Shortest Dubins Path to a Circle

The Dubins path problem had enormous applications in path planning for autonomous vehicles. In this paper, we consider a generalization of the Dubins path planning problem, which is to find a shortest Dubins path that starts from a given initial position and heading, and ends on a given target circle with the heading in the tangential direction. This problem has direct applications in Dubins neighborhood traveling salesman problem, obstacle avoidance Dubins path planning problem etc. We characterize the length of the four CSC paths as a function of angular position on the target circle, and derive the conditions which to find the shortest Dubins path to the target circle

Perception-driven sparse graphs for optimal motion planning

Most existing motion planning algorithms assume that a map (of some quality) is fully determined prior to generating a motion plan. In many emerging applications of robotics, e.g., fast-moving agile aerial robots with constrained embedded computational platforms and visual sensors, dense maps of the world are not immediately available, and they are computationally expensive to construct. We propose a new algorithm for generating plan graphs which couples the perception and motion planning processes for computational efficiency. In a nutshell, the proposed algorithm iteratively switches between the planning sub-problem and the mapping sub-problem, each updating based on the other until a valid trajectory is found. The resulting trajectory retains a provable property of providing an optimal trajectory with respect to the full (unmapped) environment, while utilizing only a fraction of the sensing data in computational experiments.Comment: 2018 IEEE/RSJ International Conference on Intelligent Robots and System

Multi-Goal Path Planning for Spray Writing with Unmanned Aerial Vehicle

Tato práce se zabývá plánováním přes více cílů pro bezpilotní vzdušné prostředky v úloze psaní textu. Motivací je použití bezpilotní helikoptéry k preciznímu sprejování nápisů například na střechy průmyslových budov. Problém psaní textu bezpilotní helikoptérou formulujeme jako plánování přes více cílů a navrhujeme nový font vhodný pro tuto aplikaci. Helikoptéra poté musí při psaní nápisu letět podél zadaného textu s využitím navrhovaného fontu. Problém hledání cesty podél textu lze formulovat jako zobecnění problému obchodního cestujícího, kde trajektorie spojující jednotlivé segmenty písmen musí respektovat dynamická omezení helikoptéry. Na spojení segmentů písmen je použit model Dubinsova vozítka, který umožňuje průlet nalezené trajektorie konstantní rychlostí bez brzdících manévrů. Navržená metoda plánování byla otestována v realistickém simulátoru a experimenty ukazují její použitelnost pro vícerotorovou helikoptéru v úloze psaní textu.This thesis describes the multi-goal path planning method for an Unmanned Aerial Vehicle (UAV) feasible for the spray writing task. The motivation is to use an autonomous UAV for precise spray writing on, e.g., roofs of industrial buildings. We formulate the writing with the UAV as a multi-goal path planning problem, and therefore, a new font suitable for the multi-goal path planning has been designed. In order to perform writing, the UAV has to travel along the input text characters. The problem can be formulated as the generalized traveling salesman problem, in which trajectories between input text segments respect the UAV constraints. We employed the Dubins vehicle to connect input text segments that allow us to traverse the final trajectory on constant speed without sharp and braking maneuvers. The implemented method has been tested in a realistic simulation environment. The experiments showed that the proposed method is feasible for the considered multirotor UAV

Optimal Spherical Geodesic Curvature Constrained Paths

Path planning for vehicles is an essential study that must be undertaken to make good use of resources such as fuel (which is always a limited resource) to ascertain that a vehicle/robot completes its mission efficiently. The current study deals with the path planning of a Dubins’ vehicle on a sphere. A Dubins’ vehicle is one that moves only forwards, with a constant speed and with a minimum turning radius constraint; and is named after L.E. Dubins due to his seminal work [1] on the nature of optimal curves in the plane. The result being that optimal paths must be of the following types only: CSC, CCC, SC, CS, CC, or C can be optimal. This study aims to understand the nature of optimality of the Dubins’ type paths on a sphere. The main tools employed are Pontryagin’s Minimum Principle and the Sabban frame (same setup as in Monroy-Pérez’s work [2]). The final result obtained as a result of analytical study and corroboration with numerical computation is that Dubins’ type paths are optimal on the sphere for r in the interval (0,(1/sqrt(2))] on account of the CCCC type path being non-optimal in the same interval

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