Quaternion Neuro-Fuzzy Learning Algorithm for Fuzzy Rule Generation

Abstract—In order to generate or tune fuzzy rules, Neuro- Fuzzy learning algorithms with Gaussian type membership functions based on gradient-descent method are well known. In this paper, we propose a new learning approach, the Quaternion Neuro-Fuzzy learning algorithm. This method is an extension of the conventional method to four-dimensional space by using a quaternion neural network that maps quaternion to real values. Input, antecedent membership functions and consequent singletons are quaternion, and output is real. Four-dimensional input can be better represented by quaternion than by real values. We compared it with the conventional method by several function identification problems, and revealed that the proposed method outperformed the counterpart: The number of rules was reduced to 5 from 625, the number of epochs by one fortieth, and error by one tenth in the best cases.The Second International Conference on Robot, Vision and Signal Processing December 10-12, 2013 Kitakyushu, Japa

Selected aspects of complex, hypercomplex and fuzzy neural networks

This short report reviews the current state of the research and methodology on theoretical and practical aspects of Artificial Neural Networks (ANN). It was prepared to gather state-of-the-art knowledge needed to construct complex, hypercomplex and fuzzy neural networks. The report reflects the individual interests of the authors and, by now means, cannot be treated as a comprehensive review of the ANN discipline. Considering the fast development of this field, it is currently impossible to do a detailed review of a considerable number of pages. The report is an outcome of the Project 'The Strategic Research Partnership for the mathematical aspects of complex, hypercomplex and fuzzy neural networks' meeting at the University of Warmia and Mazury in Olsztyn, Poland, organized in September 2022.Comment: 46 page

Controlling a drone: Comparison between a based model method and a fuzzy inference system

International audienceThe work describes an automatically on-line self-tunable fuzzy inference system (STFIS) of a new configuration of mini-flying called XSF (X4 Stationnary Flyer) drone. A fuzzy controller based on on-line optimization of a zero order Takagi-Sugeno fuzzy inference system (FIS) by a back propagation-like algorithm is successfully applied. It is used to minimize a cost function that is made up of a quadratic error term and a weight decay term that prevents an excessive growth of parameters. Thus, we carried out control for the continuation of simple trajectories such as the follow-up of straight lines, and complex (half circle, corner, and helicoidal) by using the STFIS technique. This permits to prove the effectiveness of the proposed control law. Simulation results and a comparison with a static feedback linearization controller (SFL) are presented and discussed. We studied the robustness of the two controllers used in the presence of disturbances. We presented two types of disturbances, the case of a breakdown of an engine as well as a gust of wind

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

1999 Flight Mechanics Symposium

This conference publication includes papers and abstracts presented at the Flight Mechanics Symposium held on May 18-20, 1999. Sponsored by the Guidance, Navigation and Control Center of Goddard Space Flight Center, this symposium featured technical papers on a wide range of issues related to orbit-attitude prediction, determination, and control; attitude sensor calibration; attitude determination error analysis; attitude dynamics; and orbit decay and maneuver strategy. Government, industry, and the academic community participated in the preparation and presentation of these papers

Robust Sliding Mode Fuzzy Control of Industrial Robots using an Extended Kalman Filter Inverse Kinematic Solver

This paper presents a sliding mode fuzzy control approach for industrial robots at their static and near static speed (linear velocities less than 5 cm/s). The extended Kalman filter with its covariance resetting is used to translate the coordinates from Cartesian to joint angle space. The translated joint angles are then used as a reference signal to control the industrial robot dynamics using a sliding mode fuzzy controller. The stability and robustness of the proposed controller is proven using an appropriate Lyapunov function in the presence of parameter uncertainty and unknown dynamic friction. The proposed controller is simulated on a 6-DOF industrial robot, namely the Universal Robot-UR5, considering the maximum allowable joint torques. It is observed that the proposed controller can successfully control UR5 under uncertainties in terms of unknown dynamic friction and parameter uncertainties. The tracking performance of the proposed controller is compared with that of the sliding mode control approach. The simulation results demonstrate superior performance of the proposed approach over the sliding mode control method in the presence of uncertainties

Feature-based hybrid inspection planning for complex mechanical parts

Globalization and emerging new powers in the manufacturing world are among many challenges, major manufacturing enterprises are facing. This resulted in increased alternatives to satisfy customers\u27 growing needs regarding products\u27 aesthetic and functional requirements. Complexity of part design and engineering specifications to satisfy such needs often require a better use of advanced and more accurate tools to achieve good quality. Inspection is a crucial manufacturing function that should be further improved to cope with such challenges. Intelligent planning for inspection of parts with complex geometric shapes and free form surfaces using contact or non-contact devices is still a major challenge. Research in segmentation and localization techniques should also enable inspection systems to utilize modern measurement technologies capable of collecting huge number of measured points. Advanced digitization tools can be classified as contact or non-contact sensors. The purpose of this thesis is to develop a hybrid inspection planning system that benefits from the advantages of both techniques. Moreover, the minimization of deviation of measured part from the original CAD model is not the only characteristic that should be considered when implementing the localization process in order to accept or reject the part; geometric tolerances must also be considered. A segmentation technique that deals directly with the individual points is a necessary step in the developed inspection system, where the output is the actual measured points, not a tessellated model as commonly implemented by current segmentation tools. The contribution of this work is three folds. First, a knowledge-based system was developed for selecting the most suitable sensor using an inspection-specific features taxonomy in form of a 3D Matrix where each cell includes the corresponding knowledge rules and generate inspection tasks. A Travel Salesperson Problem (TSP) has been applied for sequencing these hybrid inspection tasks. A novel region-based segmentation algorithm was developed which deals directly with the measured point cloud and generates sub-point clouds, each of which represents a feature to be inspected and includes the original measured points. Finally, a new tolerance-based localization algorithm was developed to verify the functional requirements and was applied and tested using form tolerance specifications. This research enhances the existing inspection planning systems for complex mechanical parts with a hybrid inspection planning model. The main benefits of the developed segmentation and tolerance-based localization algorithms are the improvement of inspection decisions in order not to reject good parts that would have otherwise been rejected due to misleading results from currently available localization techniques. The better and more accurate inspection decisions achieved will lead to less scrap, which, in turn, will reduce the product cost and improve the company potential in the market