Minimizing the error of linear separators on linearly inseparable data

Given linearly inseparable sets R of red points and B of blue points, we consider several measures of how far they are from being separable. Intuitively, given a potential separator (‘‘classifier’’), we measure its quality (‘‘error’’) according to how much work it would take to move the misclassified points across the classifier to yield separated sets. We consider several measures of work and provide algorithms to find linear classifiers that minimize the error under these different measures.Ministerio de Educación y Ciencia MTM2008-05866-C03-0

An iterated local search algorithm based on nonlinear programming for the irregular strip packing problem

The irregular strip packing problem is a combinatorial optimization problem that requires to place a given set of two-dimensional polygons within a rectangular container so that no polygon overlaps with other polygons or protrudes from the container, where each polygon is not necessarily convex. The container has a fixed width, while its length can change so that all polygons are placed in it. The objective is to find a layout of the set of polygons that minimizes the length of the container. We propose an algorithm that separates overlapping polygons based on nonlinear programming, and an algorithm that swaps two polygons in a layout so as to find their new positions in the layout with the least overlap. We incorporate these algorithms as components into an iterated local search algorithm for the overlap minimization problem and then develop an algorithm for the irregular strip packing problem using the iterated local search algorithm. Computational comparisons on representative instances disclose that our algorithm is competitive with other existing algorithms. Moreover, our algorithm updates several best known results

Detecting the intersection of two convex shapes by searching on the 2-sphere

Special issue: Proceedings of Solid and Physical Modeling (SPM 2017)International audienceWe take a look at the problem of deciding whether two convex shapes intersect or not. We do so through the well known lens of Minkowski sums and with a bias towards applications in computer graphics and robotics. We describe a new technique that works explicitly on the unit sphere, interpreted as the sphere of directions. In extensive benchmarks against various well-known techniques, ours is found to be slightly more efficient, much more robust and comparatively easy to implement. In particular, our technique is compared favourably to the ubiquitous algorithm of Gilbert, Johnson and Keerthi (GJK), and its decision variant by Gilbert and Foo. We provide an in-depth geometrical understanding of the differences between GJK and our technique and conclude that our technique is probably a good drop-in replacement when one is not interested in the actual distance between two non-intersecting shapes

An approach to reducing parameter uncertainty for robotic surface assembly tasks

In contrast to hard automation, which relies on the precise knowledge of all parameters and special-purpose machinery, the goal of flexible assembly is to overcome the inherent uncertainty in the location of the parts. The main result of this dissertation is that, for rigid, non-deformable objects, more accurate estimates of parameters, which describe their position and orientation in Cartesian space, can be obtained through active part interaction and estimation using numerical methods. If the objects have large polyhedral or convex features, the parameter estimation problem can be recasting terms of fitting the collected empirical data to a suitable geometrical model. The planning and execution steps are treated as conceptually separate from the estimation.Additionally, an algorithm for automatic conversion of a compliant path from the Cartesian to the joint space of a general-purpose, 7 degrees of freedom robotic arm is described. This allows for the assembly strategies to be planned in terms of objects'topological features in the task frame. A `back-drivable' Barrett WAM robotic arm without a force sensor was used in all experiments, and approximate compliant motion was achieved by relying on torque limits and impedance. Consequently, the primary focus is on planning, control, and assembly without force sensing. The underlying concepts, however, are much more general and could be extended to incorporate force feedback. Grasping is outside of the scope of this work, and it is assumed throughout that one of the parts is rigidly attached to the end-effector of the robot

Multi-robot cooperative platform : a task-oriented teleoperation paradigm

This thesis proposes the study and development of a teleoperation system based on multi-robot cooperation under the task oriented teleoperation paradigm: Multi-Robot Cooperative Paradigm, MRCP. In standard teleoperation, the operator uses the master devices to control the remote slave robot arms. These arms reproduce the desired movements and perform the task. With the developed work, the operator can virtually manipulate an object. MRCP automatically generates the arms orders to perform the task. The operator does not have to solve situations arising from possible restrictions that the slave arms may have. The research carried out is therefore aimed at improving the accuracy teleoperation tasks in complex environments, particularly in the field of robot assisted minimally invasive surgery. This field requires patient safety and the workspace entails many restrictions to teleoperation. MRCP can be defined as a platform composed of several robots that cooperate automatically to perform a teleoperated task, creating a robotic system with increased capacity (workspace volume, accessibility, dexterity ...). The cooperation is based on transferring the task between robots when necessary to enable a smooth task execution. The MRCP control evaluates the suitability of each robot to continue with the ongoing task and the optimal time to execute a task transfer between the current selected robot and the best candidate to continue with the task. From the operator¿s point of view, MRCP provides an interface that enables the teleoperation though the task-oriented paradigm: operator orders are translated into task actions instead of robot orders. This thesis is structured as follows: The first part is dedicated to review the current solutions in the teleoperation of complex tasks and compare them with those proposed in this research. The second part of the thesis presents and reviews in depth the different evaluation criteria to determine the suitability of each robot to continue with the execution of a task, considering the configuration of the robots and emphasizing the criterion of dexterity and manipulability. The study reviews the different required control algorithms to enable the task oriented telemanipulation. This proposed teleoperation paradigm is transparent to the operator. Then, the Thesis presents and analyses several experimental results using MRCP in the field of minimally invasive surgery. These experiments study the effectiveness of MRCP in various tasks requiring the cooperation of two hands. A type task is used: a suture using minimally invasive surgery technique. The analysis is done in terms of execution time, economy of movement, quality and patient safety (potential damage produced by undesired interaction between the tools and the vital tissues of the patient). The final part of the thesis proposes the implementation of different virtual aids and restrictions (guided teleoperation based on haptic visual and audio feedback, protection of restricted workspace regions, etc.) using the task oriented teleoperation paradigm. A framework is defined for implementing and applying a basic set of virtual aids and constraints within the framework of a virtual simulator for laparoscopic abdominal surgery. The set of experiments have allowed to validate the developed work. The study revealed the influence of virtual aids in the learning process of laparoscopic techniques. It has also demonstrated the improvement of learning curves, which paves the way for its implementation as a methodology for training new surgeons.Aquesta tesi doctoral proposa l'estudi i desenvolupament d'un sistema de teleoperació basat en la cooperació multi-robot sota el paradigma de la teleoperació orientada a tasca: Multi-Robot Cooperative Paradigm, MRCP. En la teleoperació clàssica, l'operador utilitza els telecomandaments perquè els braços robots reprodueixin els seus moviments i es realitzi la tasca desitjada. Amb el treball realitzat, l'operador pot manipular virtualment un objecte i és mitjançant el MRCP que s'adjudica a cada braç les ordres necessàries per realitzar la tasca, sense que l'operador hagi de resoldre les situacions derivades de possibles restriccions que puguin tenir els braços executors. La recerca desenvolupada està doncs orientada a millorar la teleoperació en tasques de precisió en entorns complexos i, en particular, en el camp de la cirurgia mínimament invasiva assistida per robots. Aquest camp imposa condicions de seguretat del pacient i l'espai de treball comporta moltes restriccions a la teleoperació. MRCP es pot definir com a una plataforma formada per diversos robots que cooperen de forma automàtica per dur a terme una tasca teleoperada, generant un sistema robòtic amb capacitats augmentades (volums de treball, accessibilitat, destresa,...). La cooperació es basa en transferir la tasca entre robots a partir de determinar quin és aquell que és més adequat per continuar amb la seva execució i el moment òptim per realitzar la transferència de la tasca entre el robot actiu i el millor candidat a continuar-la. Des del punt de vista de l'operari, MRCP ofereix una interfície de teleoperació que permet la realització de la teleoperació mitjançant el paradigma d'ordres orientades a la tasca: les ordres es tradueixen en accions sobre la tasca en comptes d'estar dirigides als robots. Aquesta tesi està estructurada de la següent manera: Primerament es fa una revisió de l'estat actual de les diverses solucions desenvolupades actualment en el camp de la teleoperació de tasques complexes, comparant-les amb les proposades en aquest treball de recerca. En el segon bloc de la tesi es presenten i s'analitzen a fons els diversos criteris per determinar la capacitat de cada robot per continuar l'execució d'una tasca, segons la configuració del conjunt de robots i fent especial èmfasi en el criteri de destresa i manipulabilitat. Seguint aquest estudi, es presenten els diferents processos de control emprats per tal d'assolir la telemanipulació orientada a tasca de forma transparent a l'operari. Seguidament es presenten diversos resultats experimentals aplicant MRCP al camp de la cirurgia mínimament invasiva. En aquests experiments s'estudia l'eficàcia de MRCP en diverses tasques que requereixen de la cooperació de dues mans. S'ha escollit una tasca tipus: sutura amb tècnica de cirurgia mínimament invasiva. L'anàlisi es fa en termes de temps d'execució, economia de moviment, qualitat i seguretat del pacient (potencials danys causats per la interacció no desitjada entre les eines i els teixits vitals del pacient). Finalment s'ha estudiat l'ús de diferents ajudes i restriccions virtuals (guiat de la teleoperació via retorn hàptic, visual o auditiu, protecció de regions de l'espai de treball, etc) dins el paradigma de teleoperació orientada a tasca. S'ha definint un marc d'aplicació base i implementant un conjunt de restriccions virtuals dins el marc d'un simulador de cirurgia laparoscòpia abdominal. El conjunt d'experiments realitzats han permès validar el treball realitzat. Aquest estudi ha permès determinar la influencia de les ajudes virtuals en el procés d'aprenentatge de les tècniques laparoscòpiques. S'ha evidenciat una millora en les corbes d'aprenentatge i obre el camí a la seva implantació com a metodologia d'entrenament de nous cirurgians.Postprint (published version

Efficient configuration space construction and optimization

The configuration space is a fundamental concept that is widely used in algorithmic robotics. Many applications in robotics, computer-aided design, and related areas can be reduced to computational problems in terms of configuration spaces. In this dissertation, we address three main computational challenges related to configuration spaces: 1) how to efficiently compute an approximate representation of high-dimensional configuration spaces; 2) how to efficiently perform geometric, proximity, and motion planning queries in high dimensional configuration spaces; and 3) how to model uncertainty in configuration spaces represented by noisy sensor data. We present new configuration space construction algorithms based on machine learning and geometric approximation techniques. These algorithms perform collision queries on many configuration samples. The collision query results are used to compute an approximate representation for the configuration space, which quickly converges to the exact configuration space. We highlight the efficiency of our algorithms for penetration depth computation and instance-based motion planning. We also present parallel GPU-based algorithms to accelerate the performance of optimization and search computations in configuration spaces. In particular, we design efficient GPU-based parallel k-nearest neighbor and parallel collision detection algorithms and use these algorithms to accelerate motion planning. In order to extend configuration space algorithms to handle noisy sensor data arising from real-world robotics applications, we model the uncertainty in the configuration space by formulating the collision probabilities for noisy data. We use these algorithms to perform reliable motion planning for the PR2 robot.Doctor of Philosoph