Research On Analyses Of Motion Characteristics And Motion Control Of Serial Robot Combining Screw Theory

The technology of robot is a cross-disciplinary integration, including mechanical, electronic, computer, control, information, artificial intelligence, bionics and other high-tech field. Also, robot is a typical MIMO nonlinear uncertain system, in the motion control problem there are always some differences between the actual plant dynamics and the nominal mathematical model used for the controller algorithm design. Unmodeled system dynamics, random disturbances, and unknown plant parameters may result in these discrepancies. Control in the presence of uncertainties is one of the hot and important topics of modern control theory. Hence, it is of great theoretical and practical significance to study the trajectory tracking robust control of robot with uncertainties. The prior research should be to establish the appropriate and effective mathematical kinematic and dynamic model for a robot. The classical robot description method is the D-H parameter description as well as the homogeneous coordinates transformation, which faces some critical disadvantages. Hence, in order to pursue the essential characteristics of kinematics, more attention should be paid to the analysis of the micro, local properties. Lie group, Lie algebra and screw theory are the kind of suitable mathematical tool.Based on the Lie groups and Lie algebra as well as screw theory, this paper strictly deduces and theoretically analyzes the forward, inverse kinematics and dynamic equation of multi-DOF serial robot to reveal the essential movement characteristics. Also it can be regarded as an effective supplement of the traditional methods. Then, to deal with the uncertainties of robot system, the sliding mode control is introduced in this paper, with the advantages of simple design and strong robustness. Moreover, to promote the control performance and reduce the chattering, many advanced control theories, such as nonlinear saturation design, fuzzy logic control and adaptive control have been combined properly and applied to sliding mode variable structure system. This dissertation is dedicated to research on the high-precision motion control of multi-DOF nonlinear serial robot system with uncertainties.This dissertation is divided into seven chapters, each of them is arranged as follows:In chapter I, we introduce the background of this topic by analyzing the latest progress of domestic and foreign research technology as well as industry applications on robot system, and highlight the great significance by stressing the present urgent demand of robot industry development of Zhejiang province. On the basis of literature review, the key technology of related research, existing problems and the development direction of them are discussed. Finally, the funding support and research content of this research topic are clarified.In chapter II, based on screw theory and Li group, the kinematic model of serial robot is established and the explicit-form error model has been built based on POE formula, then an improved and efficient inverse kinematics algorithm is proposed. First of all, Lie group and screws are used to describe rigid space motion and define the motion screw of serial robot, then taking "Qianjiang I" as an example of six DOF serial robot, the POE (product of exponentials) formula of serial robot kinematic model is given, and based on this kinematic model, the geometrical parameter error model is studied, which is the basis of geometric parameter calibration work. Focusing on the problem of real-time solutions for inverse kinematics using screw theory, we further introduce three basic known Paden-Kahan sub-problems, and propose a novel inverse kinematics sub-problem for the special structure of "Qianjiang I". Furthermore, the application strategy of certain related mathematical property is discussed in detail, such as product of exponentials, reference point selection and the principle of distance remaining the same. By combining the new sub-problem and Paden-Kahan sub-problems we complete the full real-time solutions for inverse kinematics of "Qianjiang I" successfully. The effectiveness and reliability performance of the new algorithm are analyzed and verified by checking computation and comparative experiments.In chapter Ⅲ, based on the screw theory kinematic model, the Jacobian matrix of serial robot is analyzed, then combining the screw theory and Kane’s equation a new efficient dynamic method is established and the merit of this method is verified by comparing to other common dynamic methods. Firstly, the Jacobian matrix of serial robot has been discussed in two views of POE and kinematic pair screw. Then combining the screw theory, the Kane’s equation dynamic method is introduced by selecting the suitable Jacobian matrix, and then the active force wrench, inertial force wrench, partial velocity twist, generalized active force, and generalized inertial force are defined. Finally the recursive dynamic method based on Kane’s equation and screw theory can be deduced by applying the D’alembert’s principle. Taking "Qianjiang I" as an example, we complete the dynamic modeling using software Maple, and compare it with other common methods, which shows that screw theory could promote the development of highly-efficient dynamics modeling and allow the better geometric interpretation.In chapter IV, for the uncertainties of robot system, the integral sliding mode control is adopted as it has the advantage of holding the invariance for the change of system model uncertainties, random disturbances, and system parameters. Meanwhile, in order to decrease the steady-state error and prevent from the integrator windup, a new nonlinear saturation function derived from quasi-natural potential function is designed to improve the performance of traditional integral sliding mode control. Firstly we employ the dynamic model for serial robots referred to chapter 3, and summarize some related dynamic characteristics. Then a class of quasi-natural potential function and nonlinear saturation function is projected by using the "boundary layer control" to replace the traditional integral part. When outside the boundary layer, the integral action is restricted by the adjusting factor to avoid the large overshoot and long adjustment time. When inside the boundary layer, the integral action is completed as to reduce the steady-state error and improve the robustness. Then the stability analysis of the proposed sliding mode controller for the system is performed by using Lyapunov stability theory and LaSalle invariance principle. Finally, comparative experiments are given to demonstrate the effectiveness and robustness of the proposed approach.In chapter V, aiming to improve the slow-convergence problem, achieve the global non-singular control and alleviate the chattering, a fast non-singular terminal sliding mode(FNTSM) control, incorporating the fuzzy logic controller (FLC),is presented in this paper Firstly, we discuss and theoretically analyze the convergence characteristics and control singularity problem by comparing the common sliding mode control with linear sliding mode (LSM), terminal sliding mode (TSM) and non-singular terminal sliding mode (NTSM). Then an improved fast non-singular terminal sliding mode surface is designed by bringing in appropriate exponential function and factor options to ensure the fast convergence in global system state whether it is near to equilibrium or far away from the equilibrium. Furthermore, a fuzzy control strategy instead of switching function is adopted to reduce the chattering and make the control more smooth without deteriorating the system reliability and robustness. Then the stability analysis of the proposed method is performed by using Lyapunov stability theory. Finally, comparative experiments are implemented to demonstrate the effectiveness and robustness of the proposed approach.In chapter VI, for the complicated nonlinear robot system, to achieve the low model-dependence control and to smoothen the control output, a single-input direct adaptive fuzzy sliding mode control is approached with the merit of general approximate characteristic of fuzzy systems. In case of the difficulty in modelling or various unknowns, the adaptive fuzzy logic control is applied to directly approximate the equivalent control without estimating the unknown parameters in advance. Furthermore, to reduce the fuzzy rules and improve fuzzy reasoning efficiency, we only use the sliding surface variable as a single-input instead of the traditional use of two inputs as fuzzy input. Meanwhile, the adaptive law in controller is designed to adjust its parameters according to parameter changes of the control system, which enhances the anti-interference ability. And the chattering of sliding mode control is alleviated by simplifying the fuzzy control in chapter 5. The stability of the proposed controller is proved by using Lyapunov method. Finally, without acknowledging the model parameters, some tracking experiments are implemented based on the motor-driven robot system and hydraulic-driven robot system, respectively, to demonstrate the robustness and effectiveness of the method, and the results show the control output can follow the reference position signal quickly and smoothly.In chapter VII, the conclusions of the main research are summarized, the innovations in the present work are pointed out, and some subsequent related work are also prospected.