Exploration autonome et efficiente de chantiers miniers souterrains inconnus avec un drone filaire

Abstract: Underground mining stopes are often mapped using a sensor located at the end of a pole that the operator introduces into the stope from a secure area. The sensor emits laser beams that provide the distance to a detected wall, thus creating a 3D map. This produces shadow zones and a low point density on the distant walls. To address these challenges, a research team from the Université de Sherbrooke is designing a tethered drone equipped with a rotating LiDAR for this mission, thus benefiting from several points of view. The wired transmission allows for unlimited flight time, shared computing, and real-time communication. For compatibility with the movement of the drone after tether entanglements, the excess length is integrated into an onboard spool, contributing to the drone payload. During manual piloting, the human factor causes problems in the perception and comprehension of a virtual 3D environment, as well as the execution of an optimal mission. This thesis focuses on autonomous navigation in two aspects: path planning and exploration. The system must compute a trajectory that maps the entire environment, minimizing the mission time and respecting the maximum onboard tether length. Path planning using a Rapidly-exploring Random Tree (RRT) quickly finds a feasible path, but the optimization is computationally expensive and the performance is variable and unpredictable. Exploration by the frontier method is representative of the space to be explored and the path can be optimized by solving a Traveling Salesman Problem (TSP) but existing techniques for a tethered drone only consider the 2D case and do not optimize the global path. To meet these challenges, this thesis presents two new algorithms. The first one, RRT-Rope, produces an equal or shorter path than existing algorithms in a significantly shorter computation time, up to 70% faster than the next best algorithm in a representative environment. A modified version of RRT-connect computes a feasible path, shortened with a deterministic technique that takes advantage of previously added intermediate nodes. The second algorithm, TAPE, is the first 3D cavity exploration method that focuses on minimizing mission time and unwound tether length. On average, the overall path is 4% longer than the method that solves the TSP, but the tether remains under the allowed length in 100% of the simulated cases, compared to 53% with the initial method. The approach uses a 2-level hierarchical architecture: global planning solves a TSP after frontier extraction, and local planning minimizes the path cost and tether length via a decision function. The integration of these two tools in the NetherDrone produces an intelligent system for autonomous exploration, with semi-autonomous features for operator interaction. This work opens the door to new navigation approaches in the field of inspection, mapping, and Search and Rescue missions.La cartographie des chantiers miniers souterrains est souvent réalisée à l’aide d’un capteur situé au bout d’une perche que l’opérateur introduit dans le chantier, depuis une zone sécurisée. Le capteur émet des faisceaux laser qui fournissent la distance à un mur détecté, créant ainsi une carte en 3D. Ceci produit des zones d’ombres et une faible densité de points sur les parois éloignées. Pour relever ces défis, une équipe de recherche de l’Université de Sherbrooke conçoit un drone filaire équipé d’un LiDAR rotatif pour cette mission, bénéficiant ainsi de plusieurs points de vue. La transmission filaire permet un temps de vol illimité, un partage de calcul et une communication en temps réel. Pour une compatibilité avec le mouvement du drone lors des coincements du fil, la longueur excédante est intégrée dans une bobine embarquée, qui contribue à la charge utile du drone. Lors d’un pilotage manuel, le facteur humain entraîne des problèmes de perception et compréhension d’un environnement 3D virtuel, et d’exécution d’une mission optimale. Cette thèse se concentre sur la navigation autonome sous deux aspects : la planification de trajectoire et l’exploration. Le système doit calculer une trajectoire qui cartographie l’environnement complet, en minimisant le temps de mission et en respectant la longueur maximale de fil embarquée. La planification de trajectoire à l’aide d’un Rapidly-exploring Random Tree (RRT) trouve rapidement un chemin réalisable, mais l’optimisation est coûteuse en calcul et la performance est variable et imprévisible. L’exploration par la méthode des frontières est représentative de l’espace à explorer et le chemin peut être optimisé en résolvant un Traveling Salesman Problem (TSP), mais les techniques existantes pour un drone filaire ne considèrent que le cas 2D et n’optimisent pas le chemin global. Pour relever ces défis, cette thèse présente deux nouveaux algorithmes. Le premier, RRT-Rope, produit un chemin égal ou plus court que les algorithmes existants en un temps de calcul jusqu’à 70% plus court que le deuxième meilleur algorithme dans un environnement représentatif. Une version modifiée de RRT-connect calcule un chemin réalisable, raccourci avec une technique déterministe qui tire profit des noeuds intermédiaires préalablement ajoutés. Le deuxième algorithme, TAPE, est la première méthode d’exploration de cavités en 3D qui minimise le temps de mission et la longueur du fil déroulé. En moyenne, le trajet global est 4% plus long que la méthode qui résout le TSP, mais le fil reste sous la longueur autorisée dans 100% des cas simulés, contre 53% avec la méthode initiale. L’approche utilise une architecture hiérarchique à 2 niveaux : la planification globale résout un TSP après extraction des frontières, et la planification locale minimise le coût du chemin et la longueur de fil via une fonction de décision. L’intégration de ces deux outils dans le NetherDrone produit un système intelligent pour l’exploration autonome, doté de fonctionnalités semi-autonomes pour une interaction avec l’opérateur. Les travaux réalisés ouvrent la porte à de nouvelles approches de navigation dans le domaine des missions d’inspection, de cartographie et de recherche et sauvetage

Algorithmes pour le problème de repositionnement

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Robotic Path Planning for High-Level Tasks in Discrete Environments

This thesis proposes two techniques for solving high-level multi-robot motion planning problems with discrete environments. We focus on an important class of problems that require an allocation of spatially distributed tasks to robots, along with a set of efficient paths for the robots to visit their task locations. The first technique, SAT-TSP, models the problem with a framework that allows a natural coupling between the allocation problem and the path planning problem. The allocation problem is encoded as a Boolean Satisfiability problem (SAT) and the path planning problem is encoded as a Travelling Salesman Problem (TSP). In addition, this framework can handle complex constraints such as battery life limitations, robot carrying capacities, and robot-task incompatibilities. We propose an algorithm that leverages recent advances in Satisfiability Modulo Theory to combine state-of-the-art SAT and TSP solvers. We characterize the correctness of our algorithm and evaluate it in simulation on a series of patrolling, periodic routing, and multi-robot sample collection problems. The results show that our algorithm outperforms a state-of-the-art mathematical programming solver on a majority of the problems in our benchmark, especially the more difficult problems. The second technique, Gamma-Clustering, is used to reduce the computational effort of finding good solutions for metric discrete path planning problems. This technique can be used on the set of allocation path planning problems that do not have ordering constraints (ordering only affects the cost of the solution, not its feasibility). To obtain the computational savings, we find Gamma-Clusters within the problem's environment and then restrict how feasible paths visit these clusters. We prove that solutions found using this approach are within a constant factor of the optimal. By increasing the parameter Gamma we can improve the quality of the bound but we do so with less computational savings. We provide a simple polynomial-time algorithm for finding the optimal Gamma-Clustering and show that for a given Gamma the clustering is unique. We provide two methods for using Gamma-Clusters on path planning problems, a coupled method and a hierarchical method. We demonstrate the effectiveness of these methods on travelling salesman instances, sample collection problems, and period routing problems. The results show that for many instances we obtain significant reductions in computation time with little to no reduction in solution quality. Comparing these methods to a standard integer programming approach reveals that as the problems become more difficult, the solution quality of the two methods degrade at a slower rate than the standard approach, thus for more difficult instances we can use Gamma-Clustering to find higher quality solutions

Clustering-based Algorithms for Big Data Computations

In the age of big data, the amount of information that applications need to process often exceeds the computational capabilities of single machines. To cope with this deluge of data, new computational models have been defined. The MapReduce model allows the development of distributed algorithms targeted at large clusters, where each machine can only store a small fraction of the data. In the streaming model a single processor processes on-the-fly an incoming stream of data, using only limited memory. The specific characteristics of these models combined with the necessity of processing very large datasets rule out, in many cases, the adoption of known algorithmic strategies, prompting the development of new ones. In this context, clustering, the process of grouping together elements according to some proximity measure, is a valuable tool, which allows to build succinct summaries of the input data. In this thesis we develop novel algorithms for some fundamental problems, where clustering is a key ingredient to cope with very large instances or is itself the ultimate target. First, we consider the problem of approximating the diameter of an undirected graph, a fundamental metric in graph analytics, for which the known exact algorithms are too costly to use for very large inputs. We develop a MapReduce algorithm for this problem which, for the important class of graphs of bounded doubling dimension, features a polylogarithmic approximation guarantee, uses linear memory and executes in a number of parallel rounds that can be made sublinear in the input graph's diameter. To the best of our knowledge, ours is the first parallel algorithm with these guarantees. Our algorithm leverages a novel clustering primitive to extract a concise summary of the input graph on which to compute the diameter approximation. We complement our theoretical analysis with an extensive experimental evaluation, finding that our algorithm features an approximation quality significantly better than the theoretical upper bound and high scalability. Next, we consider the problem of clustering uncertain graphs, that is, graphs where each edge has a probability of existence, specified as part of the input. These graphs, whose applications range from biology to privacy in social networks, have an exponential number of possible deterministic realizations, which impose a big-data perspective. We develop the first algorithms for clustering uncertain graphs with provable approximation guarantees which aim at maximizing the probability that nodes be connected to the centers of their assigned clusters. A preliminary suite of experiments, provides evidence that the quality of the clusterings returned by our algorithms compare very favorably with respect to previous approaches with no theoretical guarantees. Finally, we deal with the problem of diversity maximization, which is a fundamental primitive in big data analytics: given a set of points in a metric space we are asked to provide a small subset maximizing some notion of diversity. We provide efficient streaming and MapReduce algorithms with approximation guarantees that can be made arbitrarily close to the ones of the best sequential algorithms available. The algorithms crucially rely on the use of a k-center clustering primitive to extract a succinct summary of the data and their analysis is expressed in terms of the doubling dimension of the input point set. Moreover, unlike previously known algorithms, ours feature an interesting tradeoff between approximation quality and memory requirements. Our theoretical findings are supported by the first experimental analysis of diversity maximization algorithms in streaming and MapReduce, which highlights the tradeoffs of our algorithms on both real-world and synthetic datasets. Moreover, our algorithms exhibit good scalability, and a significantly better performance than the approaches proposed in previous works

New Graph Algorithms via Polyhedral Techniques

In this thesis we give new algorithms for two fundamental graph problems. We develop novel ways of using linear programming formulations, even exponential-sized ones, to extract structure from problem instances and to guide algorithms in making progress. Somewhat surprisingly, similar polyhedral techniques can be harnessed in the two seemingly disparate settings. In the first part of the thesis we address a benchmark problem in combinatorial optimization: the asymmetric traveling salesman problem (ATSP). It consists in finding the shortest tour that visits all vertices of a given directed graph with weights on edges. Due to its NP-hardness, the theoretical study of algorithms for ATSP has focused on approximation algorithms: ones that are provably both efficient and give solutions competitive with the optimum. Specifically, a rho-approximation algorithm for ATSP is one that runs in polynomial time and always outputs a tour that is at most rho times longer than the shortest tour. Finding such an approximation algorithm with rho bounded (i.e., a constant factor) had been a long-standing open problem. In this thesis, we give such an algorithm. Our approximation guarantee is analyzed with respect to the standard linear programming relaxation, and thus our result also confirms the conjectured constant integrality gap of that relaxation. Our techniques build upon the constant-factor approximation algorithm for the special case of node-weighted metrics due to Svensson. In particular, we give a generic reduction to structured instances that resemble but are more general than those arising from node-weighted metrics. This reduction takes advantage of a laminar family of vertex sets that arises from the linear programming relaxation. In the second part of the thesis we address the perfect matching problem. The first polynomial-time algorithm for it, given by Edmonds in 1965, is historically associated with the introduction of the class P and our notion that ``polynomial-time'' means ``efficient''. That algorithm is sequential and deterministic. We have also known since the 1980s that the matching problem has efficient parallel algorithms if the use of randomness is allowed. Formally, it is in the class RNC, i.e., it has randomized algorithms that use polynomially many processors and run in polylogarithmic time. However, we do not know if randomness is necessary - that is, whether the matching problem is in the class NC. In this thesis we show that the matching problem is in quasi-NC. That is, we give a deterministic parallel algorithm that runs in O(log^3 n) time on n^{O(log^2 n)} processors. The result is obtained by a derandomization of the Isolation Lemma for perfect matchings, which was introduced in the classic paper by Mulmuley, Vazirani and Vazirani to obtain an RNC algorithm. Our proof extends the framework of Fenner, Gurjar and Thierauf, who proved the analogous result in the special case of bipartite graphs. Compared to that setting, several new ingredients are needed due to the significantly more complex structure of perfect matchings in general graphs. In particular, our proof heavily relies on the laminar structure of the faces of the perfect matching polytope