Near-Optimal Motion Planning Algorithms Via A Topological and Geometric Perspective

Motion planning is a fundamental problem in robotics, which involves finding a path for an autonomous system, such as a robot, from a given source to a destination while avoiding collisions with obstacles. The properties of the planning space heavily influence the performance of existing motion planning algorithms, which can pose significant challenges in handling complex regions, such as narrow passages or cluttered environments, even for simple objects. The problem of motion planning becomes deterministic if the details of the space are fully known, which is often difficult to achieve in constantly changing environments. Sampling-based algorithms are widely used among motion planning paradigms because they capture the topology of space into a roadmap. These planners have successfully solved high-dimensional planning problems with a probabilistic-complete guarantee, i.e., it guarantees to find a path if one exists as the number of vertices goes to infinity. Despite their progress, these methods have failed to optimize the sub-region information of the environment for reuse by other planners. This results in re-planning overhead at each execution, affecting the performance complexity for computation time and memory space usage. In this research, we address the problem by focusing on the theoretical foundation of the algorithmic approach that leverages the strengths of sampling-based motion planners and the Topological Data Analysis methods to extract intricate properties of the environment. The work contributes a novel algorithm to overcome the performance shortcomings of existing motion planners by capturing and preserving the essential topological and geometric features to generate a homotopy-equivalent roadmap of the environment. This roadmap provides a mathematically rich representation of the environment, including an approximate measure of the collision-free space. In addition, the roadmap graph vertices sampled close to the obstacles exhibit advantages when navigating through narrow passages and cluttered environments, making obstacle-avoidance path planning significantly more efficient. The application of the proposed algorithms solves motion planning problems, such as sub-optimal planning, diverse path planning, and fault-tolerant planning, by demonstrating the improvement in computational performance and path quality. Furthermore, we explore the potential of these algorithms in solving computational biology problems, particularly in finding optimal binding positions for protein-ligand or protein-protein interactions. Overall, our work contributes a new way to classify routes in higher dimensional space and shows promising results for high-dimensional robots, such as articulated linkage robots. The findings of this research provide a comprehensive solution to motion planning problems and offer a new perspective on solving computational biology problems

Efficient Solutions in Path Planning for Autonomous Mobile Robots

Fecha de lectura de Tesis: 25 julio 2018.Los robots, máquinas que desempeñan un abanico de tareas de lo más variopinto. Desde realizar tareas muy específicas en cadenas de montaje hasta desempeñar la mayoría de labores cotidianas que los seres humanos tenemos que afrontar cada día. Como se puede intuir, para esto se necesitan no solo máquinas, sino máquinas dotadas de cierta inteligencia, que surge de la necesidad de que las máquinas abandonen su estatismo y monotonía para comenzar a enfrentarse a un mundo dinámico y ambiguo: nuestro mundo. El principal desencadenante que ha llevado al ser humano a dotar de inteligencia y movilidad a las máquinas es su afán de dominar y, al mismo tiempo, liberarse de un entorno cada vez más estresante. Hay dos aspectos irrefutables que marcan la versatilidad de una máquina: su inteligencia y su movilidad. Hablando de robótica y movilidad surge el problema de cómo y por dónde debe moverse un robot para alcanzar un determinado objetivo sin comprometer su integridad física. Como el significado de moverse puede ser muy amplio, aquí hablaremos de desplazamiento, en el sentido literal de viajar. Y cuando viajamos a algún lugar siempre nos preguntamos lo siguiente: ¿Por dónde vamos? y ¿Cuál es el la mejor alternativa?. Esta problemática, en robótica, se conoce como el problema del Path Planning. En esta tesis doctoral se aborda, de manera innovadora y altamente paralela, el problema del Path Planing sobre mapas reales extensos en un contexto de tiempo real. Este grado de paralelismo se consigue gracias al uso intensivo de las populares GPU (Unidad Gráfica de Procesamiento) y de los bien conocidos chips multi-core. Pero aquí no solo se aborda el problema del Path Planning desde un punto de vista altamente paralelo sino que, de manera transversal, también se aborda desde un punto de vista inteligente aplicando metaheurísticas

Automated generation of geometrically-precise and semantically-informed virtual geographic environnements populated with spatially-reasoning agents

La Géo-Simulation Multi-Agent (GSMA) est un paradigme de modélisation et de simulation de phénomènes dynamiques dans une variété de domaines d'applications tels que le domaine du transport, le domaine des télécommunications, le domaine environnemental, etc. La GSMA est utilisée pour étudier et analyser des phénomènes qui mettent en jeu un grand nombre d'acteurs simulés (implémentés par des agents) qui évoluent et interagissent avec une représentation explicite de l'espace qu'on appelle Environnement Géographique Virtuel (EGV). Afin de pouvoir interagir avec son environnement géographique qui peut être dynamique, complexe et étendu (à grande échelle), un agent doit d'abord disposer d'une représentation détaillée de ce dernier. Les EGV classiques se limitent généralement à une représentation géométrique du monde réel laissant de côté les informations topologiques et sémantiques qui le caractérisent. Ceci a pour conséquence d'une part de produire des simulations multi-agents non plausibles, et, d'autre part, de réduire les capacités de raisonnement spatial des agents situés. La planification de chemin est un exemple typique de raisonnement spatial dont un agent pourrait avoir besoin dans une GSMA. Les approches classiques de planification de chemin se limitent à calculer un chemin qui lie deux positions situées dans l'espace et qui soit sans obstacle. Ces approches ne prennent pas en compte les caractéristiques de l'environnement (topologiques et sémantiques), ni celles des agents (types et capacités). Les agents situés ne possèdent donc pas de moyens leur permettant d'acquérir les connaissances nécessaires sur l'environnement virtuel pour pouvoir prendre une décision spatiale informée. Pour répondre à ces limites, nous proposons une nouvelle approche pour générer automatiquement des Environnements Géographiques Virtuels Informés (EGVI) en utilisant les données fournies par les Systèmes d'Information Géographique (SIG) enrichies par des informations sémantiques pour produire des GSMA précises et plus réalistes. De plus, nous présentons un algorithme de planification hiérarchique de chemin qui tire avantage de la description enrichie et optimisée de l'EGVI pour fournir aux agents un chemin qui tient compte à la fois des caractéristiques de leur environnement virtuel et de leurs types et capacités. Finalement, nous proposons une approche pour la gestion des connaissances sur l'environnement virtuel qui vise à supporter la prise de décision informée et le raisonnement spatial des agents situés

Geometric Approximations and their Application to Motion Planning

Geometric approximation methods are a preferred solution to handle complexities (such as a large volume or complex features such as concavities) in geometric objects or environments containing them. Complexities often pose a computational bottleneck for applications such as motion planning. Exact resolution of these complexities might introduce other complexities such as unmanageable number of components. Hence, approximation methods provide a way to handle these complexities in a manageable state by trading off some accuracy. In this dissertation, two novel geometric approximation methods are studied: aggregation hierarchy and shape primitive skeleton. The aggregation hierarchy is a hierarchical clustering of polygonal or polyhedral objects. The shape primitive skeleton provides an approximation of bounded space as a skeleton of shape primitives. These methods are further applied to improve the performance of motion planning applications. We evaluate the methods in environments with 2D and 3D objects. The aggregation hierarchy groups nearby objects into individual objects. The hierarchy is created by varying the distance threshold that determines which objects are nearby. This creates levels of detail of the environment. The hierarchy of the obstacle space is then used to create a decom-position of the complementary space (i.e, free space) into a set of sampling regions to improve the efficiency and accuracy of the sampling operation of the sampling based motion planners. Our results show that the method can improve the efficiency (10 − 70% of planning time) of sampling based motion planning algorithms. The shape primitive skeleton inscribes a set of shape primitives (e.g., sphere, boxes) inside a bounded space such that they represent the skeleton or the connectivity of the space. We apply the shape primitive skeletons of the free space and obstacle space in motion planning problems to improve the collision detection operation. Our results also show the use of shape primitive skeleton in both spaces improves the performance of collision detectors (by 20 − 70% of collision detection time) used in motion planning algorithms. In summary, this dissertation evaluates how geometric approximation methods can be applied to improve the performance of motion planning methods, especially, sampling based motion planning method

Smart Collision Avoidance System for a Dual-Arm Manipulator

A crescente automatização do quotidiano humano bem como o aumento do uso de manipuladores na industria leva a uma maior investigação na área da robótica. É neste âmbito que surge este projecto. O trabalho é realizado num manipulador constituido por dois braços com 7 graus de liberdade cada e tem por objectivo impedir que estes colidam, quer um com o outro quer com qualquer obstáculo presente ao seu redor. Para tal um estudo será realizado sobre a eficácia de planeadores já desenvolvidos com o intuito de analisar quais os mais eficazes para o cenário presente.Robots have an ever increasing importance in today's society and in our daily life. Industry wise, dual arm robots play a central role since they are designed to behave in a similar manner to a human being and present a more versatile set of behaviors and tasks than a single arm robot.This thesis aims to operate in an anthropomorphic dual arm robot, that has two arms with 7 degrees of freedom each. The main goal of this project is to avoid that, while working, the arms bump into one another or with any obstacle in the environment. In order to achieve this several motion planners will be tested and a thorough analyses on their outcome will be discussed

Workspace-based sampling for probabilistic path planning

Ph.DDOCTOR OF PHILOSOPH

Study and Development of Hierarchical Path Finding to Speed Up Crowd Simulation

We propose a new hierarchical path finding solution for large environments. We use a navigation mesh as abstract data structure to partition the 3D world. Then, we build a hierarchy of graphs that allow us to perform faster path finding calculations than a common A*

Planning in constraint space for multi-body manipulation tasks

Robots are inherently limited by physical constraints on their link lengths, motor torques, battery power and structural rigidity. To thrive in circumstances that push these limits, such as in search and rescue scenarios, intelligent agents can use the available objects in their environment as tools. Reasoning about arbitrary objects and how they can be placed together to create useful structures such as ramps, bridges or simple machines is critical to push beyond one's physical limitations. Unfortunately, the solution space is combinatorial in the number of available objects and the configuration space of the chosen objects and the robot that uses the structure is high dimensional. To address these challenges, we propose using constraint satisfaction as a means to test the feasibility of candidate structures and adopt search algorithms in the classical planning literature to find sufficient designs. The key idea is that the interactions between the components of a structure can be encoded as equality and inequality constraints on the configuration spaces of the respective objects. Furthermore, constraints that are induced by a broadly defined action, such as placing an object on another, can be grouped together using logical representations such as Planning Domain Definition Language (PDDL). Then, a classical planning search algorithm can reason about which set of constraints to impose on the available objects, iteratively creating a structure that satisfies the task goals and the robot constraints. To demonstrate the effectiveness of this framework, we present both simulation and real robot results with static structures such as ramps, bridges and stairs, and quasi-static structures such as lever-fulcrum simple machines.Ph.D

Fast Marching Methods in path and motion planning: improvements and high-level applications

Mención Internacional en el título de doctorPath planning is defined as the process to establish the sequence of states a system must go through in order to reach a desired state. Additionally, motion planning (or trajectory planning) aims to compute the sequence of motions (or actions) to take the system from one state to another. In robotics path planning can refer for instance to the waypoints a robot should follow through a maze or the sequence of points a robotic arm has to follow in order to grasp an object. Motion planning is considered a more general problem, since it includes kinodynamic constraints. As motion planning is a more complex problem, it is often solved in a two-level approach: path planning in the first level and then a control layer tries to drive the system along the specified path. However, it is hard to guarantee that the final trajectory will keep the initial characteristics. The objective of this work is to solve different path and motion planning problems under a common framework in order to facilitate the integration of the different algorithms that can be required during the nominal operation of a mobile robot. Also, other related areas such as motion learning are explored using this framework. In order to achieve this, a simple but powerful algorithm called Fast Marching will be used. Originally, it was proposed to solve optimal control problems. However, it has became very useful to other related problems such as path and motion planning. Since Fast Marching was initially proposed, many different alternative approaches have been proposed. Therefore, the first step is to formulate all these methods within a common framework and carry out an exhaustive comparison in order to give a final answer to: which algorithm is the best under which situations? This Thesis shows that the different versions of Fast Marching Methods become useful when applied to motion and path planning problems. Usually, high-level problems as motion learning or robot formation planning are solved with completely different algorithms, as the problem formulation are mixed. Under a common framework, task integration becomes much easier bringing robots closer to everyday applications. The Fast Marching Method has also inspired modern probabilistic methodologies, where computational cost is enormously improved at the cost of bounded, stochastic variations on the resulting paths and trajectories. This Thesis also explores these novel algorithms and their performance.Programa Oficial de Doctorado en Ingeniería Eléctrica, Electrónica y AutomáticaPresidente: Carlos Balaguer Bernaldo de Quirós.- Secretario: Antonio Giménez Fernández.- Vocal: Isabel Lobato de Faria Ribeir

Electromechanical Dynamics of High Photovoltaic Power Grids

This dissertation study focuses on the impact of high PV penetration on power grid electromechanical dynamics. Several major aspects of power grid electromechanical dynamics are studied under high PV penetration, including frequency response and control, inter-area oscillations, transient rotor angle stability and electromechanical wave propagation.To obtain dynamic models that can reasonably represent future power systems, Chapter One studies the co-optimization of generation and transmission with large-scale wind and solar. The stochastic nature of renewables is considered in the formulation of mixed-integer programming model. Chapter Two presents the development procedures of high PV model and investigates the impact of high PV penetration on frequency responses. Chapter Three studies the impact of PV penetration on inter-area oscillations of the U.S. Eastern Interconnection system. Chapter Four presents the impacts of high PV on other electromechanical dynamic issues, including transient rotor angle stability and electromechanical wave propagation. Chapter Five investigates the frequency response enhancement by conventional resources. Chapter Six explores system frequency response improvement through real power control of wind and PV. For improving situation awareness and frequency control, Chapter Seven studies disturbance location determination based on electromechanical wave propagation. In addition, a new method is developed to generate the electromechanical wave propagation speed map, which is useful to detect system inertia distribution change. Chapter Eight provides a review on power grid data architectures for monitoring and controlling power grids. Challenges and essential elements of data architecture are analyzed to identify various requirements for operating high-renewable power grids and a conceptual data architecture is proposed. Conclusions of this dissertation study are given in Chapter Nine