Modelling And Experimental Vibration Control Of A Two-link Three-dimensional Manipulator With Flexible Links

Current industrial and space manipulators are required to achieve higher speeds in a lighter structure without sacrificing payload capabilities. Consequently, undesirable vibration occurs during the motion. By suitable modelling of the manipulator flexibility, advanced control strategies can be formulated to improve the joint tracking performance and reduce the residual vibration of the end-point in the presence of payload uncertainties.;Toward this goal, an experimental two-link, 3D, anthropomorphic manipulator with flexible links was designed and built to be used as a test bed for the verification and refinement of the proposed modelling and control strategies.;The nonlinear equations of motion for the robot were derived using Lagrangian dynamics. The model was verified using experimental modal analysis techniques. Based on experimental results, a simplified nonlinear model, that contains the relevant modes of the system, was derived and subsequently used in controller designs and state estimation.;A conventional Proportional-plus-Derivative (PD) controller that implements joint angles feedback was designed to be used as a baseline controller due to its wide applicability on industrial manipulators.;By measuring the links tip vibration using accelerometers, several adaptive controllers and state observers were designed and implemented successfully on the manipulator, namely, a gain-scheduling linear quadratic regulator, a model reference adaptive controller, an adaptive inverse dynamics controller, a least-squares nonlinear state estimator and a robust sliding observer. The controllers performance and robustness were tested and experimentally verified against the change of the payload.;The control strategies and identification techniques, developed in this thesis, are applicable to a wide range of robot manipulators including industrial manipulators

Development of New Adaptive Control Strategies for a Two-Link Flexible Manipulator

Manipulators with thin and light weight arms or links are called as Flexible-Link Manipulators (FLMs). FLMs offer several advantages over rigid-link manipulators such as achieving highspeed operation, lower energy consumption, and increase in payload carrying capacity and find applications where manipulators are to be operated in large workspace like assembly of freeflying space structures, hazardous material management from safer distance, detection of flaws in large structure like airplane and submarines. However, designing a feedback control system for a flexible-link manipulator is challenging due the system being non-minimum phase, underactuated and non-collocated. Further difficulties are encountered when such manipulators handle unknown payloads. Overall deflection of the flexible manipulator are governed by the different vibrating modes (excited at different frequencies) present along the length of the link. Due to change in payload, the flexible modes (at higher frequencies) are excited giving rise to uncertainties in the dynamics of the FLM. To achieve effective tip trajectory tracking whilst quickly suppressing tip deflections when the FLM carries varying payloads adaptive control is necessary instead of fixed gain controller to cope up with the changing dynamics of the manipulator. Considerable research has been directed in the past to design adaptive controllers based on either linear identified model of a FLM or error signal driven intelligent supervised learning e.g. neural network, fuzzy logic and hybrid neuro-fuzzy. However, the dynamics of the FLM being nonlinear there is a scope of exploiting nonlinear modeling approach to design adaptive controllers. The objective of the thesis is to design advanced adaptive control strategies for a two-link flexible manipulator (TLFM) to control the tip trajectory tracking and its deflections while handling unknown payloads. To achieve tip trajectory control and simultaneously suppressing the tip deflection quickly when subjected to unknown payloads, first a direct adaptive control (DAC) is proposed. The proposed DAC uses a Lyapunov based nonlinear adaptive control scheme ensuring overall system stability for the control of TLFM. For the developed control laws, the stability proof of the closed-loop system is also presented. The design of this DAC involves choosing a control law with tunable TLFM parameters, and then an adaptation law is developed using the closed loop error dynamics. The performance of the developed controller is then compared with that of a fuzzy learning based adaptive controller (FLAC). The FLAC consists of three major components namely a fuzzy logic controller, a reference model and a learning mechanism. It utilizes a learning mechanism, which automatically adjusts the rule base of the fuzzy controller so that the closed loop performs according to the user defined reference model containing information of the desired behavior of the controlled system. Although the proposed DAC shows better performance compared to FLAC but it suffers from the complexity of formulating a multivariable regressor vector for the TLFM. Also, the adaptive mechanism for parameter updates of both the DAC and FLAC depend upon feedback error based supervised learning. Hence, a reinforcement learning (RL) technique is employed to derive an adaptive controller for the TLFM. The new reinforcement learning based adaptive control (RLAC) has an advantage that it attains optimal control adaptively in on-line. Also, the performance of the RLAC is compared with that of the DAC and FLAC. In the past, most of the indirect adaptive controls for a FLM are based on linear identified model. However, the considered TLFM dynamics is highly nonlinear. Hence, a nonlinear autoregressive moving average with exogenous input (NARMAX) model based new Self-Tuning Control (NMSTC) is proposed. The proposed adaptive controller uses a multivariable Proportional Integral Derivative (PID) self-tuning control strategy. The parameters of the PID are adapted online using a nonlinear autoregressive moving average with exogenous-input (NARMAX) model of the TLFM. Performance of the proposed NMSTC is compared with that of RLAC. The proposed NMSTC law suffers from over-parameterization of the controller. To overcome this a new nonlinear adaptive model predictive control using the NARMAX model of the TLFM (NMPC) developed next. For the proposed NMPC, the current control action is obtained by solving a finite horizon open loop optimal control problem on-line, at each sampling instant, using the future predicted model of the TLFM. NMPC is based on minimization of a set of predicted system errors based on available input-output data, with some constraints placed on the projected control signals resulting in an optimal control sequence. The performance of the proposed NMPC is also compared with that of the NMSTC. Performances of all the developed algorithms are assessed by numerical simulation in MATLAB/SIMULINK environment and also validated through experimental studies using a physical TLFM set-up available in Advanced Control and Robotics Research Laboratory, National Institute of Technology Rourkela. It is observed from the comparative assessment of the performances of the developed adaptive controllers that proposed NMPC exhibits superior 7performance in terms of accurate tip position tracking (steady state error ≈ 0.01°) while suppressing the tip deflections (maximum amplitude of the tip deflection ≈ 0.1 mm) when the manipulator handles variation in payload (increased payload of 0.3 kg). The adaptive control strategies proposed in this thesis can be applied to control of complex flexible space shuttle systems, long reach manipulators for hazardous waste management from safer distance and for damping of oscillations for similar vibration systems

A family of asymptotically stable control laws for flexible robots based on a passivity approach

A general family of asymptotically stabilizing control laws is introduced for a class of nonlinear Hamiltonian systems. The inherent passivity property of this class of systems and the Passivity Theorem are used to show the closed-loop input/output stability which is then related to the internal state space stability through the stabilizability and detectability condition. Applications of these results include fully actuated robots, flexible joint robots, and robots with link flexibility

Dynamic modeling, property investigation, and adaptive controller design of serial robotic manipulators modeled with structural compliance

Research results on general serial robotic manipulators modeled with structural compliances are presented. Two compliant manipulator modeling approaches, distributed and lumped parameter models, are used in this study. System dynamic equations for both compliant models are derived by using the first and second order influence coefficients. Also, the properties of compliant manipulator system dynamics are investigated. One of the properties, which is defined as inaccessibility of vibratory modes, is shown to display a distinct character associated with compliant manipulators. This property indicates the impact of robot geometry on the control of structural oscillations. Example studies are provided to illustrate the physical interpretation of inaccessibility of vibratory modes. Two types of controllers are designed for compliant manipulators modeled by either lumped or distributed parameter techniques. In order to maintain the generality of the results, neither linearization is introduced. Example simulations are given to demonstrate the controller performance. The second type controller is also built for general serial robot arms and is adaptive in nature which can estimate uncertain payload parameters on-line and simultaneously maintain trajectory tracking properties. The relation between manipulator motion tracking capability and convergence of parameter estimation properties is discussed through example case studies. The effect of control input update delays on adaptive controller performance is also studied

Control of flexible joint robotic manipulator using tuning functions design

The goal of this thesis is to design the controller for a single arm manipulator having a flexible joint for the tracking problem in two different cases. A controller is designed for a deterministic case wherein the plant parameters are assumed to be known while another is designed for an adaptive case where all the plant parameters are assumed to be unknown. In general the tracking problem is; given a smooth reference trajectory, the end effector has to track the reference while maintaining the stability. It is assumed that only the output of the manipulator, which is the link angle, is available for measurement. Also without loss of generality, the fast dynamics, that is the dynamics of the driver side of the system are neglected for the sake of simplicity; In the first case, the design procedure adopted is called observer backstepping. Since the states of the system are unavailable for measurement, an observer is designed that estimates the system states. These estimates are fed to the controller which in turn produces the control input to the system; The second case employs a design procedure called tuning functions design. In this case, since the plant parameters are unknown, the observer designed in case one cannot be used for determining the state estimates. For this purpose, parameter update laws and filters are designed for estimation of plant parameters. The filters employed are k-filters. The k-filters and the parameter update laws are given as input to the controller, which generates the control input to the system; For both cases, the mathematical models are simulated using Matlab/Simulink, and the results are verified

Experimental comparison of parameter estimation methods in adaptive robot control

In the literature on adaptive robot control a large variety of parameter estimation methods have been proposed, ranging from tracking-error-driven gradient methods to combined tracking- and prediction-error-driven least-squares type adaptation methods. This paper presents experimental data from a comparative study between these adaptation methods, performed on a two-degrees-of-freedom robot manipulator. Our results show that the prediction error concept is sensitive to unavoidable model uncertainties. We also demonstrate empirically the fast convergence properties of least-squares adaptation relative to gradient approaches. However, in view of the noise sensitivity of the least-squares method, the marginal performance benefits, and the computational burden, we (cautiously) conclude that the tracking-error driven gradient method is preferred for parameter adaptation in robotic applications

Adaptive control of a manipulator with a flexible link

An adaptive controller for a manipulator with one rigid link and one flexible link is presented. The performance and robustness of the controller are demonstrated by numerical simulation results. In the simulations, the manipulator moves in a gravitational field and a finite element model represents the flexible link

Stanford Aerospace Research Laboratory research overview

Over the last ten years, the Stanford Aerospace Robotics Laboratory (ARL) has developed a hardware facility in which a number of space robotics issues have been, and continue to be, addressed. This paper reviews two of the current ARL research areas: navigation and control of free flying space robots, and modelling and control of extremely flexible space structures. The ARL has designed and built several semi-autonomous free-flying robots that perform numerous tasks in a zero-gravity, drag-free, two-dimensional environment. It is envisioned that future generations of these robots will be part of a human-robot team, in which the robots will operate under the task-level commands of astronauts. To make this possible, the ARL has developed a graphical user interface (GUI) with an intuitive object-level motion-direction capability. Using this interface, the ARL has demonstrated autonomous navigation, intercept and capture of moving and spinning objects, object transport, multiple-robot cooperative manipulation, and simple assemblies from both free-flying and fixed bases. The ARL has also built a number of experimental test beds on which the modelling and control of flexible manipulators has been studied. Early ARL experiments in this arena demonstrated for the first time the capability to control the end-point position of both single-link and multi-link flexible manipulators using end-point sensing. Building on these accomplishments, the ARL has been able to control payloads with unknown dynamics at the end of a flexible manipulator, and to achieve high-performance control of a multi-link flexible manipulator