Inverse dynamics control and feedforward linearization techniques are typically used to convert the complex nonlinear dynamics of robots to a set of decoupled double integrators, and then a standard, outer-loop controller can be used to calculate the commanded acceleration for the linearized system. However, these methods typically depend on having a very accurate system model, which is not available in practice. While this challenge has been addressed in the literature using different learning approaches, most of these approaches do not provide safety guarantees in terms of stability of the learning-based control system. In this paper, we provide a novel, learning-based control approach based on Gaussian processes (GPs) that ensures both stability of the closed-loop system and high-accuracy tracking. In our proposed approach, we use GPs to approximate the error between the commanded acceleration and the actual acceleration of the system, and then use the predicted mean and variance of the GP to calculate an upper bound on the uncertainty of the linearization. This uncertainty bound is then used in a robust, outer-loop controller to ensure stability of the overall system. Moreover, we show that using our proposed strategy, the tracking error converges to a ball with a radius that can be made arbitrarily small through appropriate control design. Furthermore, we verify the effectiveness of the proposed approach via simulations on (i) a 2 degree-of-freedom (DOF) planar manipulator, and (ii) a 6 DOF industrial manipulator using the Gazebo simulator.
Focusing our attention on safe, learning-based inverse dynamics control, we refer to @cite_4 @cite_1 @cite_14 . In @cite_4 , a model reference adaptive control (MRAC) architecture based on Gaussian processes (GPs) is proposed, and stability of the overall control system is proved. While the approach in @cite_4 is based on adaptive control theory, our approach is based on robust control theory. In particular, in @cite_4 , the mean of the GP is used to exactly cancel the uncertainty vector, while in our approach, we use both the mean and variance of the GP to learn an upper bound on the uncertainty vector to be used in a robust, outer-loop controller. Hence, unlike @cite_4 , in our approach, the uncertainty of the learning module is not only incorporated in the stability analysis but also in the outer-loop controller design. Intuitively, the less certain our GPs are, the more robust the outer-loop controller should be for ensuring safety. When more data is collected and the GPs are more certain, the outer-loop controller can be less conservative for improved performance. While the results of @cite_4 are tested in simulations on a two-dimensional system, we test our results experimentally on a 6 DOF manipulator.
@cite_1 @cite_14 @cite_4
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This paper introduces a learning-based robust control algorithm that provides robust stability and performance guarantees during learning. The approach uses Gaussian process (GP) regression based on data gathered during operation to update an initial model of the system and to gradually decrease the uncertainty related to this model. Embedding this data-based update scheme in a robust control framework guarantees stability during the learning process. Traditional robust control approaches have not considered online adaptation of the model and its uncertainty before. As a result, their controllers do not improve performance during operation. Typical machine learning algorithms that have achieved similar high-performance behavior by adapting the model and controller online do not provide the guarantees presented in this paper. In particular, this paper considers a stabilization task, linearizes the nonlinear, GP-based model around a desired operating point, and solves a convex optimization problem to obtain a linear robust controller. The resulting performance improvements due to the learning-based controller are demonstrated in experiments on a quadrotor vehicle. In this paper we present an overview of techniques and approaches used for a load transportation system based on small size unmanned helicopters. The focus is on the control approach and on the movement of the rope connecting helicopters and load. The proposed approach is based on two control loops: an outer loop to control the translation of each helicopter in compound and an inner loop to control the orientation of helicopters. The challenge here is that in both loops the dynamics of the whole system - all helicopters and load - should be accounted for. It is shown, that for designing the outer loop controller a complex model of the helicopters and load can be replaced by a simplified model based on interconnected mass points. For designing the inner loop controller, the complete dynamics of the whole system are considered. The usage of force sensors in the ropes is proposed in order to simplify the inner loop controller and to make it robust against variations of system parameters. The presented inner loop controller is independent of the number of coupled helicopters. The outer loop controller depends on the number of helicopters. The problem of oscillations in the flexible ropes due to external disturbancies (e.g. wind gusts) is discussed and a solution based on load state observer is presented. The performance of the presented system was verified in simulations and in real flight experiments with one and three helicopters transporting the load. The worldwide first demonstration of a slung load transportation using three helicopters was performed in December 2007. High performance tracking control can only be achieved if a good model of the dynamics is available. However, such a model is often difficult to obtain from first order physics only. In this paper, we develop a data-driven control law that ensures closed loop stability of Lagrangian systems. For this purpose, we use Gaussian Process regression for the feed-forward compensation of the unknown dynamics of the system. The gains of the feedback part are adapted based on the uncertainty of the learned model. Thus, the feedback gains are kept low as long as the learned model describes the true system sufficiently precisely. We show how to select a suitable gain adaption law that incorporates the uncertainty of the model to guarantee a globally bounded tracking error. A simulation with a robot manipulator demonstrates the efficacy of the proposed control law. This paper presents an adaptive high performance control method for autonomous miniature race cars. Racing dynamics are notoriously hard to model from first principles, which is addressed by means of a cautious nonlinear model predictive control (NMPC) approach that learns to improve its dynamics model from data and safely increases racing performance. The approach makes use of a Gaussian Process (GP) and takes residual model uncertainty into account through a chance constrained formulation. We present a sparse GP approximation with dynamically adjusting inducing inputs, enabling a real-time implementable controller. The formulation is demonstrated in simulations, which show significant improvement with respect to both lap time and constraint satisfaction compared to an NMPC without model learning. 1. Introduction. 2. Linear Algebra. 3. Linear Systems. 4. H2 and Ha Spaces. 5. Internal Stability. 6. Performance Specifications and Limitations. 7. Balanced Model Reduction. 8. Uncertainty and Robustness. 9. Linear Fractional Transformation. 10. m and m- Synthesis. 11. Controller Parameterization. 12. Algebraic Riccati Equations. 13. H2 Optimal Control. 14. Ha Control. 15. Controller Reduction. 16. Ha Loop Shaping. 17. Gap Metric and ...u- Gap Metric. 18. Miscellaneous Topics. Bibliography. Index. Gaussian process (GP) regression has been widely used in supervised machine learning due to its flexibility and inherent ability to describe uncertainty in function estimation. In the context of control, it is seeing increasing use for modeling of nonlinear dynamical systems from data, as it allows the direct assessment of residual model uncertainty. We present a model predictive control (MPC) approach that integrates a nominal system with an additive nonlinear part of the dynamics modeled as a GP. Approximation techniques for propagating the state distribution are reviewed and we describe a principled way of formulating the chance constrained MPC problem, which takes into account residual uncertainties provided by the GP model to enable cautious control. Using additional approximations for efficient computation, we finally demonstrate the approach in a simulation example, as well as in a hardware implementation for autonomous racing of remote controlled race cars, highlighting improvements with regard to both performance and safety over a nominal controller. This paper addresses the optimal control problem known as the Linear Quadratic Regulator in the case when the dynamics are unknown. We propose a multi-stage procedure, called Coarse-ID control, that estimates a model from a few experimental trials, estimates the error in that model with respect to the truth, and then designs a controller using both the model and uncertainty estimate. Our technique uses contemporary tools from random matrix theory to bound the error in the estimation procedure. We also employ a recently developed approach to control synthesis called System Level Synthesis that enables robust control design by solving a convex optimization problem. We provide end-to-end bounds on the relative error in control cost that are nearly optimal in the number of parameters and that highlight salient properties of the system to be controlled such as closed-loop sensitivity and optimal control magnitude. We show experimentally that the Coarse-ID approach enables efficient computation of a stabilizing controller in regimes where simple control schemes that do not take the model uncertainty into account fail to stabilize the true system. The paper presents the design, implementation, and evaluation of an adaptive architecture to provide relative delay guarantees for different service classes on Web servers under HTTP 1.1. The first contribution of the paper is the architecture based on a feedback control loop that enforces desired relative delays among classes via dynamic connection scheduling and process reallocation. The second contribution is our use of feedback control theory to design the feedback loop with proven performance guarantees. In contrast with ad hoc approaches that often rely on laborious tuning and design iterations, our control theory approach enables us to systematically design an adaptive Web server with established analytical methods. The design methodology includes using system identification to establish a dynamic model, and using the Root Locus method to design a feedback controller to satisfy performance specifications of a Web server. The adaptive architecture has been implemented by modifying an Apache Web server. Experimental results demonstrate that our adaptive server achieves robust relative delay guarantees even when workload varies significantly. Properties of our adaptive Web server include guaranteed stability, and satisfactory efficiency and accuracy in achieving the desired relative delay differentiation. As software becomes ever more ubiquitous and complex in medical devices, it becomes increasingly important to assure that it performs safely and effectively. The critical nature of medical devices necessitates that the software used therein be reliable and free of errors. It becomes imperative, therefore, to have a conformance review process in place to ascertain the correctness of the software and to ensure that it meets all requirements and standards. Formal methods have long been suggested as a means to design and develop medical device software. However, most manufacturers shy from using these techniques, citing them as too complex and time consuming. As a result, (potentially life-threatening) errors are often not discovered until a device is already on the market. In this paper we present a reference model based approach to software conformance checking. Reference models enable the application of formal methods to software conformance checking, and provide a framework for rigorous testing. To illustrate the approach, we develop the reference model for a generic patient controlled analgesic infusion pump, and explain how it can be used to aid software conformance checking in a regulatory environment. Blimps are a promising platform for aerial robotics and have been studied extensively for this purpose. Unlike other aerial vehicles, blimps are relatively safe and also possess the ability to loiter for long periods. These advantages, however, have been difficult to exploit because blimp dynamics are complex and inherently non-linear. The classical approach to system modeling represents the system as an ordinary differential equation (ODE) based on Newtonian principles. A more recent modeling approach is based on representing state transitions as a Gaussian process (GP). In this paper, we present a general technique for system identification that combines these two modeling approaches into a single formulation. This is done by training a Gaussian process on the residual between the non-linear model and ground truth training data. The result is a GP-enhanced model that provides an estimate of uncertainty in addition to giving better state predictions than either ODE or GP alone. We show how the GP-enhanced model can be used in conjunction with reinforcement learning to generate a blimp controller that is superior to those learned with ODE or GP models alone. A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. Scholars are increasingly citing electronic “web references” which are not preserved in libraries or full text archives. WebCite is a new standard for citing web references. To “webcite” a document involves archiving the cited Web page through www.webcitation.org and citing the WebCite permalink instead of (or in addition to) the unstable live Web page. This journal has amended its “instructions for authors” accordingly, asking authors to archive cited Web pages before submitting a manuscript. Almost 200 other journals are already using the system. We discuss the rationale for WebCite, its technology, and how scholars, editors, and publishers can benefit from the service. Citing scholars initiate an archiving process of all cited Web references, ideally before they submit a manuscript. Authors of online documents and websites which are expected to be cited by others can ensure that their work is permanently available by creating an archived copy using WebCite and providing the citation information including the WebCite link on their Web document(s). Editors should ask their authors to cache all cited Web addresses (Uniform Resource Locators, or URLs) “prospectively” before submitting their manuscripts to their journal. Editors and publishers should also instruct their copyeditors to cache cited Web material if the author has not done so already. Finally, WebCite can process publisher submitted “citing articles” (submitted for example as eXtensible Markup Language [XML] documents) to automatically archive all cited Web pages shortly before or on publication. Finally, WebCite can act as a focussed crawler, caching retrospectively references of already published articles. Copyright issues are addressed by honouring respective Internet standards (robot exclusion files, no-cache and no-archive tags). Long-term preservation is ensured by agreements with libraries and digital preservation organizations. The resulting WebCite Index may also have applications for research assessment exercises, being able to measure the impact of Web services and published Web documents through access and Web citation metrics. @PARASPLIT [J Med Internet Res 2005;7(5):e60] Controlling the robot with a permanently-updated optimal trajectory, also known as model predictive control, is the Holy Grail of whole-body motion generation. Before obtaining it, several challenges should be faced: computation cost, non-linear local minima, algorithm stability, etc. In this paper, we address the problem of applying the updated optimal control in real-time on the physical robot. In particular, we focus on the problems raised by the delays due to computation and by the differences between the real robot and the simulated model. Based on the optimal-control solver MuJoCo, we implemented a complete model-predictive controller and we applied it in real-time on the physical HRP-2 robot. It is the first time that such a whole-body model predictive controller is applied in real-time on a complex dynamic robot. Aside from the technical contributions cited above, the main contribution of this paper is to report the experimental results of this premiere implementation. This paper presents an adaptive image-based visual servoing (IBVS) integratedwith adaptive slidingmode control for a vision-based operation of a quadrotor unmanned aerial vehicle (UAV). For a seamless integration with underactuated quadrotor dynamics, roll and pitch channels are decoupled from the other channels using virtual features. This allows a simple and accurate algorithm for estimating depth information and successful application of the proposed guidance and control algorithm.By employing an adaptive gain in the IBVS controlmethod, the chance of image feature loss is reduced, and performance and stability of the vision-guided UAV control system are improved. The overall setup allows image features to be placed at the desired position in the image plane of a camera mounted on the quadrotor UAV. Stability of the IBVS systemwith the controller is proved using Lyapunov stability analysis. Performance of the overall approach is validated by numerical simulation, vision integrated hardware-inthe-loop simulation, and experiments. The results confirm that the target image is successfully placed at the desired position of the image plane and the quadrotor state variables are properly regulated, showing robustness in the presence of sensor noise, parametric uncertainty, and vibration from motors. Abstract Documents in computer-readable form can be used to provide information about other documents, i.e. those they cite. To do this efficiently requires procedures for computer recognition of citing statements. This is not easy, especially for multi-sentence citing statements. Computer recognition procedures have been developed which are accurate to the following extent: 73 of the words in statements selected by computer procedures as being citing statements are words which are correctly attributable to the corresponding documents. The retrieval effectiveness of computer-recognized citing statements was tested in the following way. First, for eight retrieval requests in inorganiic chemistry, average recall by search of Chemical Abstracts Service indexing and Chemical Abstracts abstract text words was found to be 50 . Words from citing statements referring to the papers to be retrieved were then added to the index terms and abstract words as additional access points, and searching was repeated. Average recall increased to 70 . Only words from citing statements published within a year of the cited papers were used. The retrieval effect of citing statement words alone (published within a year) without index or abstract terms was the following: average recall was 40 . When just the words of the titles of the cited papers were added to those citing statement words, average recall increased to 50 . 1. Background and Preview. 2. Highlights of Classical Control Theory. 3. State Variables and the State Space Description of Dynamic Systems. 4. Fundamentals of Matrix Algebra. 5. Vectors and Linear Vector Spaces. 6. Simultaneous Linear Equations. 7. Eigenvalues and Eigenvectors. 8. Functions of Square Matrices and the Cayley-Hamilton Theorem. 9. Analysis of Continuous and Discrete Time State Equations. 10. Stability. 11. Controllability and Observability for Linear Systems. 12. The Relationship between State Variable and Transfer Function Descriptions of Systems. 13. Design of Linear Feedback Control Systems. 14. An Introduction to Optimal Control Theory. 15. An Introduction to Nonlinear Control Systems. We present a global controller for tracking nominal trajectories with a flying wing tailsitter vehicle. The control strategy is based on a first-principles model of the vehicle dynamics that captures all relevant aerodynamic effects, and we apply an onboard parameter learning scheme in order to estimate unknown aerodynamic parameters. A cascaded control architecture is used: Based on position and velocity errors an outer control loop computes a desired attitude keeping the vehicle in coordinated flight, while an inner control loop tracks the desired attitude using a lookup table with precomputed optimal attitude trajectories. The proposed algorithms can be implemented on a typical microcontroller and the performance is demonstrated in various experiments. This paper presents the design and implementation of an adaptive Web server architecture to provide relative and absolute connection delay guarantees for different service classes. The first contribution of this paper is an adaptive architecture based on feedback control loops that enforce desired connection delays via dynamic connection scheduling and process reallocation. The second contribution is the use of control theoretic techniques to model and design the feedback loops with desired dynamic performance. In contrast to heuristics-based approaches that rely on laborious hand-tuning and testing iteration, the control theoretic approach enables systematic design of an adaptive Web server with established analytical methods. The adaptive architecture has been implemented by modifying an Apache server. Experimental results demonstrate that the adaptive server provides robust delay guarantees even when workload varies significantly A neural network based approach is presented for controlling two distinct types of nonlinear systems. The first corresponds to nonlinear systems with parametric uncertainties where the parameters occur nonlinearly. The second corresponds to systems for which stabilizing control structures cannot be determined. The proposed neural controllers are shown to result in closed-loop system stability under certain conditions. Abstract A robust model predictive control (RMPC) approach for linear systems with bounded state-dependent uncertainties is proposed. Such uncertainties can arise from unmodeled non-linearities or external disturbances, for example. By explicitly considering the state dependency of the uncertainty sets in the RMPC approach, it is shown how closed-loop performance can be improved over existing approaches that consider worst-case uncertainty. Being able to handle state-dependent uncertainties is particularly relevant in learning-based MPC where the system model is learned from data and confidence in the model typically varies over the state space. The efficacy of the proposed approach for learning-based RMPC is illustrated with a numerical example, where uncertainty sets are obtained from data using Gaussian Process regression.