Tracking control of redundant mobile manipulator: An RNN based metaheuristic approach

In this paper, we propose a topology of Recurrent Neural Network (RNN) based on a metaheuristic optimization algorithm for the tracking control of mobile-manipulator while enforcing nonholonomic constraints. Traditional approaches for tracking control of mobile robots usually require the computation of Jacobian-inverse or linearization of its mathematical model. The proposed algorithm uses a nature-inspired optimization approach to directly solve the nonlinear optimization problem without any further transformation. First, we formulate the tracking control as a constrained optimization problem. The optimization problem is formulated on position-level to avoid the computationally expensive Jacobian-inversion. The nonholonomic limitation is ensured by adding equality constraints to the formulated optimization problem. We then present the Beetle Antennae Olfactory Recurrent Neural Network (BAORNN) algorithm to solve the optimization problem efficiently using very few mathematical operations. We present a theoretical analysis of the proposed algorithm and show that its computational cost is linear with respect to the degree of freedoms (DOFs), i.e., O(m). Additionally, we also prove its stability and convergence. Extensive simulation results are prepared using a simulated model of IIWA14, a 7-DOF industrial-manipulator, mounted on a differentially driven cart. Comparison results with particle swarm optimization (PSO) algorithm are also presented to prove the accuracy and numerical efficiency of the proposed controller. The results demonstrate that the proposed algorithm is several times (around 75 in the worst case) faster in execution as compared to PSO, and suitable for real-time implementation. The tracking results for three different trajectories; circular, rectangular, and rhodonea paths are presented

Inverse Kinematic Analysis of Robot Manipulators

An important part of industrial robot manipulators is to achieve desired position and orientation of end effector or tool so as to complete the pre-specified task. To achieve the above stated goal one should have the sound knowledge of inverse kinematic problem. The problem of getting inverse kinematic solution has been on the outline of various researchers and is deliberated as thorough researched and mature problem. There are many fields of applications of robot manipulators to execute the given tasks such as material handling, pick-n-place, planetary and undersea explorations, space manipulation, and hazardous field etc. Moreover, medical field robotics catches applications in rehabilitation and surgery that involve kinematic, dynamic and control operations. Therefore, industrial robot manipulators are required to have proper knowledge of its joint variables as well as understanding of kinematic parameters. The motion of the end effector or manipulator is controlled by their joint actuator and this produces the required motion in each joints. Therefore, the controller should always supply an accurate value of joint variables analogous to the end effector position. Even though industrial robots are in the advanced stage, some of the basic problems in kinematics are still unsolved and constitute an active focus for research. Among these unsolved problems, the direct kinematics problem for parallel mechanism and inverse kinematics for serial chains constitute a decent share of research domain. The forward kinematics of robot manipulator is simpler problem and it has unique or closed form solution. The forward kinematics can be given by the conversion of joint space to Cartesian space of the manipulator. On the other hand inverse kinematics can be determined by the conversion of Cartesian space to joint space. The inverse kinematic of the robot manipulator does not provide the closed form solution. Hence, industrial manipulator can achieve a desired task or end effector position in more than one configuration. Therefore, to achieve exact solution of the joint variables has been the main concern to the researchers. A brief introduction of industrial robot manipulators, evolution and classification is presented. The basic configurations of robot manipulator are demonstrated and their benefits and drawbacks are deliberated along with the applications. The difficulties to solve forward and inverse kinematics of robot manipulator are discussed and solution of inverse kinematic is introduced through conventional methods. In order to accomplish the desired objective of the work and attain the solution of inverse kinematic problem an efficient study of the existing tools and techniques has been done. A review of literature survey and various tools used to solve inverse kinematic problem on different aspects is discussed. The various approaches of inverse kinematic solution is categorized in four sections namely structural analysis of mechanism, conventional approaches, intelligence or soft computing approaches and optimization based approaches. A portion of important and more significant literatures are thoroughly discussed and brief investigation is made on conclusions and gaps with respect to the inverse kinematic solution of industrial robot manipulators. Based on the survey of tools and techniques used for the kinematic analysis the broad objective of the present research work is presented as; to carry out the kinematic analyses of different configurations of industrial robot manipulators. The mathematical modelling of selected robot manipulator using existing tools and techniques has to be made for the comparative study of proposed method. On the other hand, development of new algorithm and their mathematical modelling for the solution of inverse kinematic problem has to be made for the analysis of quality and efficiency of the obtained solutions. Therefore, the study of appropriate tools and techniques used for the solution of inverse kinematic problems and comparison with proposed method is considered. Moreover, recommendation of the appropriate method for the solution of inverse kinematic problem is presented in the work. Apart from the forward kinematic analysis, the inverse kinematic analysis is quite complex, due to its non-linear formulations and having multiple solutions. There is no unique solution for the inverse kinematics thus necessitating application of appropriate predictive models from the soft computing domain. Artificial neural network (ANN) can be gainfully used to yield the desired results. Therefore, in the present work several models of artificial neural network (ANN) are used for the solution of the inverse kinematic problem. This model of ANN does not rely on higher mathematical formulations and are adept to solve NP-hard, non-linear and higher degree of polynomial equations. Although intelligent approaches are not new in this field but some selected models of ANN and their hybridization has been presented for the comparative evaluation of inverse kinematic. The hybridization scheme of ANN and an investigation has been made on accuracies of adopted algorithms. On the other hand, any Optimization algorithms which are capable of solving various multimodal functions can be implemented to solve the inverse kinematic problem. To overcome the problem of conventional tool and intelligent based method the optimization based approach can be implemented. In general, the optimization based approaches are more stable and often converge to the global solution. The major problem of ANN based approaches are its slow convergence and often stuck in local optimum point. Therefore, in present work different optimization based approaches are considered. The formulation of the objective function and associated constrained are discussed thoroughly. The comparison of all adopted algorithms on the basis of number of solutions, mathematical operations and computational time has been presented. The thesis concludes the summary with contributions and scope of the future research work

Dynamic Modeling of a Spatial Cable-Driven Continuum Robot Using Euler-Lagrange Method

Continuum robots are kinematically redundant and their dynamic models are highly nonlinear. This study aims to overcome this difficulty by presenting a more practical dynamic model of a certain class of continuum robots called cable-driven continuum robot (CDCR). Firstly, the structural design of a CDCR with two rotational degrees of freedom (DOF) is introduced. Then, the kinematic models are derived according to the constant curvature assumption. Considering the complexity of the kinetic energy expression, it has been approximated by the well-known Taylor expansions.  This case corresponds to weak bending angles within the specified bending angle range of the robot. On the other hand, due to the low weight of the CDCR components, the gravitational energy effects can be neglected compared to those stemmed from the elastic energy. Thereafter, the corresponding dynamic model is established using Euler-Lagrange method. Static and dynamic models have been illustrated by examples. This analysis and dynamic model development have been compared with the existing scientific literature. The obtained results shown that the consistency and the efficiency of accuracy for real-time have been carried out. However, the dynamic modeling of CDCR with more than 2-DOF leads to a more complex mathematical expression, and cannot be simplified by adopting the similar assumptions and methodology used in the case of 2-DOF

Assessing the accuracy and efficiency of kinematic analysis tools for six-DOF industrial manipulators: The KUKA robot case study

Accuracy is an important factor to consider when evaluating the performance of a manipulator. The accuracy of a manipulator is determined by its ability to accurately move and position objects in a precise manner. This research paper aims to evaluate the performance of different methods for the kinematic analysis of manipulators. The study employs four distinct techniques, namely mathematical modeling using the closed form solutions method, roboanalyzer, Peter Corke toolbox, and particle swarm optimization, to perform kinematic analysis for manipulators. The KUKA industrial manipulator is used as an illustrative case study in this research due to its widespread use in various industrial applications in addition to its high precision and stability. Its wide usage in the industry makes the results of this research highly relevant and allows for a thorough evaluation of the performance of the different methods being studied. Furthermore, understanding the kinematic analysis of the manipulator can also help in improving the performance and increasing the efficiency of the robot in different tasks. This paper conducts a comparison of the accuracy of the four methods, and the results indicate that particle swarm optimization is the most accurate method. The RoboAnalyzer approach achieved the fastest execution time

Artificial neural network for solving the inverse kinematic model of a spatial and planar variable curvature continuum robot

In this paper, neural networks are presented to solve the inverse kinematic models of continuum robots. Firstly, the forward kinematic models are calculated for variable curvature continuum robots. Then, the forward kinematic models are implemented in the neural networks which present the position of the continuum robot’s end effector. After that, the inverse kinematic models are solved through neural networks without setting up any constraints. In the same context, to validate the utility of the developed neural networks, various types of trajectories are proposed to be followed by continuum robots. It is found that the developed neural networks are powerful tool to deal with the high complexity of the non-linear equations, in particular when it comes to solving the inverse kinematics model of variable curvature continuum robots. To have a closer look at the efficiency of the developed neural network models during the follow up of the proposed trajectories, 3D simulation examples through Matlab have been carried out with different configurations. It is noteworthy to say that the developed models are a needed tool for real time application since it does not depend on the complexity of the continuum robots' inverse kinematic models

Probe arm motion techniques for miradas multi-object spectrograph

Desde tiempos remotos, los humanos se han sentido atraídos por los objetos brillantes que pueblan el cielo. A pesar de lo mucho que sabemos actualmente sobre ellos, quedan por desentrañar varios misterios que aún esconde la Vía Láctea. ¿Cómo se formó? ¿Cómo ha cambiado a través del tiempo? Estas son sólo dos de las múltiples preguntas para las que la astrofísica moderna no tiene respuesta. Los científicos han estado construyendo diferentes modelos que intentan simular la evolución de nuestra galaxia. Sin embargo, muchas más observaciones son necesarias para poder dar valores razonables a las diversas variables presentes en esos modelos. Fruto de esta búsqueda, en las últimas décadas se han destinado muchos esfuerzos al desarrollo de nuevas instalaciones de espectroscopía multi-objeto. El Mid-resolution InfRAreD Astronomical Spectrograph (MIRADAS) es un espectrógrafo Echelle multi-objeto en el infrarrojo cercano para el Gran Telescopio Canarias (GTC) diseñado por un consorcio internacional. Gracias a su potente resolución y a su capacidad de multiplexación, este instrumento será clave para abordar algunos de los principales desafíos científicos de las siguientes décadas. MIRADAS, con la ayuda de sus 12 unidades autónomas de campo integral, observará simultáneamente hasta 12 objetivos celestes ubicados en distintos puntos del cielo. Cada una de estas unidades opto-mecánicos tiene la forma de un brazo robótico. Las estructuras de estos dispositivos han estado especialmente concebidas para: (i) asegurar la simplicidad del camino óptico (ii) ofrecer un gran grado de estabilidad cuando el brazo trabaje invertido. Pero, desafortunadamente, el costo de este diseño se traduce en un comportamiento del brazo complejo y nada intuitivo. En esta tesis, incluimos un estudio exhaustivo del brazo robótico de MIRADAS. En concreto, se presenta un modelo matemático, así como soluciones para los problemas de cinemática directa e inversa. Además, también se analizan las particularidades que limitan su movimiento. Primero, se estudia su espacio de articular y las regiones prohibidas del mismo debido a la naturaleza del brazo. En segundo lugar, se aborda como la incapacidad de interpolación de los controladores que gobiernan los actuadores afecta a la generación de trayectorias. Finalmente, se discuten varias estrategias de patrullaje, prestando especial atención a sus ventajas y puntos débiles. Por otro lado, los brazos de MIRADAS están distribuidos alrededor de una plataforma circular en la que no hay mucho espacio. Así pues, con el fin adquirir los objetivos requeridos por el usuario, los brazos del sistema deben moverse extremo cuidado. En MIRADAS, el cómputo de trayectorias se ha dividido en tres procesos diferentes, tratados todos en detalle en este trabajo. El primero de ellos, la segmentación de campo, organiza los distintos objetivos presentes en un campo disperso de estrellas de tal manera que estos puedan ser observados adecuadamente. Específicamente, esta fase calcula varios grupos, los integrantes de los cuales se emplean posteriormente en la etapa de asignación de brazos. Adicionalmente, también se determina el centro geométrico de cada uno de estos grupos, información requerida para apuntar correctamente el telescopio.Con respecto a la asignación de brazos, etapa responsable de determinar la asociación más adecuada . La primera se basa en programación lineal y, como demuestran las pruebas, es la que obtiene mejores resultados en términos de las diferentes métricas utilizadas. Sin embargo, este método deja de ser práctico cuando se tiene enfrente campos grandes. En estos escenarios, la segunda solución, estructurada entorno a una metaheurística, obtiene buenos resultados en un tiempo de ejecución asumible. Finalmente, los planes de asignación resultantes se pasan a un planificador de trayectorias. El planificador de trayectorias es el tercer y último paso del proceso. Este analiza individualmente cada plan de asignación, devolviendo movimientos coordinados para todos los brazos involucrados. Estos movimientos, una vez traducidos a instrucciones de bajo nivel y ejecutados por el software que controla los correspondientes actuadores, colocarán el espejo de cada brazo en en la ubicación del cielo correspondiente. Las pruebas experimentales muestran que el planificador es capaz de calcular movimientos exitosos. Esto es así tanto en un escenario típico en el que se producen varias instancies de los dos tipos de conflictos que puede surgir en MIRADAS como en una serie de escenarios con objetivos científicos reales

Applied Mathematics to Mechanisms and Machines

This book brings together all 16 articles published in the Special Issue "Applied Mathematics to Mechanisms and Machines" of the MDPI Mathematics journal, in the section “Engineering Mathematics”. The subject matter covered by these works is varied, but they all have mechanisms as the object of study and mathematics as the basis of the methodology used. In fact, the synthesis, design and optimization of mechanisms, robotics, automotives, maintenance 4.0, machine vibrations, control, biomechanics and medical devices are among the topics covered in this book. This volume may be of interest to all who work in the field of mechanism and machine science and we hope that it will contribute to the development of both mechanical engineering and applied mathematics

Control visual de un brazo manipulador con 7GDL, en base a visión monocular, para el seguimiento de objetivos

La necesidad de incrementar la producción de las grandes empresas en la Primera Revolución Industrial permitió el desarrollo de nuevas máquinas, tecnologías y actividades, configurando el entorno perfecto para la aplicación de máquinas y procedimientos autónomos como los brazos manipuladores. En la última década se han ampliado las actividades que realizan los brazos manipuladores a diversas áreas como rescate, medicina e industria aeroespacial. La principal tarea de un brazo manipulador es alcanzar un objetivo por medio de sus elementos perceptivos. Esta tarea conlleva escoger los sensores necesarios para percibir el mundo tomando en cuenta el costo, el peso y el espacio. En esta investigación se dará solución a este problema con el uso de un sensor de visión, es decir una cámara. El mecanismo de control que se presenta se basa en dividir el movimiento tridimensional en dos movimientos sobre dos planos: Uno de estos planos es el mismo que el plano de la cámara (plano XY ) y el otro plano será perpendicular al primero y se refiere a la profundidad (plano XZ). El movimiento del objetivo en el plano de la cámara será calculado por medio del flujo óptico, es decir la traslación del objetivo del tiempo t al t + 1 en el plano XY . En cambio, el movimiento en el plano de la profundidad se estimará mediante el filtro de Kalman usando las variaciones de la traslación obtenida del flujo óptico y de la rotación dada por la matriz de cinemática directa. Finalmente, el movimiento planificado en cada plano se ejecutará de forma intercalada infinitesimalmente, obteniendo así un movimiento continuo para los tres ejes coordenados (XY Z). Los resultados experimentales obtenidos, han demostrado que se realiza un camino limpio y suavizado. Se han llevado a cabo pruebas con diferentes intensidades de iluminación, mostrando un error promedio de la trayectoria de movimiento de µx,y,z = 5.05, 4.80, 3.0 en centímetros con iluminación constante, por lo que se tiene una desviación estándar σx,y,z = 2.21, 2.77, 1.45 en centímetros. Al obtener resultados satisfactorios en las pruebas elaboradas. Se puede concluir que es posible solucionar el problema del movimiento tridimensional de un brazo manipulador dividiéndolo en dos sub-problemas que trabajan en planos perpendiculares. Esta solución nos proporciona una trayectoria suave, ya que el mecanismo de control se realiza en cada instante de tiempo obteniendo un movimiento natural.Tesi

Surgical Subtask Automation for Intraluminal Procedures using Deep Reinforcement Learning

Intraluminal procedures have opened up a new sub-field of minimally invasive surgery that use flexible instruments to navigate through complex luminal structures of the body, resulting in reduced invasiveness and improved patient benefits. One of the major challenges in this field is the accurate and precise control of the instrument inside the human body. Robotics has emerged as a promising solution to this problem. However, to achieve successful robotic intraluminal interventions, the control of the instrument needs to be automated to a large extent. The thesis first examines the state-of-the-art in intraluminal surgical robotics and identifies the key challenges in this field, which include the need for safe and effective tool manipulation, and the ability to adapt to unexpected changes in the luminal environment. To address these challenges, the thesis proposes several levels of autonomy that enable the robotic system to perform individual subtasks autonomously, while still allowing the surgeon to retain overall control of the procedure. The approach facilitates the development of specialized algorithms such as Deep Reinforcement Learning (DRL) for subtasks like navigation and tissue manipulation to produce robust surgical gestures. Additionally, the thesis proposes a safety framework that provides formal guarantees to prevent risky actions. The presented approaches are evaluated through a series of experiments using simulation and robotic platforms. The experiments demonstrate that subtask automation can improve the accuracy and efficiency of tool positioning and tissue manipulation, while also reducing the cognitive load on the surgeon. The results of this research have the potential to improve the reliability and safety of intraluminal surgical interventions, ultimately leading to better outcomes for patients and surgeons