A discretization result for some optimization problems in framework spaces with polyhedral obstacles and the Manhattan metric

In this work we consider the shortest path problem and the single facility Weber location problem in any real space of finite dimension where there exist different types of polyhedral obstacles or forbidden regions. These regions are polyhedral sets and the metric considered in the space is the Manhattan metric. We present a result that reduce these continuous problems into problems in a “add hoc” graph, where the original problems can be solved using elementary techniques of Graph Theory. We show that, fixed the dimension of the space, both the reduction and the resolution can be done in polynomial time.Ministerio de Economía and CompetitividadFondo Europeo de Desarrollo Regiona

Geometric-based Optimization Algorithms for Cable Routing and Branching in Cluttered Environments

The need for designing lighter and more compact systems often leaves limited space for planning routes for the connectors that enable interactions among the system’s components. Finding optimal routes for these connectors in a densely populated environment left behind at the detail design stage has been a challenging problem for decades. A variety of deterministic as well as heuristic methods has been developed to address different instances of this problem. While the focus of the deterministic methods is primarily on the optimality of the final solution, the heuristics offer acceptable solutions, especially for such problems, in a reasonable amount of time without guaranteeing to find optimal solutions. This study is an attempt to furthering the efforts in deterministic optimization methods to tackle the routing problem in two and three dimensions by focusing on the optimality of final solutions. The objective of this research is twofold. First, a mathematical framework is proposed for the optimization of the layout of wiring connectors in planar cluttered environments. The problem looks at finding the optimal tree network that spans multiple components to be connected with the aim of minimizing the overall length of the connectors while maximizing their common length (for maintainability and traceability of connectors). The optimization problem is formulated as a bi-objective problem and two solution methods are proposed: (1) to solve for the optimal locations of a known number of breakouts (where the connectors branch out) using mixed-binary optimization and visibility notion and (2) to find the minimum length tree that spans multiple components of the system and generates the optimal layout using the previously-developed convex hull based routing. The computational performance of these methods in solving a variety of problems is further evaluated. Second, the problem of finding the shortest route connecting two given nodes in a 3D cluttered environment is considered and addressed through deterministically generating a graphical representation of the collision-free space and searching for the shortest path on the found graph. The method is tested on sample workspaces with scattered convex polyhedra and its computational performance is evaluated. The work demonstrates the NP-hardness aspect of the problem which becomes quickly intractable as added components or increase in facets are considered

Trajectory planning for industrial robot using genetic algorithms

En las últimas décadas, debido la importancia de sus aplicaciones, se han propuesto muchas investigaciones sobre la planificación de caminos y trayectorias para los manipuladores, algunos de los ámbitos en los que pueden encontrarse ejemplos de aplicación son; la robótica industrial, sistemas autónomos, creación de prototipos virtuales y diseño de fármacos asistido por ordenador. Por otro lado, los algoritmos evolutivos se han aplicado en muchos campos, lo que motiva el interés del autor por investigar sobre su aplicación a la planificación de caminos y trayectorias en robots industriales. En este trabajo se ha llevado a cabo una búsqueda exhaustiva de la literatura existente relacionada con la tesis, que ha servido para crear una completa base de datos utilizada para realizar un examen detallado de la evolución histórica desde sus orígenes al estado actual de la técnica y las últimas tendencias. Esta tesis presenta una nueva metodología que utiliza algoritmos genéticos para desarrollar y evaluar técnicas para la planificación de caminos y trayectorias. El conocimiento de problemas específicos y el conocimiento heurístico se incorporan a la codificación, la evaluación y los operadores genéticos del algoritmo. Esta metodología introduce nuevos enfoques con el objetivo de resolver el problema de la planificación de caminos y la planificación de trayectorias para sistemas robóticos industriales que operan en entornos 3D con obstáculos estáticos, y que ha llevado a la creación de dos algoritmos (de alguna manera similares, con algunas variaciones), que son capaces de resolver los problemas de planificación mencionados. El modelado de los obstáculos se ha realizado mediante el uso de combinaciones de objetos geométricos simples (esferas, cilindros, y los planos), de modo que se obtiene un algoritmo eficiente para la prevención de colisiones. El algoritmo de planificación de caminos se basa en técnicas de optimización globales, usando algoritmos genéticos para minimizar una función objetivo considerando restricciones para evitar las colisiones con los obstáculos. El camino está compuesto de configuraciones adyacentes obtenidas mediante una técnica de optimización construida con algoritmos genéticos, buscando minimizar una función multiobjetivo donde intervienen la distancia entre los puntos significativos de las dos configuraciones adyacentes, así como la distancia desde los puntos de la configuración actual a la final. El planteamiento del problema mediante algoritmos genéticos requiere de una modelización acorde al procedimiento, definiendo los individuos y operadores capaces de proporcionar soluciones eficientes para el problema.Abu-Dakka, FJM. (2011). Trajectory planning for industrial robot using genetic algorithms [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/10294Palanci

Minimum time kinematic trajectories for self-propelled rigid bodies in the unobstructed plane

The problem of moving rigid bodies efficiently is of particular interest in robotics because the simplest model of a mobile robot or of a manipulated object is often a rigid body. Path planning, controller design and robot design may all benefit from precise knowledge of optimal trajectories for a set of permitted controls. In this work, we present a general solution to the problem of finding minimum time trajectories for an arbitrary self-propelled, velocity-bounded rigid body in the obstacle-free plane. Such minimum-time trajectories depend on the vehicle’s capabilities and on and the start and goal configurations. For example, the fastest way to move a car sideways might be to execute a parallel-parking motion. The fastest longdistance trajectories for a wheelchair-like vehicle might be of a turn-drive-turn variety. Our analysis reveals a wide variety of types of optimal trajectories. We determine an exhaustive taxonomy of optimal trajectory types, presented as a branching tree. For each of the necessary leaf nodes, we develop a specific algorithm to find the fastest trajectory in that node. The fastest trajectory overall is drawn from this set

Enhanced online programming for industrial robots

The use of robots and automation levels in the industrial sector is expected to grow, and is driven by the on-going need for lower costs and enhanced productivity. The manufacturing industry continues to seek ways of realizing enhanced production, and the programming of articulated production robots has been identified as a major area for improvement. However, realizing this automation level increase requires capable programming and control technologies. Many industries employ offline-programming which operates within a manually controlled and specific work environment. This is especially true within the high-volume automotive industry, particularly in high-speed assembly and component handling. For small-batch manufacturing and small to medium-sized enterprises, online programming continues to play an important role, but the complexity of programming remains a major obstacle for automation using industrial robots. Scenarios that rely on manual data input based on real world obstructions require that entire production systems cease for significant time periods while data is being manipulated, leading to financial losses. The application of simulation tools generate discrete portions of the total robot trajectories, while requiring manual inputs to link paths associated with different activities. Human input is also required to correct inaccuracies and errors resulting from unknowns and falsehoods in the environment. This study developed a new supported online robot programming approach, which is implemented as a robot control program. By applying online and offline programming in addition to appropriate manual robot control techniques, disadvantages such as manual pre-processing times and production downtimes have been either reduced or completely eliminated. The industrial requirements were evaluated considering modern manufacturing aspects. A cell-based Voronoi generation algorithm within a probabilistic world model has been introduced, together with a trajectory planner and an appropriate human machine interface. The robot programs so achieved are comparable to manually programmed robot programs and the results for a Mitsubishi RV-2AJ five-axis industrial robot are presented. Automated workspace analysis techniques and trajectory smoothing are used to accomplish this. The new robot control program considers the working production environment as a single and complete workspace. Non-productive time is required, but unlike previously reported approaches, this is achieved automatically and in a timely manner. As such, the actual cell-learning time is minimal

Metalevel Motion Planning for Unmanned Aircraft Systems: Metrics Definition and Algorithm Selection

A diverse suite of manned and unmanned aircraft will occupy future urban airspace. Flight plans must accommodate specific aircraft characteristics, including physical volume with safety zone clearance, landing/takeoff procedures, kinodynamics, and a wide range of flight environments. No single motion planner is applicable across all possible aircraft configurations and operating conditions. This dissertation proposes the first motion planning algorithm selection capability with application to small Unmanned Aircraft System (UAS) multicopters operating in and over a complex urban landscape. Alternative data-driven fail-safe protocols are presented to improve on contemporary ``fly-home'' or automatic landing protocols, focusing on rooftops as safe urban landing sites. In a fail-safe direct strategy, the multicopter identifies, generates, and follows a flight plan to the closest available rooftop suitable for landing. In a fail-safe supervisory strategy, the multicopter examines rooftops en route to a planned landing site, diverting to a closer, clear landing site when possible. In a fail-safe coverage strategy, the multicopter cannot preplan a safe landing site due to missing data. The multicopter executes a coverage path to explore the area and evaluate overflown rooftops to find a safe landing site. These three fail-safe algorithms integrate map generation, flight planning, and area coverage capabilities. The motion planning algorithm selection problem (ASP) requires qualitative and quantitative metrics to inform the ASP of user/agent, algorithm, and configuration space preferences and constraints. Urban flight map-based, path-based, and software-based cost metrics are defined to provide insights into the urban canyon properties needed to construct safe and efficient flight plans. Map-based metrics describe the operating environment by constructing a collection of GPS/Lidar navigation performance, population density, and obstacle risk exposure metric maps. Path-based metrics account for a vehicle's energy consumption and distance traveled. Software-based metrics measure memory consumption and execution time of an algorithm. The proposed metrics provide pre-flight insights typically ignored by obstacle-only planning environment definitions. An algorithm portfolio consisting of geometric (Point-to-Point: PTP), graph-based (A* variants), and sampling-based (BIT* variants) motion planners were considered in this work. Path cost, execution time, and success rate benchmarks were investigated using Monte Carlo problem instances with A* "plus" producing the lowest cost paths, PTP having the fastest executions, and A* "dist" having the best overall success rates. The BIT* variant paths typically had higher cost but their success rate increased relative to altitude. The problem instances and metric maps informed two new machine learning solutions for urban small UAS motion planning ASP. Rule-based decision trees were simple to construct but unable to capture both complex cost metrics and algorithm properties. The investigated neural network-based ASP formulations produced promising results, with a hybrid two-stage selection scheme having the best algorithm selection accuracy, laying the seeds for future work. The most significant innovation of this dissertation is motion planning ASP for UAS. Non-traditional open-source databases also advance the field of data-driven flight planning, contributing to fail-safe UAS operations as well as ASP. Path planning algorithms integrated a new suite of diverse cost metrics accompanied by a novel multi-objective admissible heuristic function. Neural network and decision tree ASP options were presented and evaluated as a first-case practical approach to solving the motion planning ASP for small UAS urban flight.PHDRoboticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/168060/1/cosme_1.pd

ADAPTIVE PROBABILISTIC ROADMAP CONSTRUCTION WITH MULTI-HEURISTIC LOCAL PLANNING

The motion planning problem means the computation of a collision-free motion for a movable object among obstacles from the given initial placement to the given end placement. Efficient motion planning methods have many applications in many fields, such as robotics, computer aided design, and pharmacology. The problem is known to be PSPACE-hard. Because of the computational complexity, practical applications often use heuristic or incomplete algorithms. Probabilistic roadmap is a probabilistically complete motion planning method that has been an object of intensive study over the past years. The method is known to be susceptible to the problem of “narrow passages”: Finding a motion that passes a narrow, winding tunnel can be very expensive. This thesis presents a probabilistic roadmap method that addresses the narrow passage problem with a local planner based on heuristic search. The algorithm is suitable for planning motions for rigid bodies and articulated robots including multirobot systems with many degrees-of-freedom. Variants of the algorithm are describe

Automatic motion of manipulator using sampling based motion planning algorithms - application in service robotics

The thesis presents new approaches for autonomous motion execution of a robotic arm. The calculation of the motion is called motion planning and requires the computation of robot arm's path. The text covers the calculation of the path and several algorithms have been therefore implemented and tested in several real scenarios. The work focuses on sampling based planners, which means that the path is created by connecting explicitly random generated points in the free space. The algorithms can be divided into three categories: those that are working in configuration space(C-Space)(C- Space is the set of all possible joint angles of a robotic arm) , the mixed approaches using both Cartesian and C-Space and those that are using only the Cartesian space. Although Cartesian space seems more appropriate, due to dimensionality, this work illustrates that the C-Space planners can achieve comparable or better results. Initially an enhanced approach for efficient collision detection in C-Space, used by the planners, is presented. Afterwards the N dimensional cuboid region, notated as Rq, is defined. The Rq configures the C-Space so that the sampling is done close to a selected, called center, cell. The approach is enhanced by the decomposition of the Cartesian space into cells. A cell is selected appropriately if: (a) is closer to the target position and (b) lies inside the constraints. Inverse kinematics(IK) are applied to calculate a centre configuration used later by the Rq. The CellBiRRT is proposed and combines all the features. Continuously mixed approaches that do not require goal configuration or an analytic solution of IK are presented. Rq regions as well as Cells are also integrated in these approaches. A Cartesian sampling based planner using quaternions for linear interpolation is also proposed and tested. The common feature of the so far algorithms is the feasibility which is normally against the optimality. Therefore an additional part of this work deals with the optimality of the path. An enhanced approach of CellBiRRT, called CellBiRRT*, is developed and promises to compute shorter paths in a reasonable time. An on-line method using both CellBiRRT and CellBiRRT* is proposed where the path of the robot arm is improved and recalculated even if sudden changes in the environment are detected. Benchmarking with the state of the art algorithms show the good performance of the proposed approaches. The good performance makes the algorithms suitable for real time applications. In this work several applications are described: Manipulative skills, an approach for an semi-autonomous control of the robot arm and a motion planning library. The motion planning library provides the necessary interface for easy use and further development of the motion planning algorithms. It can be used as the part connecting the manipulative skill designing and the motion of a robotic arm

Learning to Optimize: from Theory to Practice

Optimization is at the heart of everyday applications, from finding the fastest route for navigation to designing efficient drugs for diseases. The study of optimization algorithms has focused on developing general approaches that do not adapt to specific problem instances. While they enjoy wide applicability, they forgo the potentially useful information embedded in the structure of an instance. Furthermore, as new optimization problems appear, the algorithm development process relies heavily on domain expertise to identify special properties and design methods to exploit them. Such design philosophy is labor-intensive and difficult to deploy efficiently to a broad range of domain-specific optimization problems, which are becoming ubiquitous in the pursuit of ever more personalized applications. In this dissertation, we consider different hybrid versions of classical optimization algorithms with data-driven techniques. We aim to equip classical algorithms with the ability to adapt their behaviors on the fly based on specific problem instances. A common theme in our approaches is to train the data-driven components on a pre-collected batch of representative problem instances to optimize some performance metrics, e.g., wall-clock time. Varying the integration details, we present several approaches to learning data-driven optimization modules for combinatorial optimization problems and study the corresponding fundamental research questions on policy learning. We provide multiple practical experimental results to showcase the practicality of our methods which lead to state-of-the-art performance on some classes of problems.</p