طرح حل افزونگی عملگرها با هدف کاهش زمان محاسباتی برای ربات‌‌های موازی کابلی با درنظرگرفتن حد گسیختگی کابل

نوع مقاله : مقاله پژوهشی

نویسندگان

1 مربی سازمان آموزش فنی و حرفه ای

2 پیام نور تهران*مهندسی مکانیک

چکیده

معمولا در ربات‌‌های موازی کابلی حداقل به یک نیروی محرک افزون‌‌تر علاوه بر درجات آزادی نیاز است تا کابل‌‌ها را در تمام جهت‌‌های فضای کاری در حال کشش نگه دارد که این موضوع حل یک مساله بهینه‌سازی برای تعیین نیروی کشش کابل‌‌ها را به دنبال دارد. در این مقاله، یک مساله‌‌ی بهینه‌‌سازی محدب، بر روی ربات موازی کابلی صفحه‌‌ای با بکارگیری شرایط بهینگی از طریق تئوری کاروش‌‌ـ‌کان‌‌ـ‌‌‌تاکر و روش تحلیلی‌ـ‌تکرار، جهت دستیابی به کمینه‌‌ بردار نیرویی عملگرها که زمان و حجم محاسباتی کمتری داشته باشد، فرموله‌بندی شده‌‌است که در آن حدود پایین و بالا‌‌ی متغیرهای بهینه‌‌سازی به ترتیب، برای اطمینان از درکشش‌ماندن کابل‌‌ها و درنظرگرفتن حد اشباع عملگرها یا حد گسیختگی کابل‌‌ها (هر کدام کمتر باشد)، اعمال شده‌‌است و قیود مساوی که رابطه بین نیروی عملگرها و نیروی واردشده به پلتفرم متحرک را بیان می‌‌کنند، با تعریف نیروی عملگرها به صورت مجموع پاسخ پایه و همگن (که در فضای پوچی ماتریس ترانهاده ژاکوبین ربات قرار ‌‌دارد) حذف شده‌‌اند. مقایسه نتایج حل تحلیلی‌ـ‌تکرار ارائه‌‌شده در این مقاله با الگوریتم‌‌های عددی بهینه‌‌‌سازی نرم‌‌‌افزار متلب نشان می‌‌دهد که این روش، بسیار سریع‌‌تر از این الگوریتم‌‌ها به پاسخ بهینه همگرا می‌‌باشد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Actuators redundancy resolution scheme with computational time reduction purpose for parallel cable robots with considering the rupture limits of the cables

نویسندگان [English]

  • Ali Haidar Felegari 1
  • Javad Ahmadi 2
1 Instructor of Technical and Vocational Education Organization
2 assistant prof.
چکیده [English]

Cable parallel robots usually require at least one additional actuator force in addition to degrees of freedom to keep the cables in all directions in the workspace, which solves an optimization problem to determine the cable tensile force. In this paper, a convex optimization problem is formulated on a parallel cable robot using optimization conditions through the Karush-Kuhn-Tucker theory and the analytical-iteration method to achieve a minimum force vector of actuators that has less computational time and volume. Where the lower and upper limits of the optimization variables are applied, respectively, to ensure that the cables remain in tension and take into account the saturation limit of the actuators or the rupture limit of the cables (whichever is less), and equal constraints that the relationship between actuator force and force are expressed in the moving platform, defined by the force of the actuators as the sum of the basic solution and the homogeneous solution, -located in the null space of the transpose of Jacobin matrix. Comparison of the results of analytical-iterative solution presented in this paper with numerical algorithms of MATLAB software optimization shows that this method is much faster than these algorithms to converge to the optimal response.

کلیدواژه‌ها [English]

  • Parallel cable robot
  • Redundant Parallel Robot
  • Redundancy Resolution
  • Analytical Solution
  • Karush-Kuhn-Tucker Theory
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