21 research outputs found

    Resilient Distributed Energy Management for Systems of Interconnected Microgrids

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    In this paper, distributed energy management of interconnected microgrids, which is stated as a dynamic economic dispatch problem, is studied. Since the distributed approach requires cooperation of all local controllers, when some of them do not comply with the distributed algorithm that is applied to the system, the performance of the system might be compromised. Specifically, it is considered that adversarial agents (microgrids with their controllers) might implement control inputs that are different than the ones obtained from the distributed algorithm. By performing such behavior, these agents might have better performance at the expense of deteriorating the performance of the regular agents. This paper proposes a methodology to deal with this type of adversarial agents such that we can still guarantee that the regular agents can still obtain feasible, though suboptimal, control inputs in the presence of adversarial behaviors. The methodology consists of two steps: (i) the robustification of the underlying optimization problem and (ii) the identification of adversarial agents, which uses hypothesis testing with Bayesian inference and requires to solve a local mixed-integer optimization problem. Furthermore, the proposed methodology also prevents the regular agents to be affected by the adversaries once the adversarial agents are identified. In addition, we also provide a sub-optimality certificate of the proposed methodology.Comment: 8 pages, Conference on Decision and Control (CDC) 201

    Formation control of mobile robots and unmanned aerial vehicles

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    In this dissertation, the nonlinear control of nonholonomic mobile robot formations and unmanned aerial vehicle (UAV) formations is undertaken and presented in six papers. In the first paper, an asymptotically stable combined kinematic/torque control law is developed for leader-follower based formation control of mobile robots using backstepping. A neural network (NN) is introduced along with robust integral of the sign of the error (RISE) feedback to approximate the dynamics of the follower as well as its leader using online weight tuning. Subsequently, in the second paper, a novel NN observer is designed to estimate the linear and angular velocities of both the follower and its leader robot and a NN output feedback control law is developed. On the other hand, in the third paper, a NN-based output feedback control law is presented for the control of an underactuated quad rotor UAV, and a NN virtual control input scheme is proposed which allows all six degrees of freedom to be controlled using only four control inputs. The results of this paper are extended to include the control of quadrotor UAV formations, and a novel three-dimensional leader-follower framework is proposed in the fourth paper. Next, in the fifth paper, the discrete-time nonlinear optimal control is undertaken using two online approximators (OLA\u27s) to solve the infinite horizon Hamilton-Jacobi-Bellman (HJB) equation forward-in-time to achieve nearly optimal regulation and tracking control. In contrast, paper six utilizes a single OLA to solve the infinite horizon HJB and Hamilton-Jacobi-Isaacs (HJI) equations forward-intime for the near optimal regulation and tracking control of continuous affine nonlinear systems. The effectiveness of the optimal tracking controllers proposed in the fifth and sixth papers are then demonstrated using nonholonomic mobile robot formation control --Abstract, page iv

    Event-triggered near optimal adaptive control of interconnected systems

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    Increased interest in complex interconnected systems like smart-grid, cyber manufacturing have attracted researchers to develop optimal adaptive control schemes to elicit a desired performance when the complex system dynamics are uncertain. In this dissertation, motivated by the fact that aperiodic event sampling saves network resources while ensuring system stability, a suite of novel event-sampled distributed near-optimal adaptive control schemes are introduced for uncertain linear and affine nonlinear interconnected systems in a forward-in-time and online manner. First, a novel stochastic hybrid Q-learning scheme is proposed to generate optimal adaptive control law and to accelerate the learning process in the presence of random delays and packet losses resulting from the communication network for an uncertain linear interconnected system. Subsequently, a novel online reinforcement learning (RL) approach is proposed to solve the Hamilton-Jacobi-Bellman (HJB) equation by using neural networks (NNs) for generating distributed optimal control of nonlinear interconnected systems using state and output feedback. To relax the state vector measurements, distributed observers are introduced. Next, using RL, an improved NN learning rule is derived to solve the HJB equation for uncertain nonlinear interconnected systems with event-triggered feedback. Distributed NN identifiers are introduced both for approximating the uncertain nonlinear dynamics and to serve as a model for online exploration. Next, the control policy and the event-sampling errors are considered as non-cooperative players and a min-max optimization problem is formulated for linear and affine nonlinear systems by using zero-sum game approach for simultaneous optimization of both the control policy and the event based sampling instants. The net result is the development of optimal adaptive event-triggered control of uncertain dynamic systems --Abstract, page iv

    Decentralized adaptive neural network control of interconnected nonlinear dynamical systems with application to power system

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    Traditional nonlinear techniques cannot be directly applicable to control large scale interconnected nonlinear dynamic systems due their sheer size and unavailability of system dynamics. Therefore, in this dissertation, the decentralized adaptive neural network (NN) control of a class of nonlinear interconnected dynamic systems is introduced and its application to power systems is presented in the form of six papers. In the first paper, a new nonlinear dynamical representation in the form of a large scale interconnected system for a power network free of algebraic equations with multiple UPFCs as nonlinear controllers is presented. Then, oscillation damping for UPFCs using adaptive NN control is discussed by assuming that the system dynamics are known. Subsequently, the dynamic surface control (DSC) framework is proposed in continuous-time not only to overcome the need for the subsystem dynamics and interconnection terms, but also to relax the explosion of complexity problem normally observed in traditional backstepping. The application of DSC-based decentralized control of power system with excitation control is shown in the third paper. On the other hand, a novel adaptive NN-based decentralized controller for a class of interconnected discrete-time systems with unknown subsystem and interconnection dynamics is introduced since discrete-time is preferred for implementation. The application of the decentralized controller is shown on a power network. Next, a near optimal decentralized discrete-time controller is introduced in the fifth paper for such systems in affine form whereas the sixth paper proposes a method for obtaining the L2-gain near optimal control while keeping a tradeoff between accuracy and computational complexity. Lyapunov theory is employed to assess the stability of the controllers --Abstract, page iv

    Economic Model Predictive Control for Large-Scale and Distributed Energy Systems

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    ๊ตฌ์กฐ๋กœ๋ด‡์„ ์œ„ํ•œ ๊ฐ•๊ฑดํ•œ ๊ณ„์ธต์  ๋™์ž‘ ๊ณ„ํš ๋ฐ ์ œ์–ด

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    ํ•™์œ„๋…ผ๋ฌธ(๋ฐ•์‚ฌ) -- ์„œ์šธ๋Œ€ํ•™๊ต๋Œ€ํ•™์› : ๊ณต๊ณผ๋Œ€ํ•™ ๊ธฐ๊ณ„ํ•ญ๊ณต๊ณตํ•™๋ถ€, 2021.8. ๋ฐ•์ข…์šฐ.Over the last several years, robotics has experienced a striking development, and a new generation of robots has emerged that shows great promise in being able to accomplish complex tasks associated with human behavior. Nowadays the objectives of the robots are no longer restricted to the automaton in the industrial process but are changing into explorers for hazardous, harsh, uncooperative, and extreme environments. As these robots usually operate in dynamic and unstructured environments, they should be robust, adaptive, and reactive under various changing operation conditions. We propose online hierarchical optimization-based planning and control methodologies for a rescue robot to execute a given mission in such a highly unstructured environment. A large number of degrees of freedom is provided to robots in order to achieve diverse kinematic and dynamic tasks. However, accomplishing such multiple objectives renders on-line reactive motion planning and control problems more difficult to solve due to the incompatible tasks. To address this problem, we exploit a hierarchical structure to precisely resolve conflicts by creating a priority in which every task is achieved as much as possible according to the levels. In particular, we concentrate on the reasoning about the task regularization to ensure the convergence and robustness of a solution in the face of singularity. As robotic systems with real-time motion planners or controllers often execute unrehearsed missions, a desired task cannot always be driven to a singularity free configuration. We develop a generic solver for regularized hierarchical quadratic programming without resorting to any off-the-shelf QP solver to take advantage of the null-space projections for computational efficiency. Therefore, the underlying principles are thoroughly investigated. The robust optimal solution is obtained under both equality and inequality tasks or constraints while addressing all problems resulting from the regularization. Especially as a singular value decomposition centric approach is leveraged, all hierarchical solutions and Lagrange multipliers for properly handling the inequality constraints are analytically acquired in a recursive procedure. The proposed algorithm works fast enough to be used as a practical means of real-time control system, so that it can be used for online motion planning, motion control, and interaction force control in a single hierarchical optimization. Core system design concepts of the rescue robot are presented. The goals of the robot are to safely extract a patient and to dispose a dangerous object instead of humans. The upper body is designed humanoid in form with replaceable modularized dual arms. The lower body is featured with a hybrid tracked and legged mobile platform to simultaneously acquire versatile manipulability and all-terrain mobility. Thus, the robot can successfully execute a driving task, dangerous object manipulation, and casualty extraction missions by changing the pose and modularized equipments in an optimized manner. Throughout the dissertation, all proposed methods are validated through extensive numerical simulations and experimental tests. We highlight precisely how the rescue robot can execute a casualty extraction and a dangerous object disposal mission both in indoor and outdoor environments that none of the existing robots has performed.์ตœ๊ทผ์— ๋“ฑ์žฅํ•œ ์ƒˆ๋กœ์šด ์„ธ๋Œ€์˜ ๋กœ๋ด‡์€ ๊ธฐ์กด์—๋Š” ์ธ๊ฐ„๋งŒ์ด ํ•  ์ˆ˜ ์žˆ์—ˆ๋˜ ๋ณต์žกํ•œ ์ผ์„ ๋กœ๋ด‡ ๋˜ํ•œ ์ˆ˜ํ–‰ํ•  ์ˆ˜ ์žˆ์Œ์„ ๋ณด์—ฌ์ฃผ์—ˆ๋‹ค. ํŠนํžˆ DARPA Robotics Challenge๋ฅผ ํ†ตํ•ด ์ด๋Ÿฌํ•œ ์‚ฌ์‹ค์„ ์ž˜ ํ™•์ธํ•  ์ˆ˜ ์žˆ์œผ๋ฉฐ, ์ด ๋กœ๋ด‡๋“ค์€ ๊ณต์žฅ๊ณผ ๊ฐ™์€ ์ •ํ˜•ํ™”๋œ ํ™˜๊ฒฝ์—์„œ ์ž๋™ํ™”๋œ ์ผ์„ ๋ฐ˜๋ณต์ ์œผ๋กœ ์ˆ˜ํ–‰ํ•˜๋˜ ์ž„๋ฌด์—์„œ ๋” ๋‚˜์•„๊ฐ€ ๊ทนํ•œ์˜ ํ™˜๊ฒฝ์—์„œ ์ธ๊ฐ„์„ ๋Œ€์‹ ํ•˜์—ฌ ์œ„ํ—˜ํ•œ ์ž„๋ฌด๋ฅผ ์ˆ˜ํ–‰ํ•  ์ˆ˜ ์žˆ๋Š” ๋ฐฉํ–ฅ์œผ๋กœ ๋ฐœ์ „ํ•˜๊ณ  ์žˆ๋‹ค. ๊ทธ๋ž˜์„œ ์‚ฌ๋žŒ๋“ค์€ ์žฌ๋‚œํ™˜๊ฒฝ์—์„œ ์•ˆ์ „ํ•˜๊ณ  ์‹œ์˜ ์ ์ ˆํ•˜๊ฒŒ ๋Œ€์‘ํ•  ์ˆ˜ ์žˆ๋Š” ์—ฌ๋Ÿฌ ๊ฐ€์ง€ ๋Œ€์•ˆ ์ค‘์—์„œ ์‹คํ˜„ ๊ฐ€๋Šฅ์„ฑ์ด ๋†’์€ ๋Œ€์ฒ˜ ๋ฐฉ์•ˆ์œผ๋กœ ๋กœ๋ด‡์„ ์ƒ๊ฐํ•˜๊ฒŒ ๋˜์—ˆ๋‹ค. ํ•˜์ง€๋งŒ ์ด๋Ÿฌํ•œ ๋กœ๋ด‡์€ ๋™์ ์œผ๋กœ ๋ณ€ํ™”ํ•˜๋Š” ๋น„์ •ํ˜• ํ™˜๊ฒฝ์—์„œ ์ž„๋ฌด๋ฅผ ์ˆ˜ํ–‰ํ•  ์ˆ˜ ์žˆ์–ด์•ผ ํ•˜๊ธฐ ๋•Œ๋ฌธ์— ๋ถˆํ™•์‹ค์„ฑ์— ๋Œ€ํ•ด ๊ฐ•๊ฑดํ•ด์•ผํ•˜๊ณ , ๋‹ค์–‘ํ•œ ํ™˜๊ฒฝ ์กฐ๊ฑด์—์„œ ๋Šฅ๋™์ ์œผ๋กœ ๋ฐ˜์‘์„ ํ•  ์ˆ˜ ์žˆ์–ด์•ผ ํ•œ๋‹ค. ๋ณธ ํ•™์œ„๋…ผ๋ฌธ์—์„œ๋Š” ๋กœ๋ด‡์ด ๋น„์ •ํ˜• ํ™˜๊ฒฝ์—์„œ ๊ฐ•๊ฑดํ•˜๋ฉด์„œ๋„ ์ ์‘์ ์œผ๋กœ ๋™์ž‘ํ•  ์ˆ˜ ์žˆ๋Š” ์‹ค์‹œ๊ฐ„ ์ตœ์ ํ™” ๊ธฐ๋ฐ˜์˜ ๋™์ž‘ ๊ณ„ํš ๋ฐ ์ œ์–ด ๋ฐฉ๋ฒ•๊ณผ ๊ตฌ์กฐ ๋กœ๋ด‡์˜ ์„ค๊ณ„ ๊ฐœ๋…์„ ์ œ์•ˆํ•˜๊ณ ์ž ํ•œ๋‹ค. ์ธ๊ฐ„์€ ๋งŽ์€ ์ž์œ ๋„๋ฅผ ๊ฐ€์ง€๊ณ  ์žˆ์œผ๋ฉฐ, ํ•˜๋‚˜์˜ ์ „์‹  ๋™์ž‘์„ ์ƒ์„ฑํ•  ๋•Œ ๋‹ค์–‘ํ•œ ๊ธฐ๊ตฌํ•™ ํ˜น์€ ๋™์—ญํ•™์  ํŠน์„ฑ์„ ๊ฐ€์ง€๋Š” ์„ธ๋ถ€ ๋™์ž‘ ํ˜น์€ ์ž‘์—…์„ ์ •์˜ํ•˜๊ณ , ์ด๋ฅผ ํšจ๊ณผ์ ์œผ๋กœ ์ข…ํ•ฉํ•  ์ˆ˜ ์žˆ๋‹ค. ๊ทธ๋ฆฌ๊ณ  ํ•™์Šต์„ ํ†ตํ•ด ๊ฐ ๋™์ž‘ ์š”์†Œ๋“ค์„ ์ตœ์ ํ™”ํ•  ๋ฟ๋งŒ ์•„๋‹ˆ๋ผ ์ƒํ™ฉ ์— ๋”ฐ๋ผ ๊ฐ ๋™์ž‘ ์š”์†Œ์— ์šฐ์„ ์ˆœ์œ„๋ฅผ ๋ถ€์—ฌํ•˜์—ฌ ์ด๋ฅผ ํšจ๊ณผ์ ์œผ๋กœ ๊ฒฐํ•ฉํ•˜๊ฑฐ๋‚˜ ๋ถ„๋ฆฌํ•˜์—ฌ ์‹ค์‹œ๊ฐ„์œผ๋กœ ์ตœ์ ์˜ ๋™์ž‘์„ ์ƒ์„ฑํ•˜๊ณ  ์ œ์–ดํ•œ๋‹ค. ์ฆ‰, ์ƒํ™ฉ์— ๋”ฐ๋ผ ์ค‘์š”ํ•œ ๋™์ž‘์š”์†Œ๋ฅผ ์šฐ์„ ์ ์œผ๋กœ ์ˆ˜ํ–‰ํ•˜๊ณ  ์šฐ์„ ์ˆœ์œ„๊ฐ€ ๋‚ฎ์€ ๋™์ž‘์š”์†Œ๋Š” ๋ถ€๋ถ„ ํ˜น์€ ์ „์ฒด์ ์œผ๋กœ ํฌ๊ธฐํ•˜๊ธฐ๋„ ํ•˜๋ฉด์„œ ๋งค์šฐ ์œ ์—ฐํ•˜๊ฒŒ ์ „์ฒด ๋™์ž‘์„ ์ƒ์„ฑํ•˜๊ณ  ์ตœ์ ํ™” ํ•œ๋‹ค. ์ธ๊ฐ„๊ณผ ๊ฐ™์ด ๋‹ค์ž์œ ๋„๋ฅผ ๋ณด์œ ํ•œ ๋กœ๋ด‡ ๋˜ํ•œ ๊ธฐ๊ตฌํ•™๊ณผ ๋™์—ญํ•™์  ํŠน์„ฑ์„ ๊ฐ€์ง€๋Š” ๋‹ค์–‘ํ•œ ์„ธ๋ถ€ ๋™์ž‘ ํ˜น์€ ์ž‘์—…์„ ์ž‘์—…๊ณต๊ฐ„(task space) ํ˜น์€ ๊ด€์ ˆ๊ณต๊ฐ„(configuration space)์—์„œ ์ •์˜ํ•  ์ˆ˜ ์žˆ์œผ๋ฉฐ, ์šฐ์„ ์ˆœ์œ„์— ๋”ฐ๋ผ ์ด๋ฅผ ํšจ๊ณผ์ ์œผ๋กœ ๊ฒฐํ•ฉํ•˜์—ฌ ์ „์ฒด ๋™์ž‘์„ ์ƒ ์„ฑํ•˜๊ณ  ์ œ์–ดํ•  ์ˆ˜ ์žˆ๋‹ค. ์„œ๋กœ ์–‘๋ฆฝํ•˜๊ธฐ ์–ด๋ ค์šด ๋กœ๋ด‡์˜ ๋™์ž‘ ๋ฌธ์ œ๋ฅผ ํ•ด๊ฒฐํ•˜๊ธฐ ์œ„ํ•ด ๋™์ž‘๋“ค ์‚ฌ์ด์— ์šฐ์„ ์ˆœ์œ„๋ฅผ ๋ถ€์—ฌํ•˜์—ฌ ๊ณ„์ธต์„ ์ƒ์„ฑํ•˜๊ณ , ์ด์— ๋”ฐ๋ผ ๋กœ๋ด‡์˜ ์ „์‹  ๋™์ž‘์„ ๊ตฌํ˜„ํ•˜๋Š” ๋ฐฉ๋ฒ•์€ ์˜ค๋žซ๋™์•ˆ ์—ฐ๊ตฌ๊ฐ€ ์ง„ํ–‰๋˜์–ด ์™”๋‹ค. ์ด๋Ÿฌํ•œ ๊ณ„์ธต์  ์ตœ์ ํ™”๋ฅผ ์ด์šฉํ•˜๋ฉด ์šฐ์„ ์ˆœ์œ„๊ฐ€ ๋†’์€ ๋™์ž‘๋ถ€ํ„ฐ ์ˆœ์ฐจ์ ์œผ๋กœ ์‹คํ–‰ํ•˜์ง€๋งŒ, ์šฐ์„ ์ˆœ์œ„๊ฐ€ ๋‚ฎ์€ ๋™์ž‘์š”์†Œ๋“ค๋„ ๊ฐ€๋Šฅํ•œ ๋งŒ์กฑ์‹œํ‚ค๋Š” ์ตœ์ ์˜ ํ•ด๋ฅผ ์ฐพ์„ ์ˆ˜ ์žˆ๋‹ค. ํ•˜์ง€๋งŒ ๊ด€์ ˆ์˜ ๊ตฌ๋™ ๋ฒ”์œ„์™€ ๊ฐ™์€ ๋ถ€๋“ฑ์‹์˜ ์กฐ๊ฑด์ด ํฌํ•จ๋œ ๊ณ„์ธต์  ์ตœ์ ํ™” ๋ฌธ์ œ์—์„œ ํŠน์ด์ ์— ๋Œ€ํ•œ ๊ฐ•๊ฑด์„ฑ๊นŒ์ง€ ํ™•๋ณดํ•  ์ˆ˜ ์žˆ๋Š” ๋ฐฉ๋ฒ•์— ๋Œ€ํ•ด์„œ๋Š” ์•„์ง๊นŒ์ง€ ๋งŽ์€ ๋ถ€๋ถ„์ด ๋ฐ ํ˜€์ง„ ๋ฐ”๊ฐ€ ์—†๋‹ค. ๋”ฐ๋ผ์„œ ๋ณธ ํ•™์œ„๋…ผ๋ฌธ์—์„œ๋Š” ๋“ฑ์‹๊ณผ ๋ถ€๋“ฑ์‹์œผ๋กœ ํ‘œํ˜„๋˜๋Š” ๊ตฌ์†์กฐ๊ฑด ํ˜น์€ ๋™์ž‘์š”์†Œ๋ฅผ ๊ณ„์ธต์  ์ตœ์ ํ™”์— ๋™์‹œ์— ํฌํ•จ์‹œํ‚ค๊ณ , ํŠน์ด์ ์ด ์กด์žฌํ•˜๋”๋ผ๋„ ๊ฐ•๊ฑด์„ฑ๊ณผ ์ˆ˜๋ ด์„ฑ์„ ๋ณด์žฅํ•˜๋Š” ๊ด€์ ˆ๊ณต๊ฐ„์—์„œ์˜ ์ตœ์ ํ•ด๋ฅผ ํ™•๋ณดํ•˜๋Š”๋ฐ ์ง‘์ค‘ํ•œ๋‹ค. ์™œ๋‚˜ํ•˜๋ฉด ๋น„์ •ํ˜• ์ž„๋ฌด๋ฅผ ์ˆ˜ํ–‰ํ•˜๋Š” ๋กœ๋ด‡์€ ์‚ฌ์ „์— ๊ณ„ํš๋œ ๋™์ž‘์„ ์ˆ˜ํ–‰ํ•˜๋Š” ๊ฒƒ์ด ์•„๋‹Œ ๋ณ€ํ™”ํ•˜๋Š” ํ™˜๊ฒฝ์กฐ๊ฑด์— ๋”ฐ๋ผ ์‹ค์‹œ๊ฐ„์œผ๋กœ ๋™์ž‘์„ ๊ณ„ํšํ•˜๊ณ  ์ œ์–ดํ•ด์•ผ ํ•˜๊ธฐ ๋•Œ๋ฌธ์— ํŠน์ด์ ์ด ์—†๋Š” ์ž์„ธ๋กœ ๋กœ๋ด‡์„ ํ•ญ์ƒ ์ œ์–ดํ•˜๊ธฐ๊ฐ€ ์–ด๋ ต๋‹ค. ๊ทธ๋ฆฌ๊ณ  ์ด๋ ‡๊ฒŒ ํŠน์ด์ ์„ ํšŒํ”ผํ•˜๋Š” ๋ฐฉํ–ฅ์œผ๋กœ ๋กœ๋ด‡์„ ์ œ์–ดํ•˜๋Š” ๊ฒƒ์€ ๋กœ๋ด‡์˜ ์šด์šฉ์„ฑ์„ ์‹ฌ๊ฐํ•˜๊ฒŒ ์ €ํ•ด์‹œํ‚ฌ ์ˆ˜ ์žˆ๋‹ค. ํŠน์ด์  ๊ทผ๋ฐฉ์—์„œ์˜ ํ•ด์˜ ๊ฐ•๊ฑด์„ฑ์ด ๋ณด์žฅ๋˜์ง€ ์•Š์œผ๋ฉด ๋กœ๋ด‡ ๊ด€์ ˆ์— ๊ณผ๋„ํ•œ ์†๋„ ํ˜น์€ ํ† ํฌ๊ฐ€ ๋ฐœ์ƒํ•˜์—ฌ ๋กœ๋ด‡์˜ ์ž„๋ฌด ์ˆ˜ํ–‰์ด ๋ถˆ๊ฐ€๋Šฅํ•˜๊ฑฐ๋‚˜ ํ™˜๊ฒฝ๊ณผ ๋กœ๋ด‡์˜ ์†์ƒ์„ ์ดˆ๋ž˜ํ•  ์ˆ˜ ์žˆ์œผ๋ฉฐ, ๋‚˜์•„๊ฐ€ ๋กœ๋ด‡๊ณผ ํ•จ๊ป˜ ์ž„๋ฌด๋ฅผ ์ˆ˜ํ–‰ํ•˜๋Š” ์‚ฌ๋žŒ์—๊ฒŒ ์ƒํ•ด๋ฅผ ๊ฐ€ํ•  ์ˆ˜๋„ ์žˆ๋‹ค. ํŠน์ด์ ์— ๋Œ€ํ•œ ๊ฐ•๊ฑด์„ฑ์„ ํ™•๋ณดํ•˜๊ธฐ ์œ„ํ•ด ์šฐ์„ ์ˆœ์œ„ ๊ธฐ๋ฐ˜์˜ ๊ณ„์ธต์  ์ตœ์ ํ™”์™€ ์ •๊ทœํ™” (regularization)๋ฅผ ํ†ตํ•ฉํ•˜์—ฌ ์ •๊ทœํ™”๋œ ๊ณ„์ธต์  ์ตœ์ ํ™” (RHQP: Regularized Hierarchical Quadratic Program) ๋ฌธ์ œ๋ฅผ ๋‹ค๋ฃฌ๋‹ค. ๋ถ€๋“ฑ์‹์ด ํฌํ•จ๋œ ๊ณ„์ธต์  ์ตœ์ ํ™”์— ์ •๊ทœํ™”๋ฅผ ๋™์‹œ์— ๊ณ ๋ คํ•จ์œผ๋กœ์จ ์•ผ๊ธฐ๋˜๋Š” ๋งŽ์€ ๋ฌธ์ œ์ ๋“ค์„ ํ•ด๊ฒฐํ•˜๊ณ  ํ•ด์˜ ์ตœ์ ์„ฑ๊ณผ ๊ฐ•๊ฑด์„ฑ์„ ํ™•๋ณดํ•  ์ˆ˜ ์žˆ๋Š” ๋ฐฉ๋ฒ•์„ ์ œ์•ˆํ•œ๋‹ค. ํŠนํžˆ ์™ธ๋ถ€์˜ ์ตœ์ ํ™” ํ”„๋กœ๊ทธ๋žจ์„ ์‚ฌ์šฉํ•˜์ง€ ์•Š๊ณ  ์ˆ˜์น˜์  ์ตœ์ ํ™” (numerical optimization) ์ด๋ก ๊ณผ ์šฐ์„ ์ˆœ์œ„์— ๊ธฐ๋ฐ˜์„ ๋‘๋Š” ์—ฌ์œ ์ž์œ ๋„ ๋กœ๋ด‡์˜ ํ•ด์„ ๊ธฐ๋ฒ•์„ ์ด์šฉํ•˜์—ฌ ๊ณ„์‚ฐ์˜ ํšจ์œจ์„ฑ์„ ๊ทน๋Œ€ํ™”ํ•  ์ˆ˜ ์žˆ๋Š” ์ด์ฐจ ํ”„๋กœ๊ทธ๋žจ(quadratic programming)์„ ์ œ์•ˆํ•œ๋‹ค. ๋˜ํ•œ ์ด์™€ ๋™์‹œ์— ์ •๊ทœํ™”๋œ ๊ณ„์ธต์  ์ตœ์ ํ™” ๋ฌธ์ œ์˜ ์ด๋ก ์  ๊ตฌ์กฐ๋ฅผ ์ฒ ์ €ํ•˜๊ฒŒ ๋ถ„์„ํ•œ๋‹ค. ํŠนํžˆ ํŠน์ด๊ฐ’ ๋ถ„ํ•ด (singular value decomposition)๋ฅผ ํ†ตํ•ด ์ตœ์ ํ•ด์™€ ๋ถ€๋“ฑ์‹ ์กฐ๊ฑด์„ ์ฒ˜๋ฆฌํ•˜๋Š”๋ฐ ํ•„์š”ํ•œ ๋ผ๊ทธ๋ž‘์ง€ ์Šน์ˆ˜๋ฅผ ์žฌ๊ท€์ ์ธ ๋ฐฉ๋ฒ•์œผ๋กœ ํ•ด์„์  ํ˜•ํƒœ๋กœ ๊ตฌํ•จ์œผ๋กœ์จ ๊ณ„์‚ฐ์˜ ํšจ์œจ์„ฑ์„ ์ฆ๋Œ€์‹œํ‚ค๊ณ  ๋™์‹œ์— ๋ถ€๋“ฑ์‹์˜ ์กฐ๊ฑด์„ ์˜ค๋ฅ˜ ์—†์ด ์ •ํ™•ํ•˜๊ฒŒ ์ฒ˜๋ฆฌํ•  ์ˆ˜ ์žˆ๋„๋ก ํ•˜์˜€๋‹ค. ๊ทธ๋ฆฌ๊ณ  ์ •๊ทœํ™”๋œ ๊ณ„์ธต์  ์ตœ์ ํ™”๋ฅผ ํž˜์ œ์–ด๊นŒ์ง€ ํ™•์žฅํ•˜์—ฌ ํ™˜๊ฒฝ๊ณผ ๋กœ๋ด‡์˜ ์•ˆ์ „ํ•œ ์ƒํ˜ธ์ž‘์šฉ์„ ๋ณด์žฅํ•˜์—ฌ ๋กœ๋ด‡์ด ์ ์ ˆํ•œ ํž˜์œผ๋กœ ํ™˜๊ฒฝ๊ณผ ์ ‘์ด‰ํ•  ์ˆ˜ ์žˆ๋„๋ก ํ•˜์˜€๋‹ค. ๋ถˆํ™•์‹ค์„ฑ์ด ์กด์žฌํ•˜๋Š” ๋น„์ •ํ˜• ํ™˜๊ฒฝ์—์„œ ๋น„์ •ํ˜• ์ž„๋ฌด๋ฅผ ์ˆ˜ํ–‰ํ•  ์ˆ˜ ์žˆ๋Š” ๊ตฌ์กฐ๋กœ๋ด‡์˜ ํ•ต์‹ฌ ์„ค๊ณ„ ๊ฐœ๋…์„ ์ œ์‹œํ•œ๋‹ค. ๋น„์ •ํ˜• ํ™˜๊ฒฝ์—์„œ์˜ ์กฐ์ž‘ ์„ฑ๋Šฅ๊ณผ ์ด๋™ ์„ฑ๋Šฅ์„ ๋™์‹œ์— ํ™•๋ณดํ•  ์ˆ˜ ์žˆ๋Š” ํ˜•์ƒ์œผ๋กœ ๋กœ๋ด‡์„ ์„ค๊ณ„ํ•˜์—ฌ ๊ตฌ์กฐ ๋กœ๋ด‡์œผ๋กœ ํ•˜์—ฌ๊ธˆ ์ตœ์ข… ๋ชฉ์ ์œผ๋กœ ์„ค์ •๋œ ์ธ๊ฐ„์„ ๋Œ€์‹ ํ•˜์—ฌ ๋ถ€์ƒ์ž๋ฅผ ๊ตฌ์กฐํ•˜๊ณ  ์œ„ํ—˜๋ฌผ์„ ์ฒ˜๋ฆฌํ•˜๋Š” ์ž„๋ฌด๋ฅผ ํšจ๊ณผ์ ์œผ๋กœ ์ˆ˜ํ–‰ํ•  ์ˆ˜ ์žˆ๋„๋ก ํ•œ๋‹ค. ๊ตฌ์กฐ ๋กœ๋ด‡์— ํ•„์š”ํ•œ ๋งค๋‹ˆํ“ฐ๋ ˆ์ดํ„ฐ๋Š” ๋ถ€์ƒ์ž ๊ตฌ์กฐ ์ž„๋ฌด์™€ ์œ„ํ—˜๋ฌผ ์ฒ˜๋ฆฌ ์ž„๋ฌด์— ๋”ฐ๋ผ ๊ต์ฒด ๊ฐ€๋Šฅํ•œ ๋ชจ๋“ˆํ˜•์œผ๋กœ ์„ค๊ณ„ํ•˜์—ฌ ๊ฐ๊ฐ์˜ ์ž„๋ฌด์— ๋”ฐ๋ผ ์ตœ์ ํ™”๋œ ๋งค๋‹ˆํ“ฐ ๋ ˆ์ดํ„ฐ๋ฅผ ์žฅ์ฐฉํ•˜์—ฌ ์ž„๋ฌด๋ฅผ ์ˆ˜ํ–‰ํ•  ์ˆ˜ ์žˆ๋‹ค. ํ•˜์ฒด๋Š” ํŠธ๋ž™๊ณผ ๊ด€์ ˆ์ด ๊ฒฐํ•ฉ๋œ ํ•˜์ด๋ธŒ๋ฆฌ๋“œ ํ˜•ํƒœ๋ฅผ ์ทจํ•˜๊ณ  ์žˆ์œผ๋ฉฐ, ์ฃผํ–‰ ์ž„๋ฌด์™€ ์กฐ์ž‘์ž„๋ฌด์— ๋”ฐ๋ผ ํ˜•์ƒ์„ ๋ณ€๊ฒฝํ•  ์ˆ˜ ์žˆ๋‹ค. ํ˜•์ƒ ๋ณ€๊ฒฝ๊ณผ ๋ชจ๋“ˆํ™”๋œ ๋งค๋‹ˆํ“ฐ๋ ˆ์ดํ„ฐ๋ฅผ ํ†ตํ•ด์„œ์กฐ์ž‘ ์„ฑ๋Šฅ๊ณผ ํ—˜ํ•œ ์ง€ํ˜•์—์„œ ์ด๋™ํ•  ์ˆ˜ ์žˆ๋Š” ์ฃผํ–‰ ์„ฑ๋Šฅ์„ ๋™์‹œ์— ํ™•๋ณดํ•˜์˜€๋‹ค. ์ตœ์ข…์ ์œผ๋กœ ๊ตฌ์กฐ๋กœ๋ด‡์˜ ์„ค๊ณ„์™€ ์‹ค์‹œ๊ฐ„ ๊ณ„์ธต์  ์ œ์–ด๋ฅผ ์ด์šฉํ•˜์—ฌ ๋น„์ •ํ˜• ์‹ค๋‚ด์™ธ ํ™˜๊ฒฝ์—์„œ ๊ตฌ์กฐ๋กœ๋ด‡์ด ์ฃผํ–‰์ž„๋ฌด, ์œ„ํ—˜๋ฌผ ์กฐ์ž‘์ž„๋ฌด, ๋ถ€์ƒ์ž ๊ตฌ์กฐ ์ž„๋ฌด๋ฅผ ์„ฑ๊ณต์ ์œผ๋กœ ์ˆ˜ ํ–‰ํ•  ์ˆ˜ ์žˆ์Œ์„ ํ•ด์„๊ณผ ์‹คํ—˜์„ ํ†ตํ•˜์—ฌ ์ž…์ฆํ•จ์œผ๋กœ์จ ๋ณธ ํ•™์œ„๋…ผ๋ฌธ์—์„œ ์ œ์•ˆํ•œ ์„ค๊ณ„์™€ ์ •๊ทœํ™”๋œ ๊ณ„์ธต์  ์ตœ์ ํ™” ๊ธฐ๋ฐ˜์˜ ์ œ์–ด ์ „๋žต์˜ ์œ ์šฉ์„ฑ์„ ๊ฒ€์ฆํ•˜์˜€๋‹ค.1 Introduction 1 1.1 Motivations 1 1.2 Related Works and Research Problems for Hierarchical Control 3 1.2.1 Classical Approaches 3 1.2.2 State-of-the-Art Strategies 4 1.2.3 Research Problems 7 1.3 Robust Rescue Robots 9 1.4 Research Goals 12 1.5 Contributions of ThisThesis 13 1.5.1 Robust Hierarchical Task-Priority Control 13 1.5.2 Design Concepts of Robust Rescue Robot 16 1.5.3 Hierarchical Motion and ForceControl 17 1.6 Dissertation Preview 18 2 Preliminaries for Task-Priority Control Framework 21 2.1 Introduction 21 2.2 Task-Priority Inverse Kinematics 23 2.3 Recursive Formulation of Null Space Projector 28 2.4 Conclusion 31 3 Robust Hierarchical Task-Priority Control 33 3.1 Introduction 33 3.1.1 Motivations 35 3.1.2 Objectives 36 3.2 Task Function Approach 37 3.3 Regularized Hierarchical Optimization with Equality Tasks 41 3.3.1 Regularized Hierarchical Optimization 41 3.3.2 Optimal Solution 45 3.3.3 Task Error and Hierarchical Matrix Decomposition 49 3.3.4 Illustrative Examples for Regularized Hierarchical Optimization 56 3.4 Regularized Hierarchical Optimization with Inequality Constraints 60 3.4.1 Lagrange Multipliers 61 3.4.2 Modified Active Set Method 66 3.4.3 Illustrative Examples of Modified Active Set Method 70 3.4.4 Examples for Hierarchical Optimization with Inequality Constraint 72 3.5 DLS-HQP Algorithm 79 3.6 Concluding Remarks 80 4 Rescue Robot Design and Experimental Results 83 4.1 Introduction 83 4.2 Rescue Robot Design 85 4.2.1 System Design 86 4.2.2 Variable Configuration Mobile Platform 92 4.2.3 Dual Arm Manipulators 95 4.2.4 Software Architecture 97 4.3 Performance Verification for Hierarchical Motion Control 99 4.3.1 Real-Time Motion Generation 99 4.3.2 Task Specifications 103 4.3.3 Singularity Robust Task Priority 106 4.3.4 Inequality Constraint Handling and Computation Time 111 4.4 Singularity Robustness and Inequality Handling for Rescue Mission 117 4.5 Field Tests 122 4.6 Concluding Remarks 126 5 Hierarchical Motion and Force Control 129 5.1 Introduction 129 5.2 Operational Space Control 132 5.3 Acceleration-Based Hierarchical Motion Control 134 5.4 Force Control 137 5.4.1 Force Control with Inner Position Loop 141 5.4.2 Force Control with Inner Velocity Loop 144 5.5 Motion and Force Control 145 5.6 Numerical Results for Acceleration-Based Motion and Force Control 148 5.6.1 Task Specifications 150 5.6.2 Force Control Performance 151 5.6.3 Singularity Robustness and Inequality Constraint Handling 155 5.7 Velocity Resolved Motion and Force Control 160 5.7.1 Velocity-Based Motion and Force Control 161 5.7.2 Experimental Results 163 5.8 Concluding Remarks 167 6 Conclusion 169 6.1 Summary 169 6.2 Concluding Remarks 173 A Appendix 175 A.1 Introduction to PID Control 175 A.2 Inverse Optimal Control 176 A.3 Experimental Results and Conclusion 181 Bibliography 183 Abstract 207๋ฐ•

    Nonlinear Model Predictive Control for Motion Generation of Humanoids

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    Das Ziel dieser Arbeit ist die Untersuchung und Entwicklung numerischer Methoden zur Bewegungserzeugung von humanoiden Robotern basierend auf nichtlinearer modell-prรคdiktiver Regelung. Ausgehend von der Modellierung der Humanoiden als komplexe Mehrkรถrpermodelle, die sowohl durch unilaterale Kontaktbedingungen beschrรคnkt als auch durch die Formulierung unteraktuiert sind, wird die Bewegungserzeugung als Optimalsteuerungsproblem formuliert. In dieser Arbeit werden numerische Erweiterungen basierend auf den Prinzipien der Automatischen Differentiation fรผr rekursive Algorithmen, die eine effiziente Auswertung der dynamischen GrรถรŸen der oben genannten Mehrkรถrperformulierung erlauben, hergeleitet, sodass sowohl die nominellen GrรถรŸen als auch deren ersten Ableitungen effizient ausgewertet werden kรถnnen. Basierend auf diesen Ideen werden Erweiterungen fรผr die Auswertung der Kontaktdynamik und der Berechnung des Kontaktimpulses vorgeschlagen. Die Echtzeitfรคhigkeit der Berechnung von Regelantworten hรคngt stark von der Komplexitรคt der fรผr die Bewegungerzeugung gewรคhlten Mehrkรถrperformulierung und der zur Verfรผgung stehenden Rechenleistung ab. Um einen optimalen Trade-Off zu ermรถglichen, untersucht diese Arbeit einerseits die mรถgliche Reduktion der Mehrkรถrperdynamik und andererseits werden maรŸgeschneiderte numerische Methoden entwickelt, um die Echtzeitfรคhigkeit der Regelung zu realisieren. Im Rahmen dieser Arbeit werden hierfรผr zwei reduzierte Modelle hergeleitet: eine nichtlineare Erweiterung des linearen inversen Pendelmodells sowie eine reduzierte Modellvariante basierend auf der centroidalen Mehrkรถrperdynamik. Ferner wird ein Regelaufbau zur GanzkรถrperBewegungserzeugung vorgestellt, deren Hauptbestandteil jeweils aus einem speziell diskretisierten Problem der nichtlinearen modell-prรคdiktiven Regelung sowie einer maรŸgeschneiderter Optimierungsmethode besteht. Die Echtzeitfรคhigkeit des Ansatzes wird durch Experimente mit den Robotern HRP-2 und HeiCub verifiziert. Diese Arbeit schlรคgt eine Methode der nichtlinear modell-prรคdiktiven Regelung vor, die trotz der Komplexitรคt der vollen Mehrkรถrperformulierung eine Berechnung der Regelungsantwort in Echtzeit ermรถglicht. Dies wird durch die geschickte Kombination von linearer und nichtlinearer modell-prรคdiktiver Regelung auf der aktuellen beziehungsweise der letzten Linearisierung des Problems in einer parallelen Regelstrategie realisiert. Experimente mit dem humanoiden Roboter Leo zeigen, dass, im Vergleich zur nominellen Strategie, erst durch den Einsatz dieser Methode eine Bewegungserzeugung auf dem Roboter mรถglich ist. Neben Methoden der modell-basierten Optimalsteuerung werden auch modell-freie Methoden des verstรคrkenden Lernens (Reinforcement Learning) fรผr die Bewegungserzeugung untersucht, mit dem Fokus auf den schwierig zu modellierenden Modellunsicherheiten der Roboter. Im Rahmen dieser Arbeit werden eine allgemeine vergleichende Studie sowie Leistungskennzahlen entwickelt, die es erlauben, modell-basierte und -freie Methoden quantitativ bezรผglich ihres Lรถsungsverhaltens zu vergleichen. Die Anwendung der Studie auf ein akademisches Beispiel zeigt Unterschiede und Kompromisse sowie Break-Even-Punkte zwischen den Problemformulierungen. Diese Arbeit schlรคgt basierend auf dieser Grundlage zwei mรถgliche Kombinationen vor, deren Eigenschaften bewiesen und in Simulation untersucht werden. AuรŸerdem wird die besser abschneidende Variante auf dem humanoiden Roboter Leo implementiert und mit einem nominellen modell-basierten Regler verglichen

    CONTROLLER SYNTHESIS AND FORMAL BEHAVIOR INFERENCE IN AUTONOMOUS SYSTEMS

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    Autonomous systems are widely used in crucial applications such as surveillance,defense, reghting, and search & rescue operations. Many of these application require systems to satisfy user-dened requirements describing the desired system behavior. Given high-level requirements, we are interested in the design of controllers that guarantee the compliance of these requirements by the system. However, ensuring that these systems satisfy a given set of requirements is challenging for many reasons, one of which is the large computational cost incurred by having to account for all possible system behaviors and environment conditions. These computational diculties are exacerbated when systems are required to satisfy requirements involving large numbers of tasks emerging from dynamic environments. In addition to computational diculties, scalability issues also arise when dealing with multi-agent applications, in which agents require coordination and communication to satisfy mission requirements. This dissertation is an eort towards addressing the computational and scalability challenges of designing controllers from highlevel requirements by employing reactive synthesis, a formal methods approach, and combining it with other decision-making processes that handle coordination among agents to alleviate the load on reactive synthesis. The proposed framework results in a more scalable solution with lower computational costs while guaranteeing that high-level requirements are met. The practicality of the proposed framework is demonstrated through various types of multi-agent applications including reghting, re monitoring, rescue, search & rescue and ship protection scenarios. Our approach incorporates methodology from computer science and control, including reactive synthesis of discrete systems, metareasoning, reachability analysis and inverse reinforcement learning. This thesis consists of two key parts: reactive synthesis from linear temporal logic specications and specication inference from demonstrations of formal behavior. First, we introduce the reactive synthesis problem for which the desired system behavior species the method by which a multi-agent system solves the problem of decentralized task allocation depending on communication availability conditions. Second, we present the synthesis problem formulated to obtain a high-level mission planner and controller for managing a team of agents ghting a wildre. Third, we present a framework for inferring linear temporal logic specications that succinctly convey and explain the observed behavior. The gained knowledge is leveraged to improve motion prediction for agents behaving according to the learned specication. The eectiveness of the inference process and motion prediction framework are demonstrated through a scenario in which humans practice social norms commonly seen in pedestrian settings
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