The Experts below are selected from a list of 49977 Experts worldwide ranked by ideXlab platform
Yufei Zhang - One of the best experts on this subject based on the ideXlab platform.
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a neural network based policy iteration algorithm with global h 2 superlinear convergence for stochastic games on domains
Foundations of Computational Mathematics, 2021Co-Authors: Kazufumi Ito, Christoph Reisinger, Yufei ZhangAbstract:In this work, we propose a class of numerical schemes for solving semilinear Hamilton–Jacobi–Bellman–Isaacs (HJBI) boundary value Problems which arise naturally from exit time Problems of diffusion processes with controlled drift. We exploit policy iteration to reduce the semilinear Problem into a sequence of linear Dirichlet Problems, which are subsequently approximated by a multilayer feedforward neural network ansatz. We establish that the numerical solutions converge globally in the $$H^2$$ -norm and further demonstrate that this convergence is superlinear, by interpreting the algorithm as an inexact Newton iteration for the HJBI equation. Moreover, we construct the optimal feedback controls from the numerical value functions and deduce convergence. The numerical schemes and convergence results are then extended to oblique derivative boundary conditions. Numerical experiments on the stochastic Zermelo Navigation Problem are presented to illustrate the theoretical results and to demonstrate the effectiveness of the method.
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A Neural Network-Based Policy Iteration Algorithm with Global $$H^2$$H2-Superlinear Convergence for Stochastic Games on Domains
Foundations of Computational Mathematics, 2020Co-Authors: Kazufumi Ito, Christoph Reisinger, Yufei ZhangAbstract:In this work, we propose a class of numerical schemes for solving semilinear Hamilton–Jacobi–Bellman–Isaacs (HJBI) boundary value Problems which arise naturally from exit time Problems of diffusion processes with controlled drift. We exploit policy iteration to reduce the semilinear Problem into a sequence of linear Dirichlet Problems, which are subsequently approximated by a multilayer feedforward neural network ansatz. We establish that the numerical solutions converge globally in the $$H^2$$ H 2 -norm and further demonstrate that this convergence is superlinear, by interpreting the algorithm as an inexact Newton iteration for the HJBI equation. Moreover, we construct the optimal feedback controls from the numerical value functions and deduce convergence. The numerical schemes and convergence results are then extended to oblique derivative boundary conditions. Numerical experiments on the stochastic Zermelo Navigation Problem are presented to illustrate the theoretical results and to demonstrate the effectiveness of the method.
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a neural network based policy iteration algorithm with global h 2 superlinear convergence for stochastic games on domains
arXiv: Numerical Analysis, 2019Co-Authors: Christoph Reisinger, Yufei ZhangAbstract:In this work, we propose a class of numerical schemes for solving semilinear Hamilton-Jacobi-Bellman-Isaacs (HJBI) boundary value Problems which arise naturally from exit time Problems of diffusion processes with controlled drift. We exploit policy iteration to reduce the semilinear Problem into a sequence of linear Dirichlet Problems, which are subsequently approximated by a multilayer feedforward neural network ansatz. We establish that the numerical solutions converge globally in the $H^2$-norm, and further demonstrate that this convergence is superlinear, by interpreting the algorithm as an inexact Newton iteration for the HJBI equation. Moreover, we construct the optimal feedback controls from the numerical value functions and deduce convergence. The numerical schemes and convergence results are then extended to HJBI boundary value Problems corresponding to controlled diffusion processes with oblique boundary reflection. Numerical experiments on the stochastic Zermelo Navigation Problem are presented to illustrate the theoretical results and to demonstrate the effectiveness of the method.
Kazufumi Ito - One of the best experts on this subject based on the ideXlab platform.
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a neural network based policy iteration algorithm with global h 2 superlinear convergence for stochastic games on domains
Foundations of Computational Mathematics, 2021Co-Authors: Kazufumi Ito, Christoph Reisinger, Yufei ZhangAbstract:In this work, we propose a class of numerical schemes for solving semilinear Hamilton–Jacobi–Bellman–Isaacs (HJBI) boundary value Problems which arise naturally from exit time Problems of diffusion processes with controlled drift. We exploit policy iteration to reduce the semilinear Problem into a sequence of linear Dirichlet Problems, which are subsequently approximated by a multilayer feedforward neural network ansatz. We establish that the numerical solutions converge globally in the $$H^2$$ -norm and further demonstrate that this convergence is superlinear, by interpreting the algorithm as an inexact Newton iteration for the HJBI equation. Moreover, we construct the optimal feedback controls from the numerical value functions and deduce convergence. The numerical schemes and convergence results are then extended to oblique derivative boundary conditions. Numerical experiments on the stochastic Zermelo Navigation Problem are presented to illustrate the theoretical results and to demonstrate the effectiveness of the method.
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A Neural Network-Based Policy Iteration Algorithm with Global $$H^2$$H2-Superlinear Convergence for Stochastic Games on Domains
Foundations of Computational Mathematics, 2020Co-Authors: Kazufumi Ito, Christoph Reisinger, Yufei ZhangAbstract:In this work, we propose a class of numerical schemes for solving semilinear Hamilton–Jacobi–Bellman–Isaacs (HJBI) boundary value Problems which arise naturally from exit time Problems of diffusion processes with controlled drift. We exploit policy iteration to reduce the semilinear Problem into a sequence of linear Dirichlet Problems, which are subsequently approximated by a multilayer feedforward neural network ansatz. We establish that the numerical solutions converge globally in the $$H^2$$ H 2 -norm and further demonstrate that this convergence is superlinear, by interpreting the algorithm as an inexact Newton iteration for the HJBI equation. Moreover, we construct the optimal feedback controls from the numerical value functions and deduce convergence. The numerical schemes and convergence results are then extended to oblique derivative boundary conditions. Numerical experiments on the stochastic Zermelo Navigation Problem are presented to illustrate the theoretical results and to demonstrate the effectiveness of the method.
Christoph Reisinger - One of the best experts on this subject based on the ideXlab platform.
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a neural network based policy iteration algorithm with global h 2 superlinear convergence for stochastic games on domains
Foundations of Computational Mathematics, 2021Co-Authors: Kazufumi Ito, Christoph Reisinger, Yufei ZhangAbstract:In this work, we propose a class of numerical schemes for solving semilinear Hamilton–Jacobi–Bellman–Isaacs (HJBI) boundary value Problems which arise naturally from exit time Problems of diffusion processes with controlled drift. We exploit policy iteration to reduce the semilinear Problem into a sequence of linear Dirichlet Problems, which are subsequently approximated by a multilayer feedforward neural network ansatz. We establish that the numerical solutions converge globally in the $$H^2$$ -norm and further demonstrate that this convergence is superlinear, by interpreting the algorithm as an inexact Newton iteration for the HJBI equation. Moreover, we construct the optimal feedback controls from the numerical value functions and deduce convergence. The numerical schemes and convergence results are then extended to oblique derivative boundary conditions. Numerical experiments on the stochastic Zermelo Navigation Problem are presented to illustrate the theoretical results and to demonstrate the effectiveness of the method.
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A Neural Network-Based Policy Iteration Algorithm with Global $$H^2$$H2-Superlinear Convergence for Stochastic Games on Domains
Foundations of Computational Mathematics, 2020Co-Authors: Kazufumi Ito, Christoph Reisinger, Yufei ZhangAbstract:In this work, we propose a class of numerical schemes for solving semilinear Hamilton–Jacobi–Bellman–Isaacs (HJBI) boundary value Problems which arise naturally from exit time Problems of diffusion processes with controlled drift. We exploit policy iteration to reduce the semilinear Problem into a sequence of linear Dirichlet Problems, which are subsequently approximated by a multilayer feedforward neural network ansatz. We establish that the numerical solutions converge globally in the $$H^2$$ H 2 -norm and further demonstrate that this convergence is superlinear, by interpreting the algorithm as an inexact Newton iteration for the HJBI equation. Moreover, we construct the optimal feedback controls from the numerical value functions and deduce convergence. The numerical schemes and convergence results are then extended to oblique derivative boundary conditions. Numerical experiments on the stochastic Zermelo Navigation Problem are presented to illustrate the theoretical results and to demonstrate the effectiveness of the method.
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a neural network based policy iteration algorithm with global h 2 superlinear convergence for stochastic games on domains
arXiv: Numerical Analysis, 2019Co-Authors: Christoph Reisinger, Yufei ZhangAbstract:In this work, we propose a class of numerical schemes for solving semilinear Hamilton-Jacobi-Bellman-Isaacs (HJBI) boundary value Problems which arise naturally from exit time Problems of diffusion processes with controlled drift. We exploit policy iteration to reduce the semilinear Problem into a sequence of linear Dirichlet Problems, which are subsequently approximated by a multilayer feedforward neural network ansatz. We establish that the numerical solutions converge globally in the $H^2$-norm, and further demonstrate that this convergence is superlinear, by interpreting the algorithm as an inexact Newton iteration for the HJBI equation. Moreover, we construct the optimal feedback controls from the numerical value functions and deduce convergence. The numerical schemes and convergence results are then extended to HJBI boundary value Problems corresponding to controlled diffusion processes with oblique boundary reflection. Numerical experiments on the stochastic Zermelo Navigation Problem are presented to illustrate the theoretical results and to demonstrate the effectiveness of the method.
Roland Siegwart - One of the best experts on this subject based on the ideXlab platform.
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path planning for motion dependent state estimation on micro aerial vehicles
International Conference on Robotics and Automation, 2013Co-Authors: Markus Achtelik, Stephan Weiss, Margarita Chli, Roland SiegwartAbstract:With Navigation algorithms reaching a certain maturity in the field of mobile robots, the community now focuses on more advanced tasks like path planning towards increased autonomy. While the goal is to efficiently compute a path to a target destination, the uncertainty in the robot's perception cannot be ignored if a realistic path is to be computed. With most state of the art Navigation systems providing the uncertainty in motion estimation, here we propose to exploit this information. This leads to a system that can plan safe avoidance of obstacles, and more importantly, it can actively aid Navigation by choosing a path that minimizes the uncertainty in the monitored states. Our proposed approach is applicable to systems requiring certain excitations in order to render all their states observable, such as a MAV with visual-inertial based localization. In this work, we propose an approach which takes into account this necessary motion during path planning: by employing Rapidly exploring Random Belief Trees (RRBT), the proposed approach chooses a path to a goal which allows for best estimation of the robot's states, while inherently avoiding motion in unobservable modes. We discuss our findings within the scenario of vision-based aerial Navigation as one of the most challenging Navigation Problem, requiring sufficient excitation to reach full observability.
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introduction to autonomous mobile robots
2004Co-Authors: Roland Siegwart, Illah Nourbakhsh, Davide ScaramuzzaAbstract:Mobile robots range from the Mars Pathfinder mission's teleoperated Sojourner to the cleaning robots in the Paris Metro. This text offers students and other interested readers an introduction to the fundamentals of mobile robotics, spanning the mechanical, motor, sensory, perceptual, and cognitive layers the field comprises. The text focuses on mobility itself, offering an overview of the mechanisms that allow a mobile robot to move through a real world environment to perform its tasks, including locomotion, sensing, localization, and motion planning. It synthesizes material from such fields as kinematics, control theory, signal analysis, computer vision, information theory, artificial intelligence, and probability theory. The book presents the techniques and technology that enable mobility in a series of interacting modules. Each chapter treats a different aspect of mobility, as the book moves from low-level to high-level details. It covers all aspects of mobile robotics, including software and hardware design considerations, related technologies, and algorithmic techniques.] This second edition has been revised and updated throughout, with 130 pages of new material on such topics as locomotion, perception, localization, and planning and Navigation. Problem sets have been added at the end of each chapter. Bringing together all aspects of mobile robotics into one volume, Introduction to Autonomous Mobile Robots can serve as a textbook or a working tool for beginning practitioners.
David Filliat - One of the best experts on this subject based on the ideXlab platform.
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real time distributed receding horizon motion planning and control for mobile multi robot dynamic systems
International Conference on Robotics and Automation, 2017Co-Authors: Jose Mendes M Filho, Eric Lucet, David FilliatAbstract:This paper proposes an improvement of a motion planning approach and a modified model predictive control (MPC) for solving the Navigation Problem of a team of dynamical wheeled mobile robots in the presence of obstacles in a realistic environment. Planning is performed by a distributed receding horizon algorithm where constrained optimization Problems are numerically solved for each prediction time-horizon. This approach allows distributed motion planning for a multi-robot system with asynchronous communication while avoiding collisions and minimizing the travel time of each robot. However, the robots dynamics prevents the planned motion to be applied directly to the robots. Using unicycle-like vehicles in a dynamic simulation, we show that deviations from the planned motion caused by the robots dynamics can be overcome by modifying the optimization Problem underlying the planning algorithm and by adding an MPC for trajectory tracking. Results also indicate that this approach can be used in systems subjected to real-time constraint.
