The rolling problem: overview and challenges

In the present paper we give a historical account -ranging from classical to modern results- of the problem of rolling two Riemannian manifolds one on the other, with the restrictions that they cannot instantaneously slip or spin one with respect to the other. On the way we show how this problem has profited from the development of intrinsic Riemannian geometry, from geometric control theory and sub-Riemannian geometry. We also mention how other areas -such as robotics and interpolation theory- have employed the rolling model.Comment: 20 page

Grasp Analysis Tools for Synergistic Underactuated Robotic Hands

Despite being a classical topic in robotics, the research on dexterous robotic hands still stirs a lively research activity. The current interest is especially attracted by underactuated robotic hands where a high number of degrees of freedom (DoFs), and a relatively low number of degrees of actuation co-exist. The correlation between the DoFs obtained through a wise distribution of actuators is aimed at simplifying the control with a minimal loss of dexterity. In this sense, the application of bio-inspired principles is bringing research toward a more conscious design. This work proposes new, general approaches for the analysis of grasps with synergistic underactuated robotic hands.After a review of the quasi-static equations describing the system, where contact preload is also considered, two different approaches to the analysis are presented. The first one is based on a systematic combination of the equations. The independent and the dependent variables are defined, and cause-effect relationships between them are found. In addition, remarkable properties of the grasp, as the subspace of controllable internal force and the grasp compliance, are worked out in symbolic form. Then, some relevant kinds of tasks, such as pure squeeze, spurious squeeze and kinematic grasp displacements, are defined, in terms of nullity or non-nullity of proper variables. The second method of analysis shows how to discover the feasibility of the pre-defined tasks, operating a systematic decomposition of the solution space of the system. As a result, the inputs to be given to the hand, in order to achieve the desired system displacements, are found. The study of the feasible variations is carried out arriving at the discovery of all the combinations of nullity and/or non-nullity variables which are allowed by the equations describing the system. Numerical results are presented both for precision and power grasps, finding forces and displacements that the hand can impose on the object, and showing which properties are preserved after the introduction of a synergistic underactuation mechanism

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

Development of Alternative Methods for Robot Kinematics

The problem of finding mathematical tools to represent rigid body motions in space has long been on the agenda of physicists and mathematicians and is considered to be a well-researched and well-understood problem. Robotics, computer vision, graphics, and other engineering disciplines require concise and efficient means of representing and applying generalized coordinate transformations in three dimensions. Robotics requires systematic ways to represent the relative position or orientation of a manipulator rigid links and objects. However, with the advent of high-speed computers and their application to the generation of animated graphical images and control of robot manipulators, new interest arose in identifying compact and computationally efficient representations of spatial transformations. The traditional methods for representing forward kinematics of manipulators have been the homogeneous matrix in line with the D-H algorithm. In robotics, this matrix is used to describe one coordinate system with respect to another one. However for online operation and manipulation of the robotic manipulator in a flexible manner the computational time plays an important role. Although this method is used extensively in kinematic analysis but it is relatively neglected in practical robotic systems due to some complications in dealing with the problem of orientation representation. On the other hand, such matrices are highly redundant to represent six independent degrees of freedom. This redundancy can introduce numerical problems in calculations, wastes storage, and often increases the computational cost of algorithms. Keeping these drawbacks in mind, alternative methods are being sought by various researchers for representing the same and reducing the computational time to make the system fast responsive in a flexible environment. Researchers in robot kinematics tried alternative methods in order to represent rigid body transformations based on concepts introduced by mathematicians and physicists such as Euler angle or Epsilon algebra. In the present work alternative representations, using quaternion algebra and lie algebra are proposed, tried and compared

Generative and predictive models for robust manipulation

Probabilistic modelling of manipulation skills, perception and uncertainty pose many challenges at different stages of a typical robot manipulation pipeline. This thesis is about devising algorithms and strategies for improving robustness in object manipulation skills acquired from demonstration and derived from learnt physical models in non-prehensile tasks such as pushing. Manipulation skills can be made robust in different ways: first by improving time performance for grasp synthesis, second by employing active perceptual strategies that exploit generated grasp action hypothesis to more efficiently gather task-relevant information for grasp generation, and finally via exploiting predictive uncertainty in learnt physical models. Hence, robust manipulation skills emerge from the interplay of a triad of capabilities: generative modelling for action synthesis, active perception, and finally learning and exploiting uncertainty in physical interactions. This thesis addresses these problems by • Showing how parametric models for approximating multimodal distributions can be used as a computationally faster method for generative grasp synthesis. • Exploiting generative methods for dexterous grasp synthesis and investigating how active vision strategies can be applied to improve grasp execution safety, success rate, and utilise fewer camera views of an object for grasp generation. • Outlining methods to model and exploit predictive uncertainty from learnt forward models to achieve robust, uncertainty-averse non-prehensile manipulation, such as push manipulation. In particular, the thesis: (i) presents a framework for generative grasp synthesis with applications for real-time grasp synthesis suitable for multi-fingered robot hands; (ii) describes a sensorisation method for under-actuated hands, such as the Pisa/IIT SoftHand, which allows us to deploy the aforementioned grasp synthesis framework to this type of robotic hand; (iii) provides an active vision approach for view selection that makes use of generative grasp synthesis methods to perform perceptual predictions in order to leverage grasp performance, taking into account grasp execution safety and contact information; and (iv) finally, going beyond prehensile skills, provides an approach to model and exploit predictive uncertainty from learnt physics applied to push manipulation. Experimental results are presented in simulation and on real robot platforms to validate the proposed methods

An Overview of Formulae for the Higher-Order Kinematics of Lower-Pair Chains with Applications in Robotics and Mechanism Theory

The motions of mechanisms can be described in terms of screw coordinates by means of an exponential mapping. The product of exponentials (POE) describes the configuration of a chain of bodies connected by lower pair joints. The kinematics is thus given in terms of joint screws. The POE serves to express loop constraints for mechanisms as well as the forward kinematics of serial manipulators. Besides the compact formulations, the POE gives rise to purely algebraic relations for derivatives wrt. joint variables. It is known that the partial derivatives of the instantaneous joint screws (columns of the geometric Jacobian) are determined by Lie brackets the joint screws. Lesser-known is that derivative of arbitrary order can be compactly expressed by Lie brackets. This has significance for higher-order forward/inverse kinematics and dynamics of robots and multibody systems. Various relations were reported but are scattered in the literature and insufficiently recognized. This paper aims to provide a comprehensive overview of the relevant relations. Its original contributions are closed form and recursive relations for higher-order derivatives and Taylor expansions of various kinematic relations. Their application to kinematic control and dynamics of robotic manipulators and multibody systems is discussed

Tactile Ergodic Control Using Diffusion and Geometric Algebra

Continuous physical interaction between robots and their environment is a requirement in many industrial and household tasks, such as sanding and cleaning. Due to the complex tactile information, these tasks are notoriously difficult to model and to sense. In this article, we introduce a closed-loop control method that is constrained to surfaces. The applications that we target have in common that they can be represented by probability distributions on the surface that correlate to the time the robot should spend in a region. These surfaces can easily be captured jointly with the target distributions using coloured point clouds. We present the extension of an ergodic control approach that can be used with point clouds, based on heat equation-driven area coverage (HEDAC). Our method enables closed-loop exploration by measuring the actual coverage using vision. Unlike existing approaches, we approximate the potential field from non-stationary diffusion using spectral acceleration, which does not require complex preprocessing steps and achieves real-time closed-loop control frequencies. We exploit geometric algebra to stay in contact with the target surface by tracking a line while simultaneously exerting a desired force along that line. Our approach is suitable for fully autonomous and human-robot interaction settings where the robot can either directly measure the coverage of the target with its sensors or by being guided online by markings or annotations of a human expert. We tested the performance of the approach in kinematic simulation using point clouds, ranging from the Stanford bunny to a variety of kitchen utensils. Our real-world experiments demonstrate that the proposed approach can successfully be used to wash kitchenware with curved surfaces, by cleaning the dirt detected by vision in an online manner. Website: https://geometric-algebra.tobiloew.ch/tactile_ergodic_controlComment: Submitted to the special issue for IEEE Transactions on Robotics (T-RO) on Tactile Robotic

Kinematic Model of the Hand using Computer Vision

La biotecnología es una ciencia en auge y en especial el diseño de interfaces humano-máquina. El objetivo de este proyecto es avanzar en dicho campo y en concreto explorar el diseño de exoesqueletos y prótesis de la mano humana. La metodología utilizada en este proyecto fundamentalmente consta de tres fases. En primer lugar, se ha establecido un modelo teórico de la cinemática de la mano recurriendo a la documentación médica especializada para concretar su anatomía. Posteriormente se ha procedido a sintetizar la mano en sus parámetros simplificados y así definir un modelo robótico. Para ajustar dicho modelo a una mano real se procede a capturar el movimiento de esta en una secuencia de imágenes mediante ordenador. Para ello se utilizan unas marcas en las uñas de la mano con una geometría específica de tal manera que permite la estimación de su pose, es decir su posición e orientación, en el espacio. Esta secuencia de poses estimadas permite caracterizar el movimiento completo de la mano. Por último, mediante la síntesis cinemática dimensional, se definen las ecuaciones de movimiento parametrizadas del modelo teórico de la mano. Estas ecuaciones permiten ajustar el modelo a la secuencia de poses estimadas mediante visión por ordenador y así crear un modelo personalizado de la mano. Gracias a este sistema, se puede realizar un estudio sobre la correspondencia entre señales electomiográficas y los movimientos de la mano y así lograr una mejor funcionalidad de las prótesis. En definitiva, este proyecto ha logrado diseñar un algoritmo robusto para el seguimiento y estimación de las poses de las uñas de las manos y ha conseguido definir las ecuaciones de movimiento y crear una aplicación para resolverlas. Asimismo, ha encontrado modelos no antropomórficos que podrían ser de utilidad en el diseño de exoesqueletos