A Fast Trajectory Tracking Adaptive Controller for Robot Manipulators

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ISBN 13 :
Total Pages : 86 pages
Book Rating : 4.:/5 (36 download)

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Book Synopsis A Fast Trajectory Tracking Adaptive Controller for Robot Manipulators by : Shinsuke Tagami

Download or read book A Fast Trajectory Tracking Adaptive Controller for Robot Manipulators written by Shinsuke Tagami and published by . This book was released on 1993 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: An adaptive decentralized nonlinear controller for a robot manipulator is presented in this thesis. Based on the adaptive control schemes designed by Seraji [18], Dai [30], and Jimenez [31], we redesigned and further simplified the control algorithm and, as a consequence, we achieved better path tracking performance. The proposed adaptive controller is made of a PD feedback controller which has time varying gains, a feedforward compensator based on the idea of inverse dynamics, and an auxiliary signal. Due to its adaptive structure, the controller shows robustness against disturbances and unmodeled dynamics. In order to ensure asymptotic tracking we select a Lyapunov function such that the controller forces the negative definiteness of the time derivative of such a Lyapunov function. To do this, the tracking position and velocity error are penalized and used as a part of the adaptive control gain. The main advantages of this scheme are the comparably faster convergence of tracking error, relatively simpler structure, and smoother control activity. This controller only requires the position and angular speed measurement, it does not require any knowledge about the mathematical model of the robot manipulator. Simulation shows the capacity of this controller and its robustness against disturbances.

Adaptive Control for Robotic Manipulators

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Publisher : CRC Press
ISBN 13 : 1498764886
Total Pages : 441 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Adaptive Control for Robotic Manipulators by : Dan Zhang

Download or read book Adaptive Control for Robotic Manipulators written by Dan Zhang and published by CRC Press. This book was released on 2017-02-03 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: The robotic mechanism and its controller make a complete system. As the robotic mechanism is reconfigured, the control system has to be adapted accordingly. The need for the reconfiguration usually arises from the changing functional requirements. This book will focus on the adaptive control of robotic manipulators to address the changed conditions. The aim of the book is to summarise and introduce the state-of-the-art technologies in the field of adaptive control of robotic manipulators in order to improve the methodologies on the adaptive control of robotic manipulators. Advances made in the past decades are described in the book, including adaptive control theories and design, and application of adaptive control to robotic manipulators.

AI based Robot Safe Learning and Control

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Publisher : Springer
ISBN 13 : 9789811555053
Total Pages : 127 pages
Book Rating : 4.5/5 (55 download)

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Book Synopsis AI based Robot Safe Learning and Control by : Xuefeng Zhou

Download or read book AI based Robot Safe Learning and Control written by Xuefeng Zhou and published by Springer. This book was released on 2020-09-18 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book mainly focuses on the safe control of robot manipulators. The control schemes are mainly developed based on dynamic neural network, which is an important theoretical branch of deep reinforcement learning. In order to enhance the safety performance of robot systems, the control strategies include adaptive tracking control for robots with model uncertainties, compliance control in uncertain environments, obstacle avoidance in dynamic workspace. The idea for this book on solving safe control of robot arms was conceived during the industrial applications and the research discussion in the laboratory. Most of the materials in this book are derived from the authors’ papers published in journals, such as IEEE Transactions on Industrial Electronics, neurocomputing, etc. This book can be used as a reference book for researcher and designer of the robotic systems and AI based controllers, and can also be used as a reference book for senior undergraduate and graduate students in colleges and universities.

Adaptive Control of Robot Manipulators

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Publisher : World Scientific
ISBN 13 : 9814307424
Total Pages : 274 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Adaptive Control of Robot Manipulators by : An-Chyau Huang

Download or read book Adaptive Control of Robot Manipulators written by An-Chyau Huang and published by World Scientific. This book was released on 2010 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces an unified function approximation approach to the control of uncertain robot manipulators containing general uncertainties. It works for free space tracking control as well as compliant motion control. It is applicable to the rigid robot and the flexible joint robot. Even with actuator dynamics, the unified approach is still feasible. All these features make the book stand out from other existing publications.

Adaptive Control of Mechanical Manipulators

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Publisher : Addison Wesley Publishing Company
ISBN 13 :
Total Pages : 152 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Adaptive Control of Mechanical Manipulators by : John J. Craig

Download or read book Adaptive Control of Mechanical Manipulators written by John J. Craig and published by Addison Wesley Publishing Company. This book was released on 1988 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Switching Adaptive Control of Robot Manipulators

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ISBN 13 :
Total Pages : 163 pages
Book Rating : 4.:/5 (872 download)

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Book Synopsis Switching Adaptive Control of Robot Manipulators by : Mansour Kabganian

Download or read book Switching Adaptive Control of Robot Manipulators written by Mansour Kabganian and published by . This book was released on 1994 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Accurate Trajectory Control of Robotic Manipulators

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Publisher :
ISBN 13 :
Total Pages : 50 pages
Book Rating : 4.:/5 (132 download)

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Book Synopsis Accurate Trajectory Control of Robotic Manipulators by : J. C. Van Winssen

Download or read book Accurate Trajectory Control of Robotic Manipulators written by J. C. Van Winssen and published by . This book was released on 1985 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report presents a control scheme for accurate trajectory following with robotic manipulators. The method uses feedforward control using model-based torques for fast operation and gross compensation, and adaptive feedback control for correcting deviations from the desired trajectory under feedforward control. The adaptive controller eliminates trajectory-following errors in the least squares sense. The control scheme takes into account dynamic nonlinearities (e.g., coriolis and centrifugal accelerations and payload changes), geometric nonlinearities (e.g., nonlinear coordinate-transformation matrices) and physical nonlinearities (e.g., nonlinear damping) as well as dynamic coupling in manipulators. Computer simulations are presented to indicate the effectiveness and robustness of the control scheme. When the desired trajectory is completely known before the control scheme is implemented, then off-line computations can be used to generate the adaptive feedback gains and the computational efficiency will not be a major limiting factor with this control scheme. If real-time changes in the desired trajectory have to be accommodated, the computational efficiency has to be improved using recursive relations to compute the adaptive gains. The necessary recursive relations are derived and presented in this report. (Author).

Adaptive and Iterative Learning Control for Robot Trajectory Tracking

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ISBN 13 :
Total Pages : 109 pages
Book Rating : 4.:/5 (113 download)

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Book Synopsis Adaptive and Iterative Learning Control for Robot Trajectory Tracking by : YU-HSIU LEE

Download or read book Adaptive and Iterative Learning Control for Robot Trajectory Tracking written by YU-HSIU LEE and published by . This book was released on 2019 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis develops adaptive and iterative learning control methods for robot trajectory tracking applications. Specifically, iterative learning control is applied when a desired reference trajectory is known beforehand, and adaptive control is designed to cope with unknown patient motion (disturbance) in MRI-guided robot-assisted intervention. For robot manipulator tracking, a nested-loop iterative learning control is proposed. This method requires only nominal kinematic parameters from factory setting, gives fast convergence, and can be added on top of existing servo loop. The ILC learning architecture includes an inner loop that accounts for motor dynamics, and an outer loop that addresses the static bias from the payload or imprecise kinematics. A data-based learning filter design is extended to cope with motion constraint and multivariate systems. It is experimentally verified on a 6-DOF serial robot that the proposed method mitigates the maximum dynamic tracking error by an order of magnitude, and is applicable to different payloads due to small system variation from torque shielding of gear reduction. For tracking of general nonlinear dynamic systems, an efficient data-driven ILC algorithm is proposed. As opposed to the model-based methods, for which nonlinear identification and learning law design can be cumbersome, this method uses adaptive filter to implicitly (and automatically) construct linearized system inverse for effective learning. An existing adjoint-based ILC for LTI system is also extended to cope with nonlinear dynamics, and for comparative study. The SISO algorithms are simulated and experimentally validated on a fully-actuated 2-DOF laboratory pendulum system. Algorithms are also developed to circumvent the difficulty when adapting a right inverse for MIMO systems. The automated MRI-guided intervention is motivated by the current procedural inefficiency from constraints posed by MR environment. As lots of researchers focus on either MR-safe/conditional robot to augment the reach of the physician, or MR image tracking for motion estimation of tissue/instrument, this work aims at addressing a more flexible setting: use real-time MRI for instrument control when a target is in motion. It is enabled via the integration of robot hardware, MRI sensing, and control techniques. On the control aspect, we characterize the MR imaging process and the robot dynamics, then propose adaptive control schemes to overcome the long delay and high noise variance from MRI measurement. The study is conducted on a hydrostatically actuated platform, which consists of a target motion module that emulates respiratory motion, and an instrument manipulation module regulating the instrument-target distance.

ROBOT TRAJECTORY TRACKING WITH SELF-TUNING PREDICTED CONTROL

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ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis ROBOT TRAJECTORY TRACKING WITH SELF-TUNING PREDICTED CONTROL by : XINZHONG CUI, KANG G. SHIN

Download or read book ROBOT TRAJECTORY TRACKING WITH SELF-TUNING PREDICTED CONTROL written by XINZHONG CUI, KANG G. SHIN and published by . This book was released on 1987 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Robust Tracking Control of Robot Manipulators

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ISBN 13 :
Total Pages : 276 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Robust Tracking Control of Robot Manipulators by : Zhihua Qu

Download or read book Robust Tracking Control of Robot Manipulators written by Zhihua Qu and published by . This book was released on 1996 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Learning for Adaptive and Reactive Robot Control

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Publisher : MIT Press
ISBN 13 : 0262367017
Total Pages : 425 pages
Book Rating : 4.2/5 (623 download)

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Book Synopsis Learning for Adaptive and Reactive Robot Control by : Aude Billard

Download or read book Learning for Adaptive and Reactive Robot Control written by Aude Billard and published by MIT Press. This book was released on 2022-02-08 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods by which robots can learn control laws that enable real-time reactivity using dynamical systems; with applications and exercises. This book presents a wealth of machine learning techniques to make the control of robots more flexible and safe when interacting with humans. It introduces a set of control laws that enable reactivity using dynamical systems, a widely used method for solving motion-planning problems in robotics. These control approaches can replan in milliseconds to adapt to new environmental constraints and offer safe and compliant control of forces in contact. The techniques offer theoretical advantages, including convergence to a goal, non-penetration of obstacles, and passivity. The coverage of learning begins with low-level control parameters and progresses to higher-level competencies composed of combinations of skills. Learning for Adaptive and Reactive Robot Control is designed for graduate-level courses in robotics, with chapters that proceed from fundamentals to more advanced content. Techniques covered include learning from demonstration, optimization, and reinforcement learning, and using dynamical systems in learning control laws, trajectory planning, and methods for compliant and force control . Features for teaching in each chapter: applications, which range from arm manipulators to whole-body control of humanoid robots; pencil-and-paper and programming exercises; lecture videos, slides, and MATLAB code examples available on the author’s website . an eTextbook platform website offering protected material[EPS2] for instructors including solutions.

Robot Force Control

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Publisher : Springer Science & Business Media
ISBN 13 : 1461544319
Total Pages : 154 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Robot Force Control by : Bruno Siciliano

Download or read book Robot Force Control written by Bruno Siciliano and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the fundamental requirements for the success of a robot task is the capability to handle interaction between manipulator and environment. The quantity that describes the state of interaction more effectively is the contact force at the manipulator's end effector. High values of contact force are generally undesirable since they may stress both the manipulator and the manipulated object; hence the need to seek for effective force control strategies. The book provides a theoretical and experimental treatment of robot interaction control. In the framework of model-based operational space control, stiffness control and impedance control are presented as the basic strategies for indirect force control; a key feature is the coverage of six-degree-of-freedom interaction tasks and manipulator kinematic redundancy. Then, direct force control strategies are presented which are obtained from motion control schemes suitably modified by the closure of an outer force regulation feedback loop. Finally, advanced force and position control strategies are presented which include passivity-based, adaptive and output feedback control schemes. Remarkably, all control schemes are experimentally tested on a setup consisting of a seven-joint industrial robot with open control architecture and force/torque sensor. The topic of robot force control is not treated in depth in robotics textbooks, in spite of its crucial importance for practical manipulation tasks. In the few books addressing this topic, the material is often limited to single-degree-of-freedom tasks. On the other hand, several results are available in the robotics literature but no dedicated monograph exists. The book is thus aimed at filling this gap by providing a theoretical and experimental treatment of robot force control.

Advances in Robots Trajectories Learning via Fast Neural Networks

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Publisher : Frontiers Media SA
ISBN 13 : 2889667685
Total Pages : 149 pages
Book Rating : 4.8/5 (896 download)

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Book Synopsis Advances in Robots Trajectories Learning via Fast Neural Networks by : Jose De Jesus Rubio

Download or read book Advances in Robots Trajectories Learning via Fast Neural Networks written by Jose De Jesus Rubio and published by Frontiers Media SA. This book was released on 2021-05-14 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Adaptive Tracking Control of On-Line Path Planners: Velocity Fields and Navigation Functions

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Publisher :
ISBN 13 :
Total Pages : 25 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis Adaptive Tracking Control of On-Line Path Planners: Velocity Fields and Navigation Functions by :

Download or read book Adaptive Tracking Control of On-Line Path Planners: Velocity Fields and Navigation Functions written by and published by . This book was released on 2004 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditionally, robot control research has focused on the position tracking problem where the objective is to force the robot's end-effector to follow an a priori known desired time dependent trajectory. Motivated by task objectives that are more effectively described by on-line, state-dependent trajectories, two adaptive tracking controllers are developed in this paper that accommodate on-line path planning objective. An example adaptive controller is first modified to achieve velocity field tracking in the presence of parametric uncertainty in the robot dynamics. The development aims to relax the typical assumption that the integral of the velocity field is bounded by incorporating a norm- squared gradient term in the control design so that the boundedness of all signals can be proven. An extension is then provided that targets the trajectory planning problem where the task objective can be described as the desire to move to a goal configuration while avoiding known obstacles. Specifically, an adaptive navigation function based controller is designed to provide a path from an initial condition inside the free configuration space of the robot manipulator to the goal configuration. Experimental results for each controller are provided to illustrate proof of validation of the approaches.

On the Time-optimal Trajectory Planning Along Predetermined Geometric Paths and Optimal Control Synthesis for Trajectory Tracking of Robot Manipulators

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Publisher :
ISBN 13 :
Total Pages : 115 pages
Book Rating : 4.:/5 (94 download)

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Book Synopsis On the Time-optimal Trajectory Planning Along Predetermined Geometric Paths and Optimal Control Synthesis for Trajectory Tracking of Robot Manipulators by : Pedro Reynoso Mora

Download or read book On the Time-optimal Trajectory Planning Along Predetermined Geometric Paths and Optimal Control Synthesis for Trajectory Tracking of Robot Manipulators written by Pedro Reynoso Mora and published by . This book was released on 2013 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we study two important subjects in robotics: (i) time-optimal trajectory planning, and (ii) optimal control synthesis methodologies for trajectory tracking. In the first subject, we concentrate on a rather specific sub-class of problems, the time-optimal trajectory planning along predetermined geometric paths. In this kind of problem, a purely geometric path is already known, and the task is to find out how to move along this path in the shortest time physically possible. In order to generate the true fastest solutions achievable by the actual robot manipulator, the complete nonlinear dynamic model should be incorporated into the problem formulation as a constraint that must be satisfied by the generated trajectories and feedforward torques. This important problem was studied in the 1980s, with many related methods for addressing it based on the so-called velocity limit curve and variational methods. Modern formulations directly discretize the problem and obtain a large-scale mathematical optimization problem, which is a prominent approach to tackle optimal control problems that has gained popularity over variational methods, mainly because it allows to obtain numerical solutions for harder problems. We contribute to the referred problem of time-optimal trajectory planning, by extending and improving the existing mathematical optimization formulations. We successfully incorporate the complete nonlinear dynamic model, including viscous friction because for the fastest motions it becomes even more significant than Coulomb friction; of course, Coulomb friction is likewise accommodated for in our formulation. We develop a framework that guarantees exact dynamic feasibility of the generated time-optimal trajectories and feedforward torques. Our initial formulation is carefully crafted in a rather specific manner, so that it allows to naturally propose a convex relaxation that solves exactly the original problem formulation, which is non-convex and therefore hard to solve. In order to numerically solve the proposed formulation, a discretization scheme is also developed. Unlike traditional and modern formulations, we motivate the incorporation of additional criteria to our original formulation, with simulation and experimental studies of three crucial variables for a 6-axis industrial manipulator. Namely, the resulting applied torques, the readings of a 3-axis accelerometer mounted at the manipulator end-effector, and the detrimental effects on the tracking errors induced by pure time-optimal solutions. We therefore emphasize the significance of penalizing a measure of total jerk and of imposing acceleration constraints. These two criteria are incorporated without destroying convexity. The final formulation generates near time-optimal trajectories and feedforward torques with traveling times that are slightly larger than those of pure time-optimal solutions. Nevertheless, the detrimental effects induced by pure time-optimality are eliminated. Experimental results on a 6-axis industrial manipulator confirm that our formulation generates the fastest solutions that can actually be implemented in the real robot manipulator. Following the work done on near time-optimal trajectories, we explore two controller synthesis methodologies for trajectory tracking, which are more suitable to achieve trajectory-tracking under such fast trajectories. In the first approach, we approximate the discrete-time nonlinear dynamics of robot manipulators, moving along the state-reference trajectory, as an affine time-varying (ATV) dynamical system in discrete-time. Therefore, the problem of trajectory tracking for robot manipulators is posed as a linear quadratic (LQ) optimal control problem for a class of discrete-time ATV dynamical systems. Then, an ATV control law to achieve trajectory tracking on the ATV system is developed, which uses LQ methods for linear time-varying (LTV) systems. Since the ATV dynamical system approximates the nonlinear robot dynamics along the state-reference trajectory, the resulting time-varying control law is suitable to achieve trajectory tracking on the robot manipulator. The ATV control law is implemented in experiments for the 6-axis industrial manipulator, tracking the near time-optimal trajectory. Experimental results verify the better performance achieved with the ATV control law, but also expose its shortcomings. The second approach to address trajectory tracking is related in spirit, but different in crucial aspects, which ultimately endow this approach with its superior features. In this novel approach, the highly nonlinear dynamic model of robot manipulators, moving along a state-reference trajectory, is approximated as a class of piecewise affine (PWA) dynamical systems. We propose a framework to construct the referred PWA system, which consists in: (i) choosing strategic operating points on the state-reference trajectory with their respective (local) linearized system dynamics, (ii) constructing ellipsoidal regions centered at the operating points, whose purpose is to facilitate the scheduling strategy of controller gains designed for each local dynamics. Likewise, in order to switch controller gains as the robot state traverses in the direction of the state-reference trajectory, a simple scheduling strategy is proposed. The controller synthesis near each operating point is an LQR-type that takes into account the local coupled dynamics. The referred PWA control law is implemented in experiments for the 6-axis manipulator tracking the near time-optimal trajectory. The experimental results show the feasibility and superiority of the PWA control law over the typical PID controller and the ATV control law.

Adaptive and Learning Controllers for High-Accuracy Trajectory Tracking in Changing Conditions

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Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (133 download)

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Book Synopsis Adaptive and Learning Controllers for High-Accuracy Trajectory Tracking in Changing Conditions by : Karime Pereida

Download or read book Adaptive and Learning Controllers for High-Accuracy Trajectory Tracking in Changing Conditions written by Karime Pereida and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robots are expected to perform tasks reliably in unknown and dynamic environments, which can include unknown disturbances and changing dynamics. This thesis investigates controllers for high-accuracy trajectory tracking of quadrotors in changing conditions. The proposed controllers use $\mathcal{L}_1$ adaptive control to handle disturbances and learning- and optimization-based controllers to improve tracking in changing conditions. The underlying $\Lone$ adaptive controller forces systems subject to unknown disturbances and changing dynamics to behave close to a specified reference model. Learning- and optimization-based controllers improve the tracking performance of the $\mathcal{L}_1$ controlled systems. This thesis presents five frameworks: \begin{enumerate*} \item Iterative Learning Control (ILC), \item Multi-Robot Transfer Learning, \item Multi-Robot, Multi-Task Transfer Learning, \item Adaptive Model Predictive Control (MPC), and \item Robust, Adaptive Model Predictive Control. \end{enumerate*} ILC calculates a feedforward input that minimizes tracking error by using information from previous iterations of the same trajectory. ILC assumes the system has a repeatable behaviour, which may not be true in changing conditions. Repeatability is achieved by using an underlying $\mathcal{L}_1$ adaptive controller. Dynamically different systems can behave in the same specified way if they are equipped with an $\mathcal{L}_1$ adaptive controller. Hence, trajectories learned on one system can directly be transferred to a dynamically different system in a Multi-Robot Transfer Learning framework. Typically, a new learning process has to be started for each desired trajectory. The Multi-Task Transfer Learning framework uses insights from control systems theory to generalize previously learned tasks and enable a Multi-Robot, Multi-Task Transfer Learning framework. In order to eliminate the need for a learning phase to achieve high-accuracy trajectory tracking, $\mathcal{L}_1$ adaptive control is combined with model predictive control. The proposed adaptive MPC leverages the performance guarantees of $\mathcal{L}_1$ adaptive controller to improve tracking performance on the first iteration. However, modelling errors may remain despite the presence of the $\mathcal{L}_1$ adaptive controller. Therefore, we propose and show performance guarantees of a robust adaptive MPC that is robust to modelling errors and improves the trajectory tracking performance in changing conditions. The proposed frameworks were implemented on the Parrot AR.Drone 2.0 and Bebop 2 quadrotors and showed high-accuracy trajectory tracking in changing conditions.

Robotic Manipulator Control Using Neural Networks

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Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783659289682
Total Pages : 0 pages
Book Rating : 4.2/5 (896 download)

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Book Synopsis Robotic Manipulator Control Using Neural Networks by : Al Ashi Mahmoud

Download or read book Robotic Manipulator Control Using Neural Networks written by Al Ashi Mahmoud and published by LAP Lambert Academic Publishing. This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The learning capabilities of artificial neural networks (ANNs) to identify and emulate the behavior of complicated nonlinear systems have made them effective tools that can be utilized in intelligent adaptive control strategies. The use of ANNs in the design of trajectory tracking controllers for robotic manipulators is dated back to the 1980s. Due to the flexibility of their structure as well as the continuous development and enhancement of their self-training algorithms, the use of ANNs in the field of robotic manipulator trajectory tracking control is being considered an important research area. This textbook explains in great detail the process of designing an effective controller to enhance the trajectory tracking performance of a two degree of freedom (2-DOF) robotic arm using neural networks. Feed-forward ANNs were used in both model-based and non-model-based control strategies. Since it also includes a deep explanation of the modeling of the 2-DOF robotic arm system including its actuating DC-motors and their control using a PD controller, this textbook can also serve as an effective educational tool for both undergraduate and graduate electrical engineering students.