Abstract
An optimal control design for the uncertain Delta robot is proposed in the paper. The uncertain factors of the Delta robot include the unknown dynamic parameters, the residual vibration disturbances and the nonlinear joints friction, which are (possibly fast) time-varying and bounded. A fuzzy set theoretic approach is creatively used to describe the system uncertainty. With the fuzzily depicted uncertainty, an adaptive robust control, based on the fuzzy dynamic model, is established. It designs an adaptation mechanism, consisting of the leakage term and the dead-zone, to estimate the uncertainty information. An optimal design is constructed for the Delta robot and solved by minimizing a fuzzy set-based performance index. Unlike the traditional fuzzy control methods (if-then rules-based), the proposed control scheme is deterministic and fuzzily optimized. It is proven that the global solution in the closed form for this optimal design always exists and is unique. This research provides the Delta parallel robot a novel optimal control to guarantee the system performance regardless of the uncertainty. The effectiveness of the proposed control is illustrated by a series of simulation experiments. The results reveal that the further applications in other robots are feasible.
Highlights
Delta robot, one of the most successful parallel mechanisms, has been widely applied in many sophisticated fields, such as microelectronics [1,2,3], medicine [4,5], intelligent logistics [6,7] and 3D printing [8,9]
It inherits all the virtues of the traditional parallel robot, and possesses some unique features such as lighter weight, faster motion, higher efficiency and larger payload capacity, which are elaborated in [10,11]. Due to those additional merits, certain nonlinear and uncertain factors in Delta robot could affect the system performance and can not be ignored, such as the nonlinear joints friction, the random external loads, the residual vibration caused by the effect of the lightweight material and so on, which significantly enhance the difficulty of the control design
A novel fuzzy optimal design is proposed for Delta robot with nonlinearity and uncertainty
Summary
One of the most successful parallel mechanisms, has been widely applied in many sophisticated fields, such as microelectronics [1,2,3], medicine [4,5], intelligent logistics [6,7] and 3D printing [8,9] It inherits all the virtues of the traditional parallel robot, and possesses some unique features such as lighter weight, faster motion, higher efficiency and larger payload capacity, which are elaborated in [10,11]. Many control designs are proposed for Delta robot with uncertainty, such as [14]. We propose a fuzzy performance index for Delta robot to optimize the adaptive robust control gain. Under the optimal control design, both deterministic (uniform boundedness and uniform ultimate boundedness) and fuzzy (minimizing the fuzzy performance index) performance of Delta robot could be guaranteed
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