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Journal ArticleDOI

Transfer Learning for High-Precision Trajectory Tracking Through $\mathcal{L}_1$ Adaptive Feedback and Iterative Learning

TL;DR: Results highlight that the combined adaptive control and iterative learning control framework can achieve high-precision trajectory tracking when unknown and changing disturbances are present and can achieve transfer of learned experience between dynamically different systems.
Abstract: Robust and adaptive control strategies are needed when robots or automated systems are introduced to unknown and dynamic environments where they are required to cope with disturbances, unmodeled dynamics, and parametric uncertainties. In this paper, we demonstrate the capabilities of a combined $\mathcal{L}_1$ adaptive control and iterative learning control (ILC) framework to achieve high-precision trajectory tracking in the presence of unknown and changing disturbances. The $\mathcal{L}_1$ adaptive controller makes the system behave close to a reference model; however, it does not guarantee that perfect trajectory tracking is achieved, while ILC improves trajectory tracking performance based on previous iterations. The combined framework in this paper uses $\mathcal{L}_1$ adaptive control as an underlying controller that achieves a robust and repeatable behavior, while the ILC acts as a high-level adaptation scheme that mainly compensates for systematic tracking errors. We illustrate that this framework enables transfer learning between dynamically different systems, where learned experience of one system can be shown to be beneficial for another different system. Experimental results with two different quadrotors show the superior performance of the combined $\mathcal{L}_1$-ILC framework compared with approaches using ILC with an underlying proportional-derivative controller or proportional-integral-derivative controller. Results highlight that our $\mathcal{L}_1$-ILC framework can achieve high-precision trajectory tracking when unknown and changing disturbances are present and can achieve transfer of learned experience between dynamically different systems. Moreover, our approach is able to achieve precise trajectory tracking in the first attempt when the initial input is generated based on the reference model of the adaptive controller.
Citations
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Journal ArticleDOI
TL;DR: A new two-optimization design method for the iterative learning control, which is easy to obtain and implement and applies it onto the quadrotor unmanned aerial vehicles (UAVs) trajectory tracking problem.
Abstract: This paper presents a two-step optimization-based design method for iterative learning control and applies it onto the quadrotor unmanned aerial vehicles (UAVs) trajectory tracking problem. Iterative learning control aims to improve the tracking performance through learning from errors over iterations in repetitively operated systems. The tracking errors from previous iterations are injected into a learning filter and a robust filter to generate the learning signal. The design of the two filters usually involves nontrivial tuning work. This paper presents a new two-optimization design method for the iterative learning control, which is easy to obtain and implement. In particular, the learning filter design problem is transferred into a feedback controller design problem for a purposely constructed system, which is solved based on H-infinity optimal control theory thereafter. The robust filter is then obtained by solving an additional optimization to guarantee the learning convergence. Through the proposed design method, the learning performance is optimized and the system's stability is guaranteed. The proposed two-step optimization-based design method and the regarding iterative learning control algorithm are validated by both numerical and experimental studies.

7 citations

Journal ArticleDOI
TL;DR: Model predictive control has an advantage over conventional state feedback and output feedback controllers because it predicts the response of the system, rather than simply reacting to it, and can offer improved performance in the presence of input and output constraints.
Abstract: A study o provides a control scheme that alleviates this reliance on an accurate model by applying an adaptive control augmentation to the abraic model predictive control (AMPC) control law. Adaptive MPC has been investigated previously by incorporating a parameter estimation algorithm to identify the model used by the MPC. The MPC controller is used to compute the optimal reference command, which is then augmented by the adaptive control law. The study also shows that the L1-augmented nonpredictive adaptive control schemes has more time delay as compared with the MPC- L1 scheme.

6 citations

Journal ArticleDOI
TL;DR: The Special Issue presents results of current research on learning‐based adaptive methods, merging together model‐based and data‐driven adaptive approaches, and focuses on challenging practical applications ranging from UAVs, and autonomous vehicles, to heating and ventilation systems.

3 citations

References
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Book
01 Nov 2008
TL;DR: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization, responding to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.
Abstract: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.

17,420 citations


"Transfer Learning for High-Precisio..." refers background or methods in this paper

  • ...f Z c, 1;land 2;lare Lagrange multipliers for the set V actof estimated output by j+1 active constraints and the set Z actof input r 2;j+1 active constraints. The first-order necessary conditions [28] for r 2;j+1 to be a solution of (28) subject to (29) state that there are vectors 1 and 2 such that the following system of equations is satisfied: 2 6 6 6 4 F T ILC QF ILC + W (V c;actF ILC)T Z ...

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  • ...s the matrix whose rows are V c;l8l2V actand Z c;actis the matrix whose rows are Z c;l8l2Z act. These conditions are a consequence of the first-order optimality conditions described in Theorem 12.2 in [28]. We denote L V;ZNas the number of elements in V c;act[Z c;act. We use Z to denote the N (N L V;Z) matrix whose columns are a basis for the null space of [V c;actF ILC Z c;act]T. That is, Z has full ...

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Book
01 Jan 1996
TL;DR: This book presents a rigorous, yet easily readable, introduction to the analysis and design of robust multivariable control systems and provides the reader with insights into the opportunities and limitations of feedback control.
Abstract: From the Publisher: This is a book on practical feedback control and not on system theory in general. Feedback is used in control systems to change the dynamics of the system and to reduce the sensitivity of the system to both signal and model uncertainty. The book presents a rigorous, yet easily readable, introduction to the analysis and design of robust multivariable control systems. It provides the reader with insights into the opportunities and limitations of feedback control. Its objective is to enable the engineer to design real control systems. Important topics are: extensions and classical frequency-domain methods to multivariable systems, analysis of directions using the singular value decomposition, performance limitations and input-output controllability analysis, model uncertainty and robustness including the structured singular value, control structure design, and methods for controller synthesis and model reduction. Numerous worked examples, exercises and case studies, which make frequent use of MATLAB, are included. MATLAB files for examples and figures, solutions to selected exercises, extra problems and linear state-space models for the case studies are available on the Internet.

6,279 citations


"Transfer Learning for High-Precisio..." refers background in this paper

  • ... the underlying controller must be robust enough as small changes in the conditions may otherwise result in a dramatic decrease in controller performance and could cause instability (see [1], [2] and [3]). The objective of this paper is to design a framework that makes the system achieve a repeatable behavior even in the presence of unknown disturbances and changing dynamics, that improves performanc...

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Journal ArticleDOI
TL;DR: Though beginning its third decade of active research, the field of ILC shows no sign of slowing down and includes many results and learning algorithms beyond the scope of this survey.
Abstract: This article surveyed the major results in iterative learning control (ILC) analysis and design over the past two decades. Problems in stability, performance, learning transient behavior, and robustness were discussed along with four design techniques that have emerged as among the most popular. The content of this survey was selected to provide the reader with a broad perspective of the important ideas, potential, and limitations of ILC. Indeed, the maturing field of ILC includes many results and learning algorithms beyond the scope of this survey. Though beginning its third decade of active research, the field of ILC shows no sign of slowing down.

2,645 citations


Additional excerpts

  • ...u1,ref (s) = C(s) ( r1,ref (s) − σref (s) ) , (14)...

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Journal ArticleDOI
TL;DR: In this article, a theoretical basis for model predictive control (MPC) has started to emerge and many practical problems like control objective prioritization and symptom-aided diagnosis can be integrated into the MPC framework by expanding the problem formulation to include integer variables yielding a mixed-integer quadratic or linear program.

2,320 citations


"Transfer Learning for High-Precisio..." refers background in this paper

  • ...̈̄ r2,j+1 = ⎡⎢⎢⎢⎣ ( r̄2,j+1(2) − 2r̄2,j+1(1) + r̄2,j+1(0) ) ∕(Δt)2 ( r̄2,j+1(3) − 2r̄2,j+1(2) + r̄2,j+1(1) ) ∕(Δt)2 ⋮ ( r̄2,j+1(N) − 2r̄2,j+1(N − 1) + r̄2,j+1(N − 2) ) ∕(Δt)2 ⎤⎥⎥⎥⎦ = D ̈̄ r2,j+1 , (33)...

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  • ...In Section 2, we defined the cost function (2), which tried to minimize the error e....

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Proceedings ArticleDOI
20 Mar 2017
TL;DR: This paper explores domain randomization, a simple technique for training models on simulated images that transfer to real images by randomizing rendering in the simulator, and achieves the first successful transfer of a deep neural network trained only on simulated RGB images to the real world for the purpose of robotic control.
Abstract: Bridging the ‘reality gap’ that separates simulated robotics from experiments on hardware could accelerate robotic research through improved data availability. This paper explores domain randomization, a simple technique for training models on simulated images that transfer to real images by randomizing rendering in the simulator. With enough variability in the simulator, the real world may appear to the model as just another variation. We focus on the task of object localization, which is a stepping stone to general robotic manipulation skills. We find that it is possible to train a real-world object detector that is accurate to 1.5 cm and robust to distractors and partial occlusions using only data from a simulator with non-realistic random textures. To demonstrate the capabilities of our detectors, we show they can be used to perform grasping in a cluttered environment. To our knowledge, this is the first successful transfer of a deep neural network trained only on simulated RGB images (without pre-training on real images) to the real world for the purpose of robotic control.

2,079 citations


Additional excerpts

  • ...Then, the following bounds hold: ||?̃?||∞ ≤ γ0 , (18) ||y2,ref − y2||∞ ≤ γ1 , (19)...

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