which a special setup is developed and implemented. Two different landing system variants are developed — the safety-based landing system is robust to inter-vehicle communication delays and adheres to established landing procedures, while reducing system complexity. The performance-based landing system uses optimized vehicle trajectories and bilateral position synchronization to maximize landing performance in terms of used runway, but suffers from time delay-dependent stability. An extended passivity-based stabilizing controller was implemented to cope with this issue. Both strategies impose functional requirements on the individual vehicle controllers, which imply independent controllability of the translational degrees of freedom. Energy-based flight control is utilized to provide such functionality for the aircraft. The developed landing systems are analyzed in simulation and performance bounds are determined by means of repeated random sampling. The safety-based controller was found to provide satisfactory landing performance while providing higher operational safety, and lower implementation and certification effort. The performance-based controller is promising for applications with limited runway length. The performance benefits were found to be less pronounced for slower ground vehicle dynamics. Given the slow dynamics of the demonstrator setup, the safety-based approach was chosen for first landing experiments. The landing system was validated in a number of successful landing trials, which to the author’s best knowledge was the first time such technology was demonstrated on the given scale, worldwide. Ultimately, the proposed concept offers decisive benefits and constitutes a promising strategy for future aircraft landing solutions

Robust navigation for industrial service robots

Pla de Doctorats Industrials de la Generalitat de CatalunyaRobust, reliable and safe navigation is one of the fundamental problems of robotics. Throughout the present thesis, we tackle the problem of navigation for robotic industrial mobile-bases. We identify its components and analyze their respective challenges in order to address them. The research work presented here ultimately aims at improving the overall quality of the navigation stack of a commercially available industrial mobile-base. To introduce and survey the overall problem we first break down the navigation framework into clearly identified smaller problems. We examine the Simultaneous Localization and Mapping (SLAM) problem, recalling its mathematical grounding and exploring the state of the art. We then review the problem of planning the trajectory of a mobile-base toward a desired goal in the generated environment representation. Finally we investigate and clarify the use of the subset of the Lie theory that is useful in robotics. The first problem tackled is the recognition of place for closing loops in SLAM. Loop closure refers to the ability of a robot to recognize a previously visited location and infer geometrical information between its current and past locations. Using only a 2D laser range finder sensor, we address the problem using a technique borrowed from the field of Natural Language Processing (NLP) which has been successfully applied to image-based place recognition, namely the Bag-of-Words. We further improve the method with two proposals inspired from NLP. Firstly, the comparison of places is strengthened by considering the natural relative order of features in each individual sensor reading. Secondly, topological correspondences between places in a corpus of visited places are established in order to promote together instances that are ‘close’ to one another. We then tackle the problem of motion model calibration for odometry estimation. Given a mobile-base embedding an exteroceptive sensor able to observe ego-motion, we propose a novel formulation for estimating the intrinsic parameters of an odometry motion model. Resorting to an adaptation of the pre-integration theory initially developed for inertial motion sensors, we employ iterative nonlinear on-manifold optimization to estimate the wheel radii and wheel separation. The method is further extended to jointly estimate both the intrinsic parameters of the odometry model together with the extrinsic parameters of the embedded sensor. The method is shown to accommodate to variation in model parameters quickly when the vehicle is subject to physical changes during operation. Following the generation of a map in which the robot is localized, we address the problem of estimating trajectories for motion planning. We devise a new method for estimating a sequence of robot poses forming a smooth trajectory. Regardless of the Lie group considered, the trajectory is seen as a collection of states lying on a spline with non-vanishing n-th derivatives at each point. Formulated as a multi-objective nonlinear optimization problem, it allows for the addition of cost functions such as velocity and acceleration limits, collision avoidance and more. The proposed method is evaluated for two different motion planning tasks, the planning of trajectories for a mobile-base evolving in the SE(2) manifold, and the planning of the motion of a multi-link robotic arm whose end-effector evolves in the SE(3) manifold. From our study of Lie theory, we developed a new, ready to use, programming library called `manif’. The library is open source, publicly available and is developed following good software programming practices. It is designed so that it is easy to integrate and manipulate, and allows for flexible use while facilitating the possibility to extend it beyond the already implemented Lie groups.La navegación autónoma es uno de los problemas fundamentales de la robótica, y sus diferentes desafíos se han estudiado durante décadas. El desarrollo de métodos de navegación robusta, confiable y segura es un factor clave para la creación de funcionalidades de nivel superior en robots diseñados para operar en entornos con humanos. A lo largo de la presente tesis, abordamos el problema de navegación para bases robóticas móviles industriales; identificamos los elementos de un sistema de navegación; y analizamos y tratamos sus desafíos. El trabajo de investigación presentado aquí tiene como último objetivo mejorar la calidad general del sistema completo de navegación de una base móvil industrial disponible comercialmente. Para estudiar el problema de navegación, primero lo desglosamos en problemas menores claramente identificados. Examinamos el subproblema de mapeo del entorno y localización del robot simultáneamente (SLAM por sus siglas en ingles) y estudiamos el estado del arte del mismo. Al hacerlo, recordamos y detallamos la base matemática del problema de SLAM. Luego revisamos el subproblema de planificación de trayectorias hacia una meta deseada en la representación del entorno generada. Además, como una herramienta para las soluciones que se presentarán más adelante en el desarrollo de la tesis, investigamos y aclaramos el uso de teoría de Lie, centrándonos en el subconjunto de la teoría que es útil para la estimación de estados en robótica. Como primer elemento identificado para mejoras, abordamos el problema de reconocimiento de lugares para cerrar lazos en SLAM. El cierre de lazos se refiere a la capacidad de un robot para reconocer una ubicación visitada previamente e inferí información geométrica entre la ubicación actual del robot y aquellas reconocidas. Usando solo un sensor láser 2D, la tarea es desafiante ya que la percepción del entorno que proporciona el sensor es escasa y limitada. Abordamos el problema utilizando 'bolsas de palabras', una técnica prestada del campo de procesamiento del lenguaje natural (NLP) que se ha aplicado con éxito anteriormente al reconocimiento de lugares basado en imágenes. Nuestro método incluye dos nuevas propuestas inspiradas también en NLP. Primero, la comparación entre lugares candidatos se fortalece teniendo en cuenta el orden relativo natural de las características en cada lectura individual del sensor; y segundo, se establece un corpus de lugares visitados para promover juntos instancias que están "cerca" la una de la otra desde un punto de vista topológico. Evaluamos nuestras propuestas por separado y conjuntamente en varios conjuntos de datos, con y sin ruido, demostrando mejora en la detección de cierres de lazo para sensores láser 2D, con respecto al estado del arte. Luego abordamos el problema de la calibración del modelo de movimiento para la estimación de la edometría. Dado que nuestra base móvil incluye un sensor exteroceptivo capaz de observar el movimiento de la plataforma, proponemos una nueva formulación que permite estimar los parámetros intrínsecos del modelo cinemático de la plataforma durante el cómputo de la edometría del vehículo. Hemos recurrido a una adaptación de la teoría de reintegración inicialmente desarrollado para unidades inerciales de medida, y aplicado la técnica a nuestro modelo cinemático. El método nos permite, mediante optimización iterativa no lineal, la estimación del valor del radio de las ruedas de forma independiente y de la separación entre las mismas. El método se amplía posteriormente par idéntica de forma simultánea, estos parámetros intrínsecos junto con los parámetros extrínsecos que ubican el sensor láser con respecto al sistema de referencia de la base móvil. El método se valida en simulación y en un entorno real y se muestra que converge hacia los verdaderos valores de los parámetros. El método permite la adaptación de los parámetros intrínsecos del modelo cinemático de la plataforma derivados de cambios físicos durante la operación, tales como el impacto que el cambio de carga sobre la plataforma tiene sobre el diámetro de las ruedas. Como tercer subproblema de navegación, abordamos el reto de planificar trayectorias de movimiento de forma suave. Desarrollamos un método para planificar la trayectoria como una secuencia de configuraciones sobre una spline con n-ésimas derivadas en todos los puntos, independientemente del grupo de Lie considerado. Al ser formulado como un problema de optimización no lineal con múltiples objetivos, es posible agregar funciones de coste al problema de optimización que permitan añadir límites de velocidad o aceleración, evasión de colisiones, etc. El método propuesto es evaluado en dos tareas de planificación de movimiento diferentes, la planificación de trayectorias para una base móvil que evoluciona en la variedad SE(2), y la planificación del movimiento de un brazo robótico cuyo efector final evoluciona en la variedad SE(3). Además, cada tarea se evalúa en escenarios con complejidad de forma incremental, y se muestra un rendimiento comparable o mejor que el estado del arte mientras produce resultados más consistentes. Desde nuestro estudio de la teoría de Lie, desarrollamos una nueva biblioteca de programación llamada “manif”. La biblioteca es de código abierto, está disponible públicamente y se desarrolla siguiendo las buenas prácticas de programación de software. Esta diseñado para que sea fácil de integrar y manipular, y permite flexibilidad de uso mientras se facilita la posibilidad de extenderla más allá de los grupos de Lie inicialmente implementados. Además, la biblioteca se muestra eficiente en comparación con otras soluciones existentes. Por fin, llegamos a la conclusión del estudio de doctorado. Examinamos el trabajo de investigación y trazamos líneas para futuras investigaciones. También echamos un vistazo en los últimos años y compartimos una visión personal y experiencia del desarrollo de un doctorado industrial.Postprint (published version