51 research outputs found

    Motion Control of the Hybrid Wheeled-Legged Quadruped Robot Centauro

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    Emerging applications will demand robots to deal with a complex environment, which lacks the structure and predictability of the industrial workspace. Complex scenarios will require robot complexity to increase as well, as compared to classical topologies such as fixed-base manipulators, wheeled mobile platforms, tracked vehicles, and their combinations. Legged robots, such as humanoids and quadrupeds, promise to provide platforms which are flexible enough to handle real world scenarios; however, the improved flexibility comes at the cost of way higher control complexity. As a trade-off, hybrid wheeled-legged robots have been proposed, resulting in the mitigation of control complexity whenever the ground surface is suitable for driving. Following this idea, a new hybrid robot called Centauro has been developed inside the Humanoid and Human Centered Mechatronics lab at Istituto Italiano di Tecnologia (IIT). Centauro is a wheeled-legged quadruped with a humanoid bi-manual upper-body. Differently from other platform of similar concept, Centauro employs customized actuation units, which provide high torque outputs, moderately fast motions, and the possibility to control the exerted torque. Moreover, with more than forty motors moving its limbs, Centauro is a very redundant platform, with the potential to execute many different tasks at the same time. This thesis deals with the design and development of a software architecture, and a control system, tailored to such a robot; both wheeled and legged locomotion strategies have been studied, as well as prioritized, whole-body and interaction controllers exploiting the robot torque control capabilities, and capable to handle the system redundancy. A novel software architecture, made of (i) a real-time robotic middleware, and (ii) a framework for online, prioritized Cartesian controller, forms the basis of the entire work

    ๊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•

    Planning and Control Strategies for Motion and Interaction of the Humanoid Robot COMAN+

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    Despite the majority of robotic platforms are still confined in controlled environments such as factories, thanks to the ever-increasing level of autonomy and the progress on human-robot interaction, robots are starting to be employed for different operations, expanding their focus from uniquely industrial to more diversified scenarios. Humanoid research seeks to obtain the versatility and dexterity of robots capable of mimicking human motion in any environment. With the aim of operating side-to-side with humans, they should be able to carry out complex tasks without posing a threat during operations. In this regard, locomotion, physical interaction with the environment and safety are three essential skills to develop for a biped. Concerning the higher behavioural level of a humanoid, this thesis addresses both ad-hoc movements generated for specific physical interaction tasks and cyclic movements for locomotion. While belonging to the same category and sharing some of the theoretical obstacles, these actions require different approaches: a general high-level task is composed of specific movements that depend on the environment and the nature of the task itself, while regular locomotion involves the generation of periodic trajectories of the limbs. Separate planning and control architectures targeting these aspects of biped motion are designed and developed both from a theoretical and a practical standpoint, demonstrating their efficacy on the new humanoid robot COMAN+, built at Istituto Italiano di Tecnologia. The problem of interaction has been tackled by mimicking the intrinsic elasticity of human muscles, integrating active compliant controllers. However, while state-of-the-art robots may be endowed with compliant architectures, not many can withstand potential system failures that could compromise the safety of a human interacting with the robot. This thesis proposes an implementation of such low-level controller that guarantees a fail-safe behaviour, removing the threat that a humanoid robot could pose if a system failure occurred

    Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015

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    This volume contains the full papers accepted for presentation at the ECCOMAS Thematic Conference on Multibody Dynamics 2015 held in the Barcelona School of Industrial Engineering, Universitat Politรจcnica de Catalunya, on June 29 - July 2, 2015. The ECCOMAS Thematic Conference on Multibody Dynamics is an international meeting held once every two years in a European country. Continuing the very successful series of past conferences that have been organized in Lisbon (2003), Madrid (2005), Milan (2007), Warsaw (2009), Brussels (2011) and Zagreb (2013); this edition will once again serve as a meeting point for the international researchers, scientists and experts from academia, research laboratories and industry working in the area of multibody dynamics. Applications are related to many fields of contemporary engineering, such as vehicle and railway systems, aeronautical and space vehicles, robotic manipulators, mechatronic and autonomous systems, smart structures, biomechanical systems and nanotechnologies. The topics of the conference include, but are not restricted to: โ— Formulations and Numerical Methods โ— Efficient Methods and Real-Time Applications โ— Flexible Multibody Dynamics โ— Contact Dynamics and Constraints โ— Multiphysics and Coupled Problems โ— Control and Optimization โ— Software Development and Computer Technology โ— Aerospace and Maritime Applications โ— Biomechanics โ— Railroad Vehicle Dynamics โ— Road Vehicle Dynamics โ— Robotics โ— Benchmark ProblemsPostprint (published version

    Towards Robust Bipedal Locomotion:From Simple Models To Full-Body Compliance

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    Thanks to better actuator technologies and control algorithms, humanoid robots to date can perform a wide range of locomotion activities outside lab environments. These robots face various control challenges like high dimensionality, contact switches during locomotion and a floating-base nature which makes them fall all the time. A rich set of sensory inputs and a high-bandwidth actuation are often needed to ensure fast and effective reactions to unforeseen conditions, e.g., terrain variations, external pushes, slippages, unknown payloads, etc. State of the art technologies today seem to provide such valuable hardware components. However, regarding software, there is plenty of room for improvement. Locomotion planning and control problems are often treated separately in conventional humanoid control algorithms. The control challenges mentioned above are probably the main reason for such separation. Here, planning refers to the process of finding consistent open-loop trajectories, which may take arbitrarily long computations off-line. Control, on the other hand, should be done very fast online to ensure stability. In this thesis, we want to link planning and control problems again and enable for online trajectory modification in a meaningful way. First, we propose a new way of describing robot geometries like molecules which breaks the complexity of conventional models. We use this technique and derive a planning algorithm that is fast enough to be used online for multi-contact motion planning. Similarly, we derive 3LP, a simplified linear three-mass model for bipedal walking, which offers orders of magnitude faster computations than full mechanical models. Next, we focus more on walking and use the 3LP model to formulate online control algorithms based on the foot-stepping strategy. The method is based on model predictive control, however, we also propose a faster controller with time-projection that demonstrates a close performance without numerical optimizations. We also deploy an efficient implementation of inverse dynamics together with advanced sensor fusion and actuator control algorithms to ensure a precise and compliant tracking of the simplified 3LP trajectories. Extensive simulations and hardware experiments on COMAN robot demonstrate effectiveness and strengths of our method. This thesis goes beyond humanoid walking applications. We further use the developed modeling tools to analyze and understand principles of human locomotion. Our 3LP model can describe the exchange of energy between human limbs in walking to some extent. We use this property to propose a metabolic-cost model of human walking which successfully describes trends in various conditions. The intrinsic power of the 3LP model to generate walking gaits in all these conditions makes it a handy solution for walking control and gait analysis, despite being yet a simplified model. To fill the reality gap, finally, we propose a kinematic conversion method that takes 3LP trajectories as input and generates more human-like postures. Using this method, the 3LP model, and the time-projecting controller, we introduce a graphical user interface in the end to simulate periodic and transient human-like walking conditions. We hope to use this combination in future to produce faster and more human-like walking gaits, possibly with more capable humanoid robots

    Using Model-based Optimal Control for Conceptional Motion Generation for the Humannoid Robot HRP-2 14 and Design Investigations for Exo-Skeletons

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    The research field of bipedal locomotion has been active since a few decades now. At one hand, the legged locomotion principle comprises highly flexible and robust mobility for technical applications. At the other hand, a thorough technical understanding of bipedalism supports efforts of clinicians and engineers to help people, suffering from reduced locomotion capabilities caused by fatal incidents. Since the technology enabled the construction of numerous robotic devices, among them: various humanoids, researchers started to investigate bipedalism by abstraction and adoption for technical applications. Findings from humanoid robotics are further exploited for the construction of devices for human performance augmentation and mobility support or gait rehabilitation, among them: orthosis and exo-skeletons. Although this research continuously progresses, the motion capacities of humanoid robots still lack far behind those of humans in terms of forward velocity, robustness and appearance of the overall motion. Generally, it is claimed that the difference of performance between humans and robotics is not only due to the limiting characteristics of the employed technology, e.g. constructive lack of specific determinants of gait for bipedalism or dynamic limits of the actuation system, but as well to the adopted methods for motion generation and control. For humanoid robotics, methods for motion generation are classified into optimization-based methods and those that employ heuristics, that are mostly distinguished based on the problem complexity (computation time) and the resulting dynamic error between the generated motion and the dynamics of the real robot. The implementation of the dynamic motion on the robotic platform is usually comprised with an on-line stabilizing control system. This control system must then identify and resolve instantaneously the dynamic error to maintain a continuously stable operation of the device. A large dynamic error and breach of the dynamic limits of the actuation system can quickly lead to a fatal destabilization of the device. This work proposes a contribution to the model computation and the strategy of the problem formulation of direct multiple-shooting based optimal control (Bock et. al.) for dynamically stable optimization-based motion generation. The computation of the whole-body dynamic model inside the optimization relies either on forward or inverse dynamics approach. As the inverse dynamics approach has frequently been perceived as less resource intensive than the forward dynamics approach, a new generic algorithm for insufficiently constrained, under-actuated dynamic systems has been developed and thoroughly tested to comply with all numerical restrictions of the enveloping optimization algorithm. Based on this contribution, various optimal control problems for the humanoid platform HRP-2 14 have been formulated to assess the influence of different biologically inspired optimization criteria on the final motion characteristics of walking motions. From thorough bibliographic researches a dynamically more accurate model was comprised, by taking into account the impact absorbing element in the ankle joint complex. Based on the experiences of the previous study, a problem formulation for the limiting case of, dynamically overstepping an obstacle of 20cm x 11cm (height x width) with only two steps, while maintaining its stable operation was accomplished. This is a new record for this platform. In a further part, this work proposes an iterative comprehensive model-based optimal control approach for the conception of a lower limb exo-skeleton that respects the integrated nature of such a mechatronic device. In this contribution, a human effectively wearing such a lower limb exo-skeleton is modeled. The approach then substantiates all system components in an iterative procedure, based on the complete system model, effectively resolving all complex inter-dependencies between the different components of the system. The study in this work is conducted on an important benchmark motion, walking, of a healthy human being. From this study the limiting characteristics of the system are determined and substantial propositions to the realization of various system components are formulated

    Posture control of a low-cost commercially available hexapod robot for uneven terrain locomotion

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    Legged robots hold the advantage on uneven and irregular terrain, where they exhibit superior mobility over other terrestrial, mobile robots. One of the fundamental ingredients in achieving this exceptional mobility on uneven terrain is posture control, also referred to as attitude control. Many approaches to posture control for multi-legged robots have been taken in the literature; however, the majority of this research has been conducted on custom designed platforms, with sophisticated hardware and, often, fully custom software. Commercially available robots hardly feature in research on uneven terrain locomotion of legged robots, despite the significant advantages they pose over custom designed robots, including drastically lower costs, reusability of parts, and reduced development time, giving them the serious potential to be employed as low-cost research and development platforms. Hence, the aim of this study was to design and implement a posture control system on a low-cost, commercially available hexapod robot โ€“ the PhantomX MK-II โ€“ overcoming the limitations presented by the lower cost hardware and open source software, while still achieving performance comparable to that exhibited by custom designed robots. For the initial controller development, only the case of the robot standing on all six legs was considered, without accounting for walking motion. This Standing Posture Controller made use of the Virtual Model Control (VMC) strategy, along with a simple foot force distribution rule and a direct force control method for each of the legs, the joints of which can only be position controlled (i.e. they do not have torque control capabilities). The Standing Posture Controller was experimentally tested on level and uneven terrain, as well as on a dynamic balance board. Ground truth measurements of the posture during testing exhibited satisfactory performance, which compared favourably to results of similar tests performed on custom designed platforms. Thereafter, the control system was modified for the more general case of walking. The Walking Posture Controller still made use of VMC for the high-level posture control, but the foot force distribution was expanded to also account for a tripod of ground contact legs during walking. Additionally, the foot force control structure was modified to achieve compliance control of the legs during the swing phase, while still providing direct force control during the stance phase, using the same overall control structure, with a simple switching strategy, all without the need for torque control or modification of the motion control system of the legs, resulting in a novel foot force control system for low-cost, legged robots. Experimental testing of the Walking Posture Controller, with ground truth measurements, revealed that it improved the robotโ€™s posture response by a small amount when walking on flat terrain, while on an uneven terrain setup the maximum roll and pitch angle deviations were reduced by up to 28.6% and 28.1%, respectively, as compared to the uncompensated case. In addition to reducing the maximum deviations on uneven terrain, the overall posture response was significantly improved, resulting in a response much closer to that observed on flat terrain, throughout much of the uneven terrain locomotion. Comparing these results to those obtained in similar tests performed with more sophisticated, custom designed robots, it is evident that the Walking Posture Controller exhibits favourable performance, thus fulfilling the aim of this study.Dissertation (MEng)--University of Pretoria, 2018.Mechanical and Aeronautical EngineeringMEngUnrestricte

    Multibody dynamics 2015

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    This volume contains the full papers accepted for presentation at the ECCOMAS Thematic Conference on Multibody Dynamics 2015 held in the Barcelona School of Industrial Engineering, Universitat Politรจcnica de Catalunya, on June 29 - July 2, 2015. The ECCOMAS Thematic Conference on Multibody Dynamics is an international meeting held once every two years in a European country. Continuing the very successful series of past conferences that have been organized in Lisbon (2003), Madrid (2005), Milan (2007), Warsaw (2009), Brussels (2011) and Zagreb (2013); this edition will once again serve as a meeting point for the international researchers, scientists and experts from academia, research laboratories and industry working in the area of multibody dynamics. Applications are related to many fields of contemporary engineering, such as vehicle and railway systems, aeronautical and space vehicles, robotic manipulators, mechatronic and autonomous systems, smart structures, biomechanical systems and nanotechnologies. The topics of the conference include, but are not restricted to: Formulations and Numerical Methods, Efficient Methods and Real-Time Applications, Flexible Multibody Dynamics, Contact Dynamics and Constraints, Multiphysics and Coupled Problems, Control and Optimization, Software Development and Computer Technology, Aerospace and Maritime Applications, Biomechanics, Railroad Vehicle Dynamics, Road Vehicle Dynamics, Robotics, Benchmark Problems. The conference is organized by the Department of Mechanical Engineering of the Universitat Politรจcnica de Catalunya (UPC) in Barcelona. The organizers would like to thank the authors for submitting their contributions, the keynote lecturers for accepting the invitation and for the quality of their talks, the awards and scientific committees for their support to the organization of the conference, and finally the topic organizers for reviewing all extended abstracts and selecting the awards nominees.Postprint (published version

    Applied Analysis and Synthesis of Complex Systems: Proceedings of the IIASA-Kyoto University Joint Seminar, June 28-29, 2004

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    This two-day seminar aimed at introducing the new development of the COE by Kyoto University to IIASA and discussing general modeling methodologies for complex systems consisting of many elements, mostly via nonlinear, large-scale interactions. We aimed at clarifying fundamental principles in complex phenomena as well as utilizing and synthesizing the knowledge derived out of them. The 21st Century COE (Center of Excellence) Program is an initiative by the Japanese Ministry of Education, Culture, Science and Technology (MEXT) to support universities establishing discipline-specific international centers for education and research, and to enhance the universities to be the world's apex of excellence with international competitiveness in the specific research areas. Our program of "Research and Education on Complex Functional Mechanical Systems" is successfully selected to be awarded the fund for carrying out new research and education as Centers of Excellence in the field of mechanical engineering in 2003 (five-year project), and is expected to lead Japanese research and education, and endeavor to be the top in the world. The program covers general backgrounds in diverse fields as well as a more in-depth grasp of specific branches such as complex system modeling and analysis of the problems including: nonlinear dynamics, micro-mesoscopic physics, turbulent transport phenomena, atmosphere-ocean systems, robots, human-system interactions, and behaviors of nano-composites and biomaterials. Fundamentals of those complex functional mechanical systems are macroscopic phenomena of complex systems consisting of microscopic elements, mostly via nonlinear, large-scale interactions, which typically present collective behavior such as self-organization, pattern formation, etc. Such phenomena can be observed or created in every aspect of modern technologies. Especially, we are focusing upon; turbulent transport phenomena in climate modeling, dynamical and chaotic behaviors in control systems and human-machine systems, and behaviors of mechanical materials with complex structures. As a partial attainment of this program, IIASA and Kyoto University have exchanged Consortia Agreement at the beginning of the program in 2003, and this seminar was held to introduce the outline of the COE program of Kyoto University to IIASA researchers and to deepen the shared understandings on novel complex system modeling and analysis, including novel climate modeling and carbonic cycle management, through joint academic activities by mechanical engineers and system engineers. In this seminar, we invited a distinguished researcher in Europe as a keynote speaker and our works attained so far in the project were be presented by the core members of the project as well as by the other contributing members who participated in the project. All IIASA research staff and participants of YSSP (Young Scientist Summer Program) were cordially invited to attend this seminar to discuss general modeling methodologies for complex systems
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