Observer‐based adaptive control of cooperative multiple manipulators using the Mastroianni operators as uncertainty approximator

Abstract

This article addresses the multi‐objective problem of pose and force control in a cooperative system comprised of multiple n‐degree‐of‐freedom (n‐DOF) robotic arms that move a payload. The proposed controller should be capable of maintaining the position and orientation of the payload in the desired path. In addition, the force exerted by robot end‐effectors on the object must remain limited. The system has unmodeled dynamics, and measuring the robot joint velocities is impossible. In other words, joint positions are the only measured states. Therefore, a Mastroianni operator‐based observer is first designed to estimate the uncertainty and velocities based on its universal approximation property. Then, using these estimations, a feedback controller is proposed to establish a robust and precise tracking performance. The stability of this system is confirmed based on Lyapunov's stability theorem. This article is the first study on utilizing the adaptive form of Mastroianni operators in robust adaptive controller design. Moreover, the introduced structure is regressor‐free and does not depend on velocity measurements. Finally, the proposed adaptive observer‐controller is applied on two 3‐DOF cooperative robotic arms carrying a payload, and the results are precisely analyzed. The results of the proposed approach are also compared with a state‐of‐art powerful approximation method.

Tendon-Driven Robotic Arm Control Method Based on Radial Basis Function Adaptive Tracking Algorithm

“…It is investigated that the back-stepping approach is utilized for the construction of the adaptive control module to handle the problem of the nonlinear system of RA and TT. This, in turn, solves the problem of uncertain parameters and lack of model information of RA [20]. The back-stepping method is a systematic design method for parameter uncertain systems, which uses a recursive structure to the Lyapunov function of the CLS to obtain the feedback controller.…”

Adaptive backstepping asymptotic consensus tracking control of multiple uncertain manipulators with disturbances

“…Recently, the consensus tracking issues of multiple robot manipulators (MRMs) have gradually emerged in modern industrial applications. [5][6][7] For the actual robots, networked systems, and other complex systems, it is difficult to carry out accurate mathematical modeling, and the external disturbances are very likely to occur frequently in complex working environments. 8,9 Thus, how to improve the consensus tracking precision of MRMs in the presence of model uncertainties and external disturbances has always been one of the technical difficulties, and has been widely researched recently.…”

“…The control precision has always been one of the important system performance indicators. Recently, the consensus tracking issues of multiple robot manipulators (MRMs) have gradually emerged in modern industrial applications 5–7 . For the actual robots, networked systems, and other complex systems, it is difficult to carry out accurate mathematical modeling, and the external disturbances are very likely to occur frequently in complex working environments 8,9 .…”

Robust cooperative multiple flexible-joint arms control using the q-Bernstein-Schurer operators as the uncertainty approximator: A singular perturbation approach

“…While fuzzy systems and neural networks may estimate multiple functions based on their universal approximation characteristic, they suffer limitations that turn their design and construction into complex problems (Izadbakhsh et al, 2021d; Deylami and Izadbakhsh, 2021a; Izadbakhsh et al, 2022a). In fuzzy logic-based approximators, various parameters such as types and numerical ranges of membership functions, methods of fuzzification/defuzzification, the inference system, and the rule database should be chosen properly to fulfill the design objectives.…”