An n log n algorithm for determining the congruity of polyhedra

AbstractThis paper describes an algorithm for determining whether two polyhedra are congruent. The asymptotic time complexity of the algorithm is bounded by a constant times n log n where n is the number of edges of the polyhedra, It is also shown that under some conditions the problem of partial congruity can be solved in O(n2) time

Coverage & cooperation: Completing complex tasks as quickly as possible using teams of robots

As the robotics industry grows and robots enter our homes and public spaces, they are increasingly expected to work in cooperation with each other. My thesis focuses on multirobot planning, specifically in the context of coverage robots, such as robotic lawnmowers and vacuum cleaners. Two problems unique to multirobot teams are task allocation and search. I present a task allocation algorithm which balances the workload amongst all robots in the team with the objective of minimizing the overall mission time. I also present a search algorithm which robots can use to find lost teammates. It uses a probabilistic belief of a target robot’s position to create a planning tree and then searches by following the best path in the tree. For robust multirobot coverage, I use both the task allocation and search algorithms. First the coverage region is divided into a set of small coverage tasks which minimize the number of turns the robots will need to take. These tasks are then allocated to individual robots. During the mission, robots replan with nearby robots to rebalance the workload and, once a robot has finished its tasks, it searches for teammates to help them finish their tasks faster

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

Formation Control of Localised and Decentralised Robotic Swarms

Robot swarms consist of multiple autonomous robots, which detect and interact with their local environments. The fundamental intelligence is observed when a chaotic swarm reaches a stable and orderly objective formation. The process is important because the objective formation is designed such that the swarm achieves more than the sum of its individuals. A formation is a set of positions or tasks, and intelligent swarms are capable of self-organising and task allocating. Given an objective formation, individuals of a swarm reach different objective positions and perform different tasks. This implies task allocation in different possible choices. For each individual, the path to its objective position is regarded as the efort to take, and the inclination to different objective tasks means different eforts. The challenge is that it needs to choose wisely in the interaction with its neighbourhood. Changes of choices are compromises and each progress to the objective position imposes in uence on its neighbourhood. The collective intelligence comes from series of individual decisions in the process. In this thesis, we consider four problems that arise with the challenge. We use techniques from graph theory and agent-based design to address them. Formation control algorithms should not impose heavy burden in the communication network. Thus, to start with, limited sensing and communication are assumed, and the robots have minimal access to each other's identity through locally established channels. The control strategy is proposed based on local optimisation and multi-object mapping for a team of robots. Robots are able to make mapping decisions based on local information. To achieve the local optimal mapping decisions for each robot, two novel multi-object mapping protocols are designed. The first protocol performs confict locating and resolving, and the second adopts a most-neighbour mapping strategy. The formation problem is further addressed for a scalable team of robots subject to limited sensing with no communication. The robots themselves are fully independent with no designated roles. Scalable objective formation design is proposed such that the robot formation is scalable. Under the assumption that the data transmission among the robots is not available, a novel controller and a protocol are designed that do not rely on communication. As the controller only drives the robots to a partially desired formation, a distributed coordination protocol is proposed to resolve the imperfections. The case is investigated where the objective formations are arbitrary and have fixed sizes. Multi-objective mapping is proposed for the individual robots to identify their positions in the objective formation. The fixed formation size induces mapping loops, and to avoid local optimum traps, an evaluation method imposes a weak restriction on the predened formation, rendering it almost arbitrary. To enhance the robustness, the minimal local topology is proposed, and to reduce the computation burden and avoid the infnite trajectory loop, the coordination protocol is modifed by introducing probability. The practical problem of collision avoidance is also studied. The leaderfollower scheme is implemented on a multi-robot platform. On the premise of coordinated control laws, globally desired formation is achieved. The same problem in the path-planning perspective is considered on a global scale. Disc obstacles are filtered and clusters are identified based on their intersections. The path planning algorithm is designed based on obstacle clusters.Thesis (Ph.D.) -- University of Adelaide, School of Electrical & Electronic Engineering, 201

An intelligent, free-flying robot

The ground based demonstration of the extensive extravehicular activity (EVA) Retriever, a voice-supervised, intelligent, free flying robot, is designed to evaluate the capability to retrieve objects (astronauts, equipment, and tools) which have accidentally separated from the Space Station. The major objective of the EVA Retriever Project is to design, develop, and evaluate an integrated robotic hardware and on-board software system which autonomously: (1) performs system activation and check-out; (2) searches for and acquires the target; (3) plans and executes a rendezvous while continuously tracking the target; (4) avoids stationary and moving obstacles; (5) reaches for and grapples the target; (6) returns to transfer the object; and (7) returns to base