3,699 research outputs found

    Optimization Methods for Inverse Problems

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    Optimization plays an important role in solving many inverse problems. Indeed, the task of inversion often either involves or is fully cast as a solution of an optimization problem. In this light, the mere non-linear, non-convex, and large-scale nature of many of these inversions gives rise to some very challenging optimization problems. The inverse problem community has long been developing various techniques for solving such optimization tasks. However, other, seemingly disjoint communities, such as that of machine learning, have developed, almost in parallel, interesting alternative methods which might have stayed under the radar of the inverse problem community. In this survey, we aim to change that. In doing so, we first discuss current state-of-the-art optimization methods widely used in inverse problems. We then survey recent related advances in addressing similar challenges in problems faced by the machine learning community, and discuss their potential advantages for solving inverse problems. By highlighting the similarities among the optimization challenges faced by the inverse problem and the machine learning communities, we hope that this survey can serve as a bridge in bringing together these two communities and encourage cross fertilization of ideas.Comment: 13 page

    Spatially regularized estimation for the analysis of DCE-MRI data

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    Competing compartment models of different complexities have been used for the quantitative analysis of Dynamic Contrast-Enhanced Magnetic Resonance Imaging data. We present a spatial Elastic Net approach that allows to estimate the number of compartments for each voxel such that the model complexity is not fixed a priori. A multi-compartment approach is considered, which is translated into a restricted least square model selection problem. This is done by using a set of basis functions for a given set of candidate rate constants. The form of the basis functions is derived from a kinetic model and thus describes the contribution of a specific compartment. Using a spatial Elastic Net estimator, we chose a sparse set of basis functions per voxel, and hence, rate constants of compartments. The spatial penalty takes into account the voxel structure of an image and performs better than a penalty treating voxels independently. The proposed estimation method is evaluated for simulated images and applied to an in-vivo data set

    Dynamical systems and forward-backward algorithms associated with the sum of a convex subdifferential and a monotone cocoercive operator

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    In a Hilbert framework, we introduce continuous and discrete dynamical systems which aim at solving inclusions governed by structured monotone operators A=โˆ‚ฮฆ+BA=\partial\Phi+B, where โˆ‚ฮฆ\partial\Phi is the subdifferential of a convex lower semicontinuous function ฮฆ\Phi, and BB is a monotone cocoercive operator. We first consider the extension to this setting of the regularized Newton dynamic with two potentials. Then, we revisit some related dynamical systems, namely the semigroup of contractions generated by AA, and the continuous gradient projection dynamic. By a Lyapunov analysis, we show the convergence properties of the orbits of these systems. The time discretization of these dynamics gives various forward-backward splitting methods (some new) for solving structured monotone inclusions involving non-potential terms. The convergence of these algorithms is obtained under classical step size limitation. Perspectives are given in the field of numerical splitting methods for optimization, and multi-criteria decision processes.Comment: 25 page

    ๊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•
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