Workspace and singularity determination of a 7-DoF wrist-partitioned serial manipulator towards graffiti painting

Els robots estan sent utilitzats, cada cop més, en la realització de tasques en la indústria. Molts d'ells també són dissenyats pensats per a realitzar les tasques de la llar. En general, els robots són dissenyats per a facilitar el dia a dia del éssers humans. Però quan es tracta d'obres artístiques, és menys comú trobar-se robots realitzant-les. Nosaltres pretenem sortir de la norma mitjançant l'ús d'un robot per a pintar un grafiti. La motivació per a aconseguir-ho convergeix en la formulació de dues preguntes: "Quin és el volum de treball d'un robot, quan l'orientació del seu efector final està fixada?" i "Donat un pla arbitrari, quina és la major àrea de treball lliure de singularitats en aquest?" Aquesta tesi proposa un mètode per a l'obtenció de les singularitats de posició en un pla qualsevol d'un manipulador serial amb un canell esfèric. El mètode s'ha obtingut mitjançant la combinació d'un mètode de determinació de singularitats de posició, el qual està basat en una tècnica per al decoplat de manipuladors que presenten un canell esfèric, i un algorisme branch-and-prune per a la resolució de sistemes d'equacions. S'ha obtingut el volum de treball d'un manipulador serial de 7 graus de llibertat a través d'un enfocament de cinemàtica directa. Es presenta una metodologia per a obtenir el volum de treball del manipulador serial quan el seu efector final té l'orientació constant i s'aplica per a obtenir aproximacions per al cas de certes orientacions. Es mostra com les singularitats poden ser analitades a través de separar-les en singularitats de posició i d'orientació. el mètode proposat formula i resol les equacions que determinen les singularitats de posició. Pel que fa a les singularitats d'orientació, es mostra que poden ser evitades sense perdre una quantitat significant de volum de treball, des del punt de vista de la posició.Los robots estén siendo utilizados, cada vez más, en la realización de tareas en la industria. Muchos de ellos también son diseñados pensados para realizar las tareas del hogar. En general, los robots son diseñados para facilitar el día a día de los seres humanos. Pero cuando se trata de obras artíticas, es menos común encontrarse a robots realizándolas. Nosotros pretendemos salirnos de lo común mediante el uso de un robot para pintar un grafiti. La motivación por lograrlo converge en la formulación de dos preguntas: "¿Cuál es el volumen de trabajo de un robot, cuando la orientación de su efector final está fijada?" y "Dado un plano arbitrario, ¿cuál es la mayor área de trabajo libre de singularidades en éste?" Esta tesis propone un método para la obtención de las singularidades de posición en un plano cualquiera de un manipulador serial con una muñeca esférica. El método ha sido obtenido mediante la combinación de un método de determinación de singularidades de posición, el cual está basado en una técnica para el decoplado de manipuladores que presentan una muñeca esférica, y un algoritmo branch-and-prune para la resolución de sistemas de ecuaciones. Se ha obtenido el volumen de trabajo de un manipulador serial de 7 grados de libertad a través de un enfoque de cinemática directa. Se presenta la metodología para obtener el volumen de trabajo del manipulador serial cuando su efector final tiene una orientación constante y se aplica para obtener aproximaciones para el caso de ciertas orientaciones. Se muestra cómo las singularidades pueden ser analizadas a través de separarlas en singularidades de posición y de orientación. El método propuesto formula y resuelve las ecuaciones que determinan las singularidades de posición. En cuanto a las singularidades de orientación, se muestra que pueden ser evitadas sin perder una cantidad significante de volumen de trabajo, desde el punto de vista de la posición.Robots are overtaking every day more tasks in the industry. A lot of them are even designed for performing household chores. In general, robots are designed to facilitate the day-to-day of human beings. But when it comes to artistic tasks, it is less usual to see robots performing them. We pretend to stay out of the crowd by using a robot to paint a graffiti. The motivation to achieve this task converges into the statement of two questions: "What is the workspace of a robot, when the orientation of its end-effector is fixed?" and "For a given plane, what is the largest singularity free surface on it?". This thesis proposes a method for the computation of the position singularities of a wrist-partitioned serial manipulator for a given plane. The method is obtained from the combination of a position singularity determination method, which is based on the decoupling technique of a wrist-partitioned manipulator, and a branch-and-prune algorithm for the resolution of systems of equations. The workspace of a 7-DoF serial manipulator is obtained by a forward kinematics approach. A methodology to obtain the constant orientation workspace of a serial manipulator is presented and applied to get approximations for some specific orientations. It is shown how singularities can be analyzed by decoupling them into position singularities and orientation singularities. The proposed method formulates and solves the equation that determines the position singularities. In the case of the orientation singularities, it is shown that they can be avoided without losing a significant amount of the workspace's volume, from the point of view of the position.Outgoin

A Novel Approach for Simplification of Industrial Robot Dynamic Model Using Interval Method

This paper proposes a new approach to simplify the dynamic model of industrial robot by means of interval method. Due to strong nonlinearities, some components of robot dynamic model such as the inertia matrix and the vector of centrifugal, Coriolis and gravitational torques, are very complicated for real-time control of industrial robots. Thus, a simplification algorithm is presented in this study in order to reduce the computation time and memory occupation. More importantly, this simplification is suitable for arbitrary trajectories in whole robot workspace. Furthermore, the method devotes to finding negligible inertia parameters, which is useful for robot model identification. A simulation has been carried out on a test trajectory using a 6-DOF industrial robot model, and the results have shown good performance and effectiveness of this method.ANR COROUSS

Multirepresentations and multiconstraints approach to the numerical synthesis of serial kinematic structures of manipulators

This paper presents a set of algorithms for the synthesis of kinematic structures of serial manipulators using multiple constraint formulation and provides a performance comparison of different kinematic representations, the Denavit-Hartenberg notation, the Product of Exponentials (screws), and Roll-Pitch-Yaw angles with translation parameters. Synthesis is performed for five given tasks, and both revolute and prismatic joints can be synthesized. Two different non-linear programming optimization algorithms were used to support the findings. The results are compared and discussed. Data show that the choice of the constraint design method has a significant impact on the success rate of optimization convergence. The choice of representation has a lower impact on convergence, but there are differences in the optimization time and the length of the designed manipulators. Furthermore, the best results are obtained when multiple methodologies are used in combination. An arbitrary manipulator was designed and assembled based on a trajectory in the collision environment to demonstrate the advantages of the proposed methodology. The input/output data and synthesis methodology algorithms are provided through an open repository.Web of Science10689516893

Biokinematic analysis of human body

Thesis (Doctoral)--Izmir Institute of Technology, Mechanical Engineering, Izmir, 2011Includes bibliographical references (leaves: 118-123)Text in English; Abstract: Turkish and Englishxiii, 123 leavesThis thesis concentrates on the development of rigid body geometries by using method of intersections, where simple geometric shapes representing revolute (R) and prismatic (P) joint motions are intersected by means of desired space or subspace requirements to create specific rigid body geometries in predefined octahedral fixed frame. Using the methodical approach, space and subspace motions are clearly visualized by the help of resulting geometrical entities that have physical constraints with respect to the fixed working volume. Also, this work focuses on one of the main areas of the fundamental mechanism and machine science, which is the structural synthesis of robot manipulators by inserting recurrent screws into the theory. After the transformation unit screw equations are presented, physical representations and kinematic representations of kinematic pairs with recurrent screws are given and the new universal mobility formulations for mechanisms and manipulators are introduced. Moreover the study deals with the synthesis of mechanisms by using quaternion and dual quaternion algebra to derive the objective function. Three different methods as interpolation approximation, least squares approximation and Chebyshev approximation is introduced in the function generation synthesis procedures of spherical four bar mechanism in six precision points. Separate examples are given for each section and the results are tabulated. Comparisons between the methods are also given. As an application part of the thesis, the most important elements of the human body and skeletal system is investigated by means of their kinematic structures and degrees of freedom. At the end of each section, an example is given as a mechanism or manipulator that can represent the behavior of the related element in the human body

Separable Nonlinear Least Squares Algorithm for Robust Kinematic Calibration of Serial Robots

Kinematic calibration of robots is an effective way to guarantee and promote their performance characteristics. There are many mature researches on kinematic calibration, and methods based on MDH model are the most common ones. However, when employing these calibration methods, it occasionally happens that the objective function cannot converge during iterations. Through analyzing robotic forward kinematics, we found out that the Cartesian coordinates of the end-point are affine to length-related MDH parameters, where linear and nonlinear parameters can be separated. Thanks to the distinctive characteristic of the MDH model, the kinematic calibration problem can be converted into a separable nonlinear least squares problem, which can further be partitioned into two subproblems: a linear least squares problem and a reduced problem involving only nonlinear parameters. Eventually, the optimal structural parameters can be identified by solving this problem iteratively. The results of numerical and experimental validations show that: 1) the robustness during identification procedure is enhanced by eliminating the partial linear structural parameters, the convergence rate is promoted from 68.98% to 100% with different deviation vector pairs; 2) the initial values to be pre-set for kinematic calibration problem are fewer and 3) fewer parameters are to be identified by nonlinear least squares regression, resulting in fewer iterations and faster convergence, where average runtime is reduced from 33.931s to 1.874s

Trajectory Generation for a Multibody Robotic System: Modern Methods Based on Product of Exponentials

This work presents several trajectory generation algorithms for multibody robotic systems based on the Product of Exponentials (PoE) formulation, also known as screw theory. A PoE formulation is first developed to model the kinematics and dynamics of a multibody robotic manipulator (Sawyer Robot) with 7 revolute joints and an end-effector. In the first method, an Inverse Kinematics (IK) algorithm based on the Newton-Raphson iterative method is applied to generate constrained joint-space trajectories corresponding to straight-line and curvilinear motions of the end effector in Cartesian space with finite jerk. The second approach describes Constant Screw Axis (CSA) trajectories which are generated using Machine Learning (ML) and Artificial Neural Networks (ANNs) techniques. The CSA method smooths the trajectory in the Special Euclidean (SE(3)) space. In the third approach, a multi-objective Swarm Intelligence (SI) trajectory generation algorithm is developed, where the IK problem is tackled using a combined SI-PoE ML technique resulting in a joint trajectory that avoids obstacles in the workspace, and satisfies the finite jerk constraint on end-effector while minimizing the torque profiles. The final method is a different approach to solving the IK problem using the Deep Q-Learning (DQN) Reinforcement Learning (RL) algorithm which can generate different joint space trajectories given the Cartesian end-effector path. For all methods above, the Newton-Euler recursive algorithm is implemented to compute the inverse dynamics, which generates the joint torques profiles. The simulated torque profiles are experimentally validated by feeding the generated joint trajectories to the Sawyer robotic arm through the developed Robot Operating System (ROS) - Python environment in the Software Development Kit (SDK) mode. The developed algorithms can be used to generate various trajectories for robotic arms (e.g. spacecraft servicing missions)

A SERIAL-PARALLEL HYBRID ROBOT FOR MACHINING OF COMPLEX SURFACES

Ph.DDOCTOR OF PHILOSOPH

Kinematics and Robot Design I, KaRD2018

This volume collects the papers published on the Special Issue “Kinematics and Robot Design I, KaRD2018” (https://www.mdpi.com/journal/robotics/special_issues/KARD), which is the first issue of the KaRD Special Issue series, hosted by the open access journal “MDPI Robotics”. The KaRD series aims at creating an open environment where researchers can present their works and discuss all the topics focused on the many aspects that involve kinematics in the design of robotic/automatic systems. Kinematics is so intimately related to the design of robotic/automatic systems that the admitted topics of the KaRD series practically cover all the subjects normally present in well-established international conferences on “mechanisms and robotics”. KaRD2018 received 22 papers and, after the peer-review process, accepted only 14 papers. The accepted papers cover some theoretical and many design/applicative aspects

Contribution to improving the accuracy of serial robots

The goal of the present study is to improve the accuracy of six-revolute industrial robots using calibration methods. These methods identify the values of the calibrated robot model to improve the correspondence between the real robot and the mathematical model used in its controller. The calibrated robot model adds error parameters to the nominal model, which correspond to the geometric errors of the robot as well as the stiffness behavior of the robot. The developed methods focus on using low cost measurement equipment. For instance, the first work makes a comparison between a robot calibration performed using a laser tracker and a stereo camera (MMT optique) separately. The accuracy performance is validated using a telescoping ballbar for each of the two methods. While the calibration result is the same for both methods, the price of a laser tracker is more than twice the price of a stereo camera. The method is tested using an ABB IRB120 robot, a Faro ION laser tracker, and a Creaform CTrack stereo camera to calibrate the robot. A Renishaw QC20-W ballbar is used to validate the accuracy. A novel measurement system to measure a set of poses is described in the second work. The device is an extension of a known approach using an hexapod (a Stewart-Gough platform). One fixture is attached to the robot base and the other to the robot end-effector, each having three magnetic cups. By taking six ballbar measurements at a time, it is possible to measure 144 poses of the triangular fixture attached to the robot end-effector with respect to the base fixture. The position accuracy of the device is 3.2 times the accuracy of the QC20-W ballbar: ± 0.003 mm. An absolute robot calibration using this novel 6D measurement system is performed in the third work of this thesis. The robot is calibrated in 61 configurations and the absolute position accuracy of the robot after calibration is validated with a Faro laser tracker in about 10,000 robot configurations. The mean distance error is improved from 1.062 mm to 0.400 mm in 50 million pairs of measurements throughout the complete robot workspace. To allow a comparison, the robot is also calibrated using the laser tracker and the robot accuracy validated in the same 10,000 robot configurations

Geometric soft robotics: a finite element approach

Enabling remote semi-autonomous operations in hazardous environments is a challenging technological problem, given the difficulty to access in confined and constrained spaces using classical robotic systems. Inspired by biological trunks and tentacles, soft continuum robots constitute a possible solution to this problem, for their ability to traverse confined spaces, manipulate objects in complex environments, and conform their shape to nonlinear curvilinear paths. The need of reaching difficult-to-access industrial sites for maintenance and inspection procedures or anatomical sites for less invasive robotic surgery mainly motivates the current research. Despite the recent advances in the design and fabrication of soft robots, the community still suffers for the lack of a consolidate modeling framework for simulating their mechanical behavior. Such a modeling framework is the necessary condition for developing new physical design and control strategies, as well as path planning algorithms. Indeed, despite their appreciable features, soft robots usually generate undesired vibrations during normal procedures. This is one of the main reasons which still limits their potentially wide use in real scenario. Realistic modeling frameworks might leverage the development of model-based predictive controllers to compensate for the undesired vibrations, as well as design concepts and optimized trajectories to avoid the excitation of the vibration modes of the mechanical structure. The main objective of the thesis is to develop a unified mathematical framework for simulating the mechanical behavior of soft continuum robotic manipulators, which can also accommodate the dynamic simulation of classical rigid robots. The computer implementation of this theoretical framework leads to the development of SimSOFT, a physics engine for soft robots. The formulation has been validated through literature benchmark and some applications are presented. One of the major strengths of the framework is that it can accommodate the realistic simulation of kinematic trees or loops constituted either by rigid or soft arms connected by rigid or flexible joints.The simulation of hybrid mechanisms, composed by classical rigid kinematic chains and soft continuum manipulators, which can be used to have larger dexterity in smaller workspaces, as they are easily to miniaturize, is thus possible. To the best of the author's knowledge, the mathematical models developed in the thesis constitute the first attempt in the robotics community towards a unified framework for the dynamics of soft continuum multibody systems