Multilevel Motion Planning: A Fiber Bundle Formulation

Motion planning problems involving high-dimensional state spaces can often be solved significantly faster by using multilevel abstractions. While there are various ways to formally capture multilevel abstractions, we formulate them in terms of fiber bundles, which allows us to concisely describe and derive novel algorithms in terms of bundle restrictions and bundle sections. Fiber bundles essentially describe lower-dimensional projections of the state space using local product spaces. Given such a structure and a corresponding admissible constraint function, we can develop highly efficient and optimal search-based motion planning methods for high-dimensional state spaces. Our contributions are the following: We first introduce the terminology of fiber bundles, in particular the notion of restrictions and sections. Second, we use the notion of restrictions and sections to develop novel multilevel motion planning algorithms, which we call QRRT* and QMP*. We show these algorithms to be probabilistically complete and almost-surely asymptotically optimal. Third, we develop a novel recursive path section method based on an L1 interpolation over path restrictions, which we use to quickly find feasible path sections. And fourth, we evaluate all novel algorithms against all available OMPL algorithms on benchmarks of eight challenging environments ranging from 21 to 100 degrees of freedom, including multiple robots and nonholonomic constraints. Our findings support the efficiency of our novel algorithms and the benefit of exploiting multilevel abstractions using the terminology of fiber bundles.Comment: Submitted to IJR

Sampling C-obstacles border using a filtered deterministic sequence

This paper is focused on the sampling process for path planners based on probabilistic roadmaps. The paper first analyzes three sampling sources: the random sequence and two deterministic sequences, Halton and sd(k), and compares them in terms of dispersion, computational efficiency (including the finding of nearest neighbors), and sampling probabilities. Then, based on this analysis and on the recognized success of the Gaussian sampling strategy, the paper proposes a new efficient sampling strategy based on deterministic sampling that also samples more densely near the C-obstacles. The proposal is evaluated and compared with the original Gaussian strategy in both 2D and 3D configuration spaces, giving promising results

Improving Sampling-Based Motion Planning Using Library of Trajectories

Plánování pohybu je jedním z podstatných problémů robotiky. Tato práce kombinuje pokroky v plánování pohybu a hodnocení podobnosti objektů za účelem zrychlení plánování ve statických prostředích. První část této práce pojednává o současných metodách používaných pro hodnocení podobnosti objektů a plánování pohybu. Prostřední část popisuje, jak jsou tyto metody použity pro zrychlení plánování s využitím získaných znalostí o prostředí. V poslední části jsou navržené metody porovnány s ostatními plánovači v nezávislém testu. Námi navržené algoritmy se v experimentech ukázaly být často rychlejší v porovnání s ostatními plánovači. Také často nacházely cesty v prostředích, kde ostatní plánovače nebyly schopny cestu nalézt.Motion planning is one of the fundamental problems in robotics. This thesis combines the advances in motion planning and shape matching to improve planning speeds in static environments. The first part of this thesis covers current methods used in object similarity evaluation and motion planning. The middle part describes how these methods are used together to improve planning speeds by utilizing prior knowledge about the environment, along with additional modifications. In the last part, the proposed methods are tested against other state-of-the-art planners in an independent benchmarking facility. The proposed algorithms are shown to be faster than other planners in many cases, often finding paths in environments where the other planners are unable to

Efficient motion planning using generalized penetration depth computation

Motion planning is a fundamental problem in robotics and also arises in other applications including virtual prototyping, navigation, animation and computational structural biology. It has been extensively studied for more than three decades, though most practical algorithms are based on randomized sampling. In this dissertation, we address two main issues that arise with respect to these algorithms: (1) there are no good practical approaches to check for path non-existence even for low degree-of-freedom (DOF) robots; (2) the performance of sampling-based planners can degrade if the free space of a robot has narrow passages. In order to develop effective algorithms to deal with these problems, we use the concept of penetration depth (PD) computation. By quantifying the extent of the intersection between overlapping models (e.g. a robot and an obstacle), PD can provide a distance measure for the configuration space obstacle (C-obstacle). We extend the prior notion of translational PD to generalized PD, which takes into account translational as well as rotational motion to separate two overlapping models. Moreover, we formulate generalized PD computation based on appropriate model-dependent metrics and present two algorithms based on convex decomposition and local optimization. We highlight the efficiency and robustness of our PD algorithms on many complex 3D models. Based on generalized PD computation, we present the first set of practical algorithms for low DOF complete motion planning. Moreover, we use generalized PD computation to develop a retraction-based planner to effectively generate samples in narrow passages for rigid robots. The effectiveness of the resulting planner is shown by alpha puzzle benchmark and part disassembly benchmarks in virtual prototyping

Workspace-based sampling for probabilistic path planning

Ph.DDOCTOR OF PHILOSOPH

3D Motion Planning using Kinodynamically Feasible Motion Primitives in Unknown Environments

Autonomous vehicles are a great asset to society by helping perform many dangerous or tedious tasks. They have already been successfully employed for many practical applications, such as search and rescue, automated surveillance, exploration and mapping, sample collection, and remote inspection. In order to perform most tasks autonomously, the vehicle must be able to safely and efficiently navigate through its environment. The algorithms and techniques that allow an autonomous vehicle to find traversable paths to its destination defines the set of problems in robotics known as motion planning. This thesis presents a new motion planner that is capable of finding collision-free paths through an unknown environment while satisfying the kinodynamic constraints of the vehicle. This is done using a two step process. In the first step, a collision-free path is generated using a modified Probabilistic Roadmap (PRM) based planner by assuming unexplored areas are obstacle-free. As obstacles are detected, the planner will replan the path as necessary to ensure that it remains collision-free. In complex environments, it is often necessary to increase the size of the PRM graph during the replanning step so that the graph remains connected. However, this causes the algorithm to slow down significantly over time. To mitigate these issues, the novel local sampling and PRM regeneration techniques are used to increase the computational efficiency of the replanning step. The local sampling technique biases the search towards the neighborhood of the obstacle blocking the path. This encourages the planner to generate small detours around the obstacle instead of rerouting the whole path. The PRM regeneration technique is used to remove all non-critical nodes from the PRM graph. This is used to bound the size of the PRM graph so that it does not grow increasingly large over time. In the second step, the collision-free path is transformed into a series of kinodynamically feasible motion primitives using two novel algorithms: the heuristic re-sampling algorithm and the transformation algorithm. The heuristic re-sampling algorithm is a greedy heuristic algorithm that increases the clearance around the path while removing redundant segments. This algorithm can be applied to any piece-wise linear path, and is guaranteed to produce a solution that is at least as good as the initial path. The transformation algorithm is a method to convert a path into a series of kinodynamically feasible motion primitives. It is extremely efficient computationally, and can be applied to any piece-wise linear path. To achieve good computational performance with PRM based planners, it is necessary to use sampling strategies that can efficiently form connected graphs through narrow and complex regions of the configuration space. Many proposed sampling methods attempt to bias the sample density in favor of these difficult to connect areas. However, these methods do not distinguish between samples that lie inside narrow passages and those that lie along convex borders. The orthogonal bridge test is a novel sampling technique that can identify and reject samples that lie along convex borders. This allows connected PRM graphs to be constructed with fewer nodes, which leads to less collision checking and reduced runtimes. The presented algorithms are experimentally verified using an AR.Drone quadrotor unmanned aerial vehicle (UAV) and a custom built skid-steer unmanned ground vehicle (UGV). Using a simple kinematic model and a basic position controller, the AR.Drone is able to traverse a series of motion primitives with less than 0.3 m of crosstrack error. The skid-steer UGV is able to navigate through unknown environments filled with obstacles to reach a desired destination. Furthermore, the observed runtimes of the proposed motion planner suggest that it is fully capable of computing solution paths online. This is an important result, because online computation is necessary for efficient autonomous operations and it can not be achieved with many existing kinodynamic motion planners

On learning task-directed motion plans

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.Includes bibliographical references (p. 119-129).Robotic motion planning is a hard problem for robots with more than just a few degrees of freedom. Modern probabilistic planners are able to solve many problems very quickly, but for difficult problems, they are still unacceptably slow for many applications. This thesis concerns the use of previous planning experience to allow the agent to generate motion plans very quickly when faced with new but related problems. We first investigate a technique for learning from previous experience by simply remembering past solutions and applying them where relevant to new problems. We find that this approach is useful in environments with very low variability in obstacle placement and task endpoints, and that it is important to keep the set of stored plans small to improve performance. However, we would like to be able to better generalize our previous experience so we next investigate a technique for learning parameterized motion plans. A parameterized motion plan is a function from planning problem parameters to a motion plan. In our approach, we learn a set of parameterized subpaths, which we can use as suggestions for a probabilistic planner, leading to substantially reduced planning times. We find that this technique is successful in several standard motion planning domains. However, as the domains get more complex, the technique produces less of an advantage. We discover that the learning problem as we have posed it is likely to be intractible, and that the complexity of the problem is due to the redundancy of the robotics platform. We suggest several possible approaches for addressing this problem as future work.by Sarah J. Finney.Ph.D

Méthode interactive et par l'apprentissage pour la generation de trajectoire en conception du produit

The accessibility is an important factor considered in the validation and verification phase of the product design and usually dominates the time and costs in this phase. Defining the accessibility verification as the motion planning problem, the sampling based motion planners gained success in the past fifteen years. However, the performances of them are usually shackled by the narrow passage problem arising when complex assemblies are composed of large number of parts, which often leads to scenes with high obstacle densities. Unfortunately, humans’ manual manipulations in the narrow passage always show much more difficulties due to the limitations of the interactive devices or the cognitive ability. Meanwhile, the challenges of analyzing the end users’ response in the design process promote the integration with the direct participation of designers.In order to accelerate the path planning in the narrow passage and find the path complying with user’s preferences, a novel interactive motion planning method is proposed. In this method, the integration with a random retraction process helps reduce the difficulty of manual manipulations in the complex assembly/disassembly tasks and provide local guidance to the sampling based planners. Then a hypothesis is proposed about the correlation between the topological structure of the scenario and the motion path in the narrow passage. The topological structure refers to the medial axis (2D) and curve skeleton (3D) with branches pruned. The correlation runs in an opposite manner to the sampling based method and provide a new perspective to solve the narrow passage problem. The curve matching method is used to explore this correlation and an interactive motion planning framework that can learn from experience is constructed in this thesis. We highlight the performance of our framework on a challenging problem in 2D, in which a non-convex object passes through a cluttered environment filled with randomly shaped and located non-convex obstacles.L'accessibilitéest un facteur important pris en compte dans la validation et la vérification en phase de conception du produit et augmente généralement le temps et les coûts de cette phase. Ce domaine de recherche a eu un regain d’intérêt ces quinze dernières années avec notamment de nouveaux planificateurs de mouvement. Cependant, les performances de ces méthodes sont généralement très faibles lorsque le problème se caractérise par des passages étroits des assemblages complexes composées d'un grand nombre de pièces. Cela conduit souvent àdes scènes àforte densitéd'obstacles. Malheureusement, les manipulations manuelles des humains dans le passage étroit montrent toujours beaucoup de difficultés en raison des limitations des dispositifs interactifs ou la capacitécognitive. Pendant ce temps, les défis de l'analyse de la réponse finale des utilisateurs dans le processus de conception promeut l'intégration avec la participation directe des concepteurs.Afin d'accélérer la planification dans le passage étroit et trouver le chemin le plus conforme aux préférences de l'utilisateur, une nouvelle méthode de planification de mouvement interactif est proposée. Nous avons soulignéla performance de notre algorithme dans certains scénarios difficiles en 2D et 3D environnement.Ensuite, une hypothèse est proposésur la corrélation entre la structure topologique du scénario et la trajectoire dans le passage étroit. La méthode basée sur les courbures est utilisée pour explorer cette corrélation et un cadre de planification de mouvement interactif qui peut apprendre de l'expérience est construit dans cette thèse. Nous soulignons la performance de notre cadre sur un problème difficile en 2D, dans lequel un objet non-convexe passe à travers un environnement encombrérempli d'obstacles non-convexes de forme aléatoire et situés

Método de muestreo adaptativo basado en el análisis de componentes principales para la planificación de movimientos de un sistema robótico (brazo-mano)

El presente tema de tesis presenta un nuevo método de muestreo adaptativo basado en el análisis de componentes principales (PCA). El método de muestreo es iterativo y se basa en ir adaptando periódicamente la base del espacio de configuraciones del sistema robótico usado para la obtención de las muestras, a partir del análisis de componentes principales de las muestras libres de colisión obtenidas hasta el momento. Al método de muestreo se aplicara a un planificador del tipo PRM (Probalistic RoadMap Method). El desarrollo, se ha realizado en dos partes, la primera parte consiste en implementar el método de muestreo propuesto, realizando ejemplos y pruebas para garantizar la viabilidad de dicho método. La segunda parte está enfocada en optimizar la planificación de movimientos aplicando un PRM PCA (usa el método de muestreo desarrollado en la primera parte) el cual se aplica a un sistema robótico brazo-mano (brazo robot Stäubli TX90 de seis grados de libertad, equipado con una mano mecánica Shunk SAH de 13 grados de libertad), con una configuración final de aprehensión constreñida. A sí mismo para realizar una comparación y verificar el rendimiento del PRM PCA, se ha implementado un PRM Gaussiano (basado en muestreo Gaussiano), el cual tiene características similares para solucionar problemas de planificación de movimientos en espacios reducidos o pasajes estrechos. Ambos PRMs (PCA y Gaussiano) han sido bien implementados dentro del entorno de programación para aplicaciones de planificación The Kautham Project, desarrollado en el Instituto de Organización y Control de Sistemas Industriales (IOC-UPC)