The regressor-based adaptive control is useful for controlling robotic systems with uncertain parameters but with known structure of robot dynamics. Unmodeled dynamics could lead to instability problems unless modification of control law is used. In addition, exact calculation of regressor for robots with more than 6 degrees of freedom is hard to be calculated, and the task could be more complex for robots. Whereas the adaptive approximation control is a powerful tool for controlling robotic systems with unmodeled dynamics. The local (partitioned) approximation-based adaptive control includes representation of the uncertain matrices and vectors in the robot model as finite combinations of basis functions. Update laws for the weighting matrices are obtained by the Lyapunov-like design. Therefore, this work is focused function approximation-based control algorithms considering centralized and decentralized approaches. In this work, the following control algorithms are designed: (1) Adaptive hybrid regressor-approximation control. This work attempts to combine the features of both the regressor and the approximation techniques in adaptive control. The regressor technique is a powerful tool for adaptive control of the known structure of modeling while the approximation is useful for estimation of time-varying uncertainty. Therefore, this work proposes adaptive hybrid regressor and approximation control for robots in both free and constrained spaces. The control law consists of three terms: (i) regressor term for initial estimation of the known structure of the robot dynamics, e.g. inertia matrix, Coriolis and centripetal matrix and gravity vector, and (ii) approximation term for estimation of internal and external disturbances resulted from the inexact calculation of regressor matrix and unknown modeling of friction, etc, and (iii) robust term consists of switching sgn(.) function. The control law is designed based on updating the uncertain parameters and the weighting coefficients corresponding to regressor and approximation respectively with position/force tracking purposes. The proposed controller is stable in the sense of Lyapunov stability. (2) Decentralized adaptive partitioned approximation control. Partitioned approximation control is avoided in most decentralized control algorithms; however, it is essential to design feedforward control with improved tracking accuracy. As a result, this work is focused on decentralized adaptive partitioned approximation control for complex robotic systems using the orthogonal basis functions as strong approximators. In essence, the partitioned approximation technique is intrinsically decentralized with some modifications. The proposed decentralized control law consists of three terms: the partitioned approximation-based feedforward term that is necessary for precise tracking, the high gain-based feedback term, and the adaptive sliding gain-based term for compensation of modeling error. The passivity property is essential to prove the stability of local stability of the individual subsystem with guaranteed global stability. Simulation experiments on 2-link robot and 6-link biped robot are performed to prove the effectiveness of the proposed algorithms.
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Takfir is an ancient phenomenon that accompanied the emergence of Islam, and this phenomenon took its political dimension during the time of the fourth Rashidi Caliph with the emergence ofthe Kharijites sect that disbelieved many Muslims.
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