Underactuated robotics: A review <s> b. Adaptive fuzzy control <s> An adaptive fuzzy sliding-mode (AFSM) control strategy is presented to achieve position control of underactuated manipulators. Sliding surface is defined as input variable of fuzzy rules and fuzzy output is singleton, which value is adjusted by an adaptive law on-line in this method. The tuning algorithms are derived in the sense of the Lyapunov stability theorem, thus the stability of the system can be guaranteed. The controller presented is comprised of a fuzzy sliding-mode controller and an auxiliary controller. Fuzzy sliding-mode controller is developed to mimic an equivalent control law in the sliding-mode control, and an auxiliary controller is designed to compensate approximate error between the equivalent control law and the fuzzy controller. Simulation results indicate the validity and feasibility of the proposed algorithm. <s> BIB001 </s> Underactuated robotics: A review <s> b. Adaptive fuzzy control <s> Overhead cranes are common industrial structures that are used in many factories and harbors. They are usually operated manually or by some conventional control methods, such as the optimal and PLC-based methods. The theme of this paper is to provide an effective all-purpose adaptive fuzzy controller for the crane. This proposed method does not need the complex dynamic model of the crane system, but it uses trolley position and swing angle information instead to design the fuzzy controller. An adaptive algorithm is provided to tune the free parameters in the crane control system. The ways to speed the transportation and reduce the computational efforts are also given. Therefore, the designing procedure of the proposed controller will be very easy. External disturbance, such as the wind and the hit, which always deteriorates the control performance, is also discussed in this paper to verify the robustness of the proposed adaptive fuzzy algorithm. At last, several experimental results with different wire length and payload weight compare the feasibility and effectiveness of the proposed scheme with conventional methods <s> BIB002 </s> Underactuated robotics: A review <s> b. Adaptive fuzzy control <s> This paper presents a fuzzy-control method for the motion control of an acrobot. First, an explanation is given of the singularity that arises when a motion control law based on a Lyapunov function has an integrated control objective for energy and posture. Then, a fuzzy controller is designed that solves the singularity problem through regulation of a design parameter in the control law. Finally, an additional fuzzy controller is designed that improves the control performance through regulation of another design parameter in the control law. Simulation results demonstrate the effectiveness of this integrated fuzzy-control strategy. <s> BIB003 </s> Underactuated robotics: A review <s> b. Adaptive fuzzy control <s> This paper addresses the path following problem of an underactuated autonomous underwater vehicle (AUV) with the aim of dealing with parameter uncertainties and current disturbances. An adaptive robust control system was proposed by employing fuzzy logic, backstepping and sliding mode control theory. Fuzzy logic theory is adopted to approximate unknown system function, and the controller was designed by combining sliding mode control with backstepping thought. Firstly, the longitudinal speed was controlled, then the yaw angle was made as input of path following error to design the calm function and the change rate of path parameters. The controller stability was proved by Lyapunov stable theory. Simulation and outfield tests were conducted and the results showed that the controller is of excellent adaptability and robustness in the presence of parameter uncertainties and external disturbances. It is also shown to be able to avoid the chattering of AUV actuators. <s> BIB004 </s> Underactuated robotics: A review <s> b. Adaptive fuzzy control <s> This article presents a nonlinear adaptive line-of-sight path following controller for underactuated autonomous underwater vehicles in the presence of ocean currents. Firstly, a new nonsingular path following error kinematic model in the Serret–Frenet frame is developed, where a nominal course angle error is introduced to significantly simplify the guidance law design. Secondly, an adaptive line-of-sight guidance law with the introduction of the current observer is proposed to make the vehicle produce a variable sideslip angle to compensate for the drift force for any parametric curved-path path following. Benefit from the global κ-exponential convergence property of the designed current observer, the actual course angle error can be eliminated indirectly. Then, dynamic controller built on Lyapunov theory and backstepping technique guarantee the uniform global exponential stability of the yaw and relative surge velocity. In the end, stability analysis shows that the global κ-exponential stability is achieved for the closed-loop system. Simulation results demonstrate the effectiveness of the proposed control scheme. <s> BIB005 </s> Underactuated robotics: A review <s> b. Adaptive fuzzy control <s> This article investigates the three-dimensional trajectory tracking control problem for an underactuated autonomous underwater vehicle in the presence of parameter perturbations and external distur... <s> BIB006 </s> Underactuated robotics: A review <s> b. Adaptive fuzzy control <s> Abstract In this paper, robust adaptive control of a class of strict-feedback nonlinear systems with unknown control directions is investigated. A novel Nussbaum-type function is developed and a key theorem is drawn which involves quantifying the addition of multiple Nussbaum functions with different control directions in a single inequality. Global stability of the closed-loop system and asymptotic stabilization of system output are proved. A simulation example is given to illustrate the effectiveness of the proposed control scheme. <s> BIB007
After nearly 50 years of development, fuzzy control theory has been more and more widely used in practice. Adaptive fuzzy control is formed by combining fuzzy logic technology with adaptive control. An adaptive fuzzy SMC strategy is presented to achieve position control of underactuated manipulators. BIB001 It is robust, easy to master, and operate. And the control technology overcomes the difficulty of accurate modeling of complex nonlinear systems. It is possible to further correct the control rules in the controller according to its own output and external feedback during the control process. It makes the control effect more perfect. Therefore, adaptive fuzzy control has received more and more attention in modern industrial production and aerospace. It studies the 3-D trajectory tracking control problems for underactuated AUVs in the presence of parametric disturbances and external disturbances. BIB006 Based on the speed control strategy and the adaptive integral SMC algorithm, an adaptive robust controller is proposed. BIB004 Based on a novel Nussbaum-type function, Huang et al. BIB007 proposed an adaptive control scheme for a class of strictly feedback nonlinear systems. The problem of underactuating the AUV path was solved. The goal is to deal with parameter uncertainty and current disturbances. An adaptive robust control system was proposed by fuzzy logic, back push, and SMC theory. Zeng et al. BIB005 proposed a nonlinear adaptive line-of-sight path following controller for underactuated AUVs in the presence of ocean currents. Lai et al. BIB003 presented a fuzzy control method for the motion control of an Acrobot. A fuzzy controller is designed to solve the singularity problem and improve the control performance by adjusting the design parameters in the control law. Chang BIB002 provided an effective all-purpose adaptive fuzzy controller for the crane. This proposed method does not need the complex dynamic model of the crane system, but it uses trolley position and swing angle information to replace the design of fuzzy controller. It is more straightforward to implement algorithms that reduce computational complexity in practical environments.