شناسايي پارامترهاي سينماتيكي و ديناميكي يك بازوي ماهر رباتيكي صفحه‌يي با چهار درجه آزادي

IDENTIFICATION OF THE KINEMATIC AND DYNAMIC PARAMETERS OF A 4-DOF PLANAR ROBOTIC MANIPULATOR

پيچيدگي معادلات حاكم بر بازوهاي ماهر رباتيكي سبب شده است روش هاي متنوعي براي كنترل آنها ارايه ‌شود. مشخصه‌هاي ديناميكي بازوها در طراحي اين روش ها معلوم و معين در نظر گرفته مي‌شوند. اين در حالي است كه مشخصه‌هاي يادشده در بيشتر موارد به دلايلي چون نواقص ساخت، استهلاك يا طبيعت خود موضوع (مثلاً اصطكاك) به‌طور دقيق در دست نيستند. از اين رو در اين نوشتار برآنيم تا ضمن ارايه‌ي يك مدل ديناميكي ساده براي ربات و شبيه سازي آن توسط نرم‌افزار MATLAB، روشي مبتني بر كم‌ترين مربعات براي شناسايي پارامتر هاي يك بازوي ماهر صفحه‌يي با چهار درجه‌ي آزادي به دست آوريم. مدل ديناميكي ارايه‌شده شامل كم‌ترين پارامترهاي مستقل در معادلات حاكم بر حركت خواهد بود. روش ارايه‌شده براي شناسايي صحيح پارامترهاي مجهول، كمينه‌ردن مجموع درايه‌هاي قطر اصلي ماتريس هم‌پراش خروجي‌هاي آلوده به اغتشاش است. نتايج به دست آمده از شبيه سازي تخمين بسيار خوبي از مقادير مجهول برآورد مي‌كند.

Due to the complexity of governing equations on robotic manipulator motion, various methods of control have been proposed. Information about the physical parameters, which are assumed to be default, is the key point of having a successful model-based control implementation. In other words, accurate identification of model parameters is always required in the case of control tasks. Unfortunately most physical characteristics are not exactly known, due to uncertainties in manufacturing, such as tolerances, clearances; or inherent uncertainties, like friction, and so on. Thus, the main objective of this study focuses on finding the kinetic parameters of a manipulator in a system identification framework, in which the sought parameters are estimated via the least squares method. Here, system identification is indeed an instance of the robot calibration problem, by which the best estimation for physical parameters of the system is extracted for use in controlling the model. To this end, first, a four-DOF planar manipulator is considered as an instant case study, and analyzed to achieve a straightforward dynamic model. If the dynamic model of the system is available, the usual way for identifying the parameters is minimizing the error between the outputs measured from the robotic manipulator and those calculated from the mathematical model, which should to be obtained for an identical set of inputs. One of the most traditional and still most common criteria for minimizing errors is the least squares method, which is utilizable for any system that is linear in terms of unknown parameters. On the other hand, in the literature, the routine dynamical model for controlling tasks is derived based on choosing relative angles as the generalized coordinates; then, Coriolis acceleration effects, including the product of joint velocities, arise in the equations of motion. Such a modeling will possess extreme parameters in its formulation, and so, identifying kinetic characteristics, will be involved. Thus, in this paper, by choosing the absolute angles of the links as the generalized coordinates, the Coriolis acceleration terms could be hidden in the structure of the equations of motion, and, in this way, our formulation will include minimum unknown parameter numbers. The input to this system is the torque applied to the manipulator joints, which makes it an MIMO system. By considering the cost function as the error between the estimated parameters and the true ones, the trace of the error covariance matrix is minimized, and, in this way, estimation is achieved. The simulation results assert the validity of this identification.