Fast Online Control based on Homotopies for Systems subject to Time-Varying Constraints

Fast Online Control based on Homotopies for Systems subject to Time-Varying Constraints

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  • Author: Damian Kontny
  • Publisher: BoD – Books on Demand
  • ISBN: 3737608709
  • Category : Computers
  • Languages : en
  • Pages : 218

The integration of intelligent, autonomously acting systems into modern society is a rapidly growing field. After robots are established for simple, recurring processes in industry and everyday life, more complex tasks are of interest which require the systems to consider the environment in their decision making process. In the future, intelligent systems will get access to fields like autonomous driving cars, unmanned aerial vehicle (UAV), manufacturing processes, household, or the assistance to people in need of care. The fast calculation of optimal circumventing trajectories is therefore an essential component to be able to integrate intelligent systems into our environment at all. The ambitious goal of real-time interaction between a human and an autonomous system is challenging. An autonomous system has to react timely on human motion such that a real interaction can be established. Thus, the autonomous system must continuously capture its environment and adapt its solution. If the system additionally determines a solution with respect to a certain optimization criterion, the computation times quickly rise, and real-time capability moves far away. To solve this problem, the thesis proposes an algorithmic control procedure which determines optimal collision-free trajectories fast. Therefore, a concept which uses homotopy properties in the control procedure is introduced. This allows to determine near-optimal solutions much faster than by commonly used techniques. At the beginning, an algorithmic procedure is shown for linear systems. It selects an optimized, circumventing trajectory based on the current obstacle location, and adapts its trajectory when the obstacle moves. Since real physical systems always underlie actuator limitations like e.g. motor torques, the provided method also considers input constraints. The developed method is subsequently extended to consider predictions of a moving obstacle. Thus, the procedure can further reduce the costs of the executed trajectory and is able to detect and avoid a collision at an early stage. Since many real-world system are described by nonlinear dynamics, the introduced method is also extended to nonlinear systems. The effectiveness of the proposed approach is shown in several simulations. Motivated by the results, the developed approach is extended to more complex tasks, like the collision avoidance between geometric bodies, and to multi agent systems that cooperatively determine solution trajectories in real-time, by means of the homotopy properties. Simulation results of a collision avoidance scenario for a robotic manipulator show, that with the proposed technique good results can be obtained in real-time.


Documentation Abstracts

Documentation Abstracts

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  • Author:
  • Publisher:
  • ISBN:
  • Category : Documentation
  • Languages : en
  • Pages : 812


Computer-Controlled Systems

Computer-Controlled Systems

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  • Author: Karl J Åström
  • Publisher: Courier Corporation
  • ISBN: 0486284042
  • Category : Technology & Engineering
  • Languages : en
  • Pages : 578

This volume features computational tools that can be applied directly and are explained with simple calculations, plus an emphasis on control system principles and ideas. Includes worked examples, MATLAB macros, and solutions manual.


Linear Matrix Inequalities in System and Control Theory

Linear Matrix Inequalities in System and Control Theory

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  • Author: Stephen Boyd
  • Publisher: SIAM
  • ISBN: 9781611970777
  • Category : Mathematics
  • Languages : en
  • Pages : 203

In this book the authors reduce a wide variety of problems arising in system and control theory to a handful of convex and quasiconvex optimization problems that involve linear matrix inequalities. These optimization problems can be solved using recently developed numerical algorithms that not only are polynomial-time but also work very well in practice; the reduction therefore can be considered a solution to the original problems. This book opens up an important new research area in which convex optimization is combined with system and control theory, resulting in the solution of a large number of previously unsolved problems.


Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

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  • Author: Stephen Boyd
  • Publisher: Now Publishers Inc
  • ISBN: 160198460X
  • Category : Computers
  • Languages : en
  • Pages : 138

Surveys the theory and history of the alternating direction method of multipliers, and discusses its applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others.


Index to IEEE Publications

Index to IEEE Publications

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  • Author: Institute of Electrical and Electronics Engineers
  • Publisher:
  • ISBN:
  • Category : Electric engineering
  • Languages : en
  • Pages : 1404

Issues for 1973- cover the entire IEEE technical literature.


Mixed Integer Nonlinear Programming

Mixed Integer Nonlinear Programming

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  • Author: Jon Lee
  • Publisher: Springer Science & Business Media
  • ISBN: 1461419271
  • Category : Mathematics
  • Languages : en
  • Pages : 692

Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions. Mixed-integer nonlinear programming (MINLP) problems combine the numerical difficulties of handling nonlinear functions with the challenge of optimizing in the context of nonconvex functions and discrete variables. MINLP is one of the most flexible modeling paradigms available for optimization; but because its scope is so broad, in the most general cases it is hopelessly intractable. Nonetheless, an expanding body of researchers and practitioners — including chemical engineers, operations researchers, industrial engineers, mechanical engineers, economists, statisticians, computer scientists, operations managers, and mathematical programmers — are interested in solving large-scale MINLP instances.


Exploiting Direct Optimal Control for Motion Planning in Unstructured Environments

Exploiting Direct Optimal Control for Motion Planning in Unstructured Environments

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  • Author: Kristoffer Bergman
  • Publisher: Linköping University Electronic Press
  • ISBN: 9179296777
  • Category : Electronic books
  • Languages : en
  • Pages : 60

During the last decades, motion planning for autonomous systems has become an important area of research. The high interest is not the least due to the development of systems such as self-driving cars, unmanned aerial vehicles and robotic manipulators. The objective in optimal motion planning problems is to find feasible motion plans that also optimize a performance measure. From a control perspective, the problem is an instance of an optimal control problem. This thesis addresses optimal motion planning problems for complex dynamical systems that operate in unstructured environments, where no prior reference such as road-lane information is available. Some example scenarios are autonomous docking of vessels in harbors and autonomous parking of self-driving tractor-trailer vehicles at loading sites. The focus is to develop optimal motion planning algorithms that can reliably be applied to these types of problems. This is achieved by combining recent ideas from automatic control, numerical optimization and robotics. The first contribution is a systematic approach for computing local solutions to motion planning problems in challenging unstructured environments. The solutions are computed by combining homotopy methods and direct optimal control techniques. The general principle is to define a homotopy that transforms, or preferably relaxes, the original problem to an easily solved problem. The approach is demonstrated in motion planning problems in 2D and 3D environments, where the presented method outperforms a state-of-the-art asymptotically optimal motion planner based on random sampling. The second contribution is an optimization-based framework for automatic generation of motion primitives for lattice-based motion planners. Given a family of systems, the user only needs to specify which principle types of motions that are relevant for the considered system family. Based on the selected principle motions and a selected system instance, the framework computes a library of motion primitives by simultaneously optimizing the motions and the terminal states. The final contribution of this thesis is a motion planning framework that combines the strengths of sampling-based planners with direct optimal control in a novel way. The sampling-based planner is applied to the problem in a first step using a discretized search space, where the system dynamics and objective function are chosen to coincide with those used in a second step based on optimal control. This combination ensures that the sampling-based motion planner provides a feasible motion plan which is highly suitable as warm-start to the optimal control step. Furthermore, the second step is modified such that it also can be applied in a receding-horizon fashion, where the proposed combination of methods is used to provide theoretical guarantees in terms of recursive feasibility, worst-case objective function value and convergence to the terminal state. The proposed motion planning framework is successfully applied to several problems in challenging unstructured environments for tractor-trailer vehicles. The framework is also applied and tailored for maritime navigation for vessels in archipelagos and harbors, where it is able to compute energy-efficient trajectories which complies with the international regulations for preventing collisions at sea.


Parametric Optimization

Parametric Optimization

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  • Author: Jürgen Guddat
  • Publisher:
  • ISBN:
  • Category : Mathematics
  • Languages : en
  • Pages : 208

Explores optimization problems in which some or all of the individual data involved depends on one parameter. Beginning with a preliminary survey of solution algorithms in one-parametric optimization, the text moves on to examine the pathfollowing curves of local minimizers, pathfollowing along a connected component in the Karush-Kuhn-Tucker set and in the critical set, pathfollowing in the set of local minimizers and in the set of critical points. In addition, practical applications are included.


Science Abstracts

Science Abstracts

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  • Author:
  • Publisher:
  • ISBN:
  • Category : Electrical engineering
  • Languages : en
  • Pages : 1990