An efficient finite element formulation of dynamics for a flexible robot with different type of joints

If two adjacent links of a flexible robot are connected via a revolute joint or a fixed prismatic joint, the relative motion of the next link will depend on both the joint motion and the elastic displacement of the distal end of the previous link. However, if the two adjacent links are connected via a sliding prismatic joint, the relative motion of the next link will depend additionally on the elastic deformation distributed along the previous link. Therefore, formulation of the motion equations for a multi-link flexible robot consisting of the revolute joints, the fixed prismatic joints and the sliding prismatic joints is challenging. In this study, the finite element kinematic and dynamic formulation was successfully developed and validated for the flexible robot, in which a transformation matrix is proposed to describe the kinematics of both the joint motion and the link deformation. Additionally, a new recursive formulation of the dynamic equations is introduced. As compared with the previous methods, the time complexity of the formulation is reduced by O(2η), where η is the number of finite elements on all links. The numerical examples and experiments were implemented to validate the proposed kinematic and dynamic modelling method

Modelado y Resolución del Problema Dinámico Inverso y Directo en Tiempo Real de Robots Industriales

ResumenEste trabajo presenta el desarrollo y la validación de una metodología que permite el modelado y la resolución del problema dinámico en tiempo real de robots manipuladores. La ecuación dinámica del robot está basada en la ecuación de movimiento de Gibbs-Appell, proporcionando un conjunto de ecuaciones bien estructuradas que pueden ser calculadas en tiempo real.El artículo aborda el cálculo e implementación del problema dinámico directo e inverso de robots, aplicándose al control en tiempo real de un robot industrial PUMA 560 equipado con una arquitectura abierta de control basada en un computador personal industrial

Interactive Physically-Based Simulation of Roadheader Robot

Roadheader is an engineering robot widely used in underground engineering and mining industry. Interactive dynamics simulation of roadheader is a fundamental problem in unmanned excavation and virtual reality training. However, current research is only based on traditional animation techniques or commercial game engines. There are few studies that apply real-time physical simulation of computer graphics to the field of roadheader robot. This paper aims to present an interactive physically-based simulation system of roadheader robot. To this end, an improved multibody simulation method based on generalized coordinates is proposed. First, our simulation method describes robot dynamics based on generalized coordinates. Compared to state-of-the-art methods, our method is more stable and accurate. Numerical simulation results showed that our method has significantly less error than the game engine in the same number of iterations. Second, we adopt the symplectic Euler integrator instead of the conventional fourth-order Runge-Kutta (RK4) method for dynamics iteration. Compared with other integrators, our method is more stable in energy drift during long-term simulation. The test results showed that our system achieved real-time interaction performance of 60 frames per second (fps). Furthermore, we propose a model format for geometric and robotics modeling of roadheaders to implement the system. Our interactive simulation system of roadheader meets the requirements of interactivity, accuracy and stability

Reducing the Computational Complexity of Mass-Matrix Calculation for High DOF Robots

Increasingly, robots have more degrees of freedom (DOF), imposing a need for calculating more complex dynamics. As a result, better efficiency in carrying out dynamics computations is becoming more important. In this study, an efficient method for computing the joint space inertia matrix (JSIM) for high DOF serially linked robots is addressed. We call this method the Geometric Dynamics Algorithm for High number of robot Joints (GDAHJ). GDAHJ is non-symbolic, preserve simple formulation, and it is convenient for numerical implementation. This is achieved by simplifying the way to recursively derive the mass-matrix exploiting the unique property of each column of the JSIM and minimizing the number of operations with O(n2) complexity. Results compare favorably with existing methods, achieving better performance over state-of-the-art by Featherstone when applied for robots with more than 13 DOF

A review of friction models in interacting joints for durability design.

This paper presents a comprehensive review of friction modelling to provide an understanding of design for durability within interacting systems. Friction is a complex phenomenon and occurs at the interface of two components in relative motion. Over the last several decades, the effects of friction and its modelling techniques have been of significant interests in terms of industrial applications. There is however a need to develop a unified mathematical model for friction to inform design for durability within the context of varying operational conditions. Classical dynamic mechanisms model for the design of control systems has not incorporated friction phenomena due to non-linearity behaviour. Therefore, the tribological performance concurrently with the joint dynamics of a manipulator joint applied in hazardous environments needs to be fully analysed. Previously the dynamics and impact models used in mechanical joints with clearance have also been examined. The inclusion of reliability and durability during the design phase is very important for manipulators which are deployed in harsh environmental and operational conditions. The revolute joint is susceptible to failures such as in heavy manipulators these revolute joints can be represented by lubricated conformal sliding surfaces. The presence of pollutants such as debris and corrosive constituents has the potential to alter the contacting surfaces, would in turn affect the performance of revolute joints, and puts both reliability and durability of the systems at greater risks of failure. Key literature is identified and a review on the latest developments of the science of friction modelling is presented here. This review is based on a large volume of knowledge. Gaps in the relevant field have been identified to capitalise on for future developments. Therefore, this review will bring significant benefits to researchers, academics and industrial professionals

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

Examination and comparison of different methods to model closed loop kinematic chains using Lagrangian formulation with cut joint, clearance joint constraint and elastic joint approaches

This work aims at presenting, in a comprehensive manner, several approaches to model and simulate closed loop topologies using the classical Lagrangian formulation. One of the great advantages of the Lagrangian approach is its simplicity and easiness of obtaining the equations of motion. However, a critical aspect arises when the mechanical systems include closed loop topologies, since the process of deriving the equations of motion becomes a complex task. The key point of the present study is to convert the closed loop nature into open systems, which ultimately simplifies the modeling process when the Lagrangian formulation is utilized. For this purpose, three different methods are considered, namely those based on the cut joint approach, the clearance joint constraint model, and the elastic joint formulation are used. In the sequel of this process, a slider-crank mechanism is utilized as a demonstrative application example, and the main results are compared with those obtained with the well-established Newton-Euler method for constrained multibody systems. Moreover, this example allows the comparison of the main characteristics and peculiarities of the described approaches.This work has been supported by Portuguese Foundation for Science and Technology, under the national support to R&D units grant, with the reference project UIDB/04436/2020 and UIDP/04436/2020, as well as through IDMEC, under LAETA, project UIDB/50022/202