Decentralized adaptive partitioned approximation control of high degrees-of-freedom robotic manipulators considering three actuator control modes

Abstract

Partitioned approximation control is avoided in most decentralized control algorithms; however, it is essential to design a feedforward control term for improving the tracking accuracy of the desired references. In addition, consideration of actuator dynamics is important for a robot with high-velocity movement and highly varying loads. 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. Three actuator control modes are considered in this study: (i) a torque control mode in which the armature current is well controlled by a current servo amplifier and the motor torque/current constant is known, (ii) a current control mode in which the torque/current constant is unknown, and (iii) a voltage control mode with no current servo control being available. 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. Two case studies are used to prove the validity of the proposed controller: a two-link manipulator and a six-link biped robot.

FAT-based adaptive backstepping control of an electromechanical system with an unknown input coefficient

“…In the case of (6), it means selecting an adaptive control such that the parameters are unavailable. According to the work of [14,22], three control modes can be selected and should be solved in sequence (backstepping approach). These modes are (1) motor torque control mode (see (6a)) in which the torque-current constant and a current servo loop are available, (2) motor current control mode (see (6b)) with an unknown torque-current constant, and 3 where they symbol ( ) refers to estimation of parameters, K and Λ are feedback gains, the subscript d refers to the desired reference, and σ is a time-varying robust sliding gain that will be updated to avoid prerequisite to bounds of modeling/approximation error.…”

“…Then, the adaptive laws of the weighting vector/matrix are updated based on Lyapunov stability. For more details on this topic, the reader is referred to [14][15][16][17][18][19][20][21] and the references therein.…”

Proxy-Based Sliding Mode Vibration Control with an Adaptive Approximation Compensator for Euler-Bernoulli Smart Beams

“…To ensure stability, it is necessary to have ( ≥ Ω −1 ) then the tracking error is bounded and converges to ̅ . Thus, the system is stable in sense of Lyapunov stability [23][24][25][26][27][28].…”

“…To overcome PID limitations, a feedforward term is added to the PID term to obtain high bandwidth control. However, if the dynamic modelling includes uncertainties, the adaptive control is integrated such that the parameters associated with the feedforward term are updated based on Lyapunov theory [22][23][24][25][26][27][28][29][30][31][32][33]. In effect, there are two basic strategies for adaptive control: regressor-based control and approximation-based control.…”

“…In contrast to the regressor approach, the adaptive approximation technique is a model-free control includes representation of the uncertainties in terms of weighting and basis function vectors/matrices. The weighting coefficients are updates based on Lyapunov theory, see the papers [22][23][24][25][26][27][28][29][30][31][32][33] for more details. However, modelling error should be compensated by using a robust sliding term.…”