Underactuated robotics: A review <s> a. Fuzzy PID composite control <s> In this article, we look at the excellent effect of vertical force as regards the stabilization of the inverted pendulum (IP) and demonstrate how the fuzzy control design methodology can be used to construct a hybrid fuzzy control system that incorporates PD control into a Takagi–Sugeno fuzzy control structure for stabilizing the IP via a vertical force. By gaining an intuitive understanding of the dynamics of the IP, the IP state space is fuzzily divided into six regions. In each region, a PD controller is designed to satisfy the stability conditions obtained by Lyapunov’s direct and indirect methods. It shows that the proposed hybrid fuzzy control scheme provides a more flexible and intuitive way to stabilize the IP via a vertical force. © 2005 Wiley Periodicals, Inc. <s> BIB001 </s> Underactuated robotics: A review <s> a. Fuzzy PID composite control <s> Unlike statically stable wheeled mobile robots, dynamically stable mobile robots can have higher centers of gravity, smaller bases of support and can be tall and thin resembling the shape of an adult human. This paper concerns the ballbot mobile robot, which balances dynamically on a single spherical wheel. The ballbot is omni-directional and can also rotate about its vertical axis (yaw motion). It uses a triad of legs to remain statically stable when powered off. This paper presents the evolved design with a four-motor inverse mouse-ball drive, yaw drive, leg drive, control system, and results including dynamic balancing, station keeping, yaw motion while balancing, and automatic transition between statically stable and dynamically stable states. <s> BIB002 </s> Underactuated robotics: A review <s> a. Fuzzy PID composite control <s> The ballbot is a dynamically stable mobile robot that moves on a single spherical wheel and is capable of omnidirectional movement. The ballbot is an underactuated system with nonholonomic dynamic constraints. The authors propose an offline trajectory planning algorithm that provides a class of parametric trajectories to the unactuated joint in order to reach desired static configurations of the system with regard to the dynamic constraint. The parameters of the trajectories are obtained using optimization techniques. A feedback controller is proposed that ensures accurate trajectory tracking. The trajectory planning algorithm and tracking controller are validated experimentally. The authors also extend the offline trajectory planning algorithm to a generalized case of motion between non-static configurations. <s> BIB003 </s> Underactuated robotics: A review <s> a. Fuzzy PID composite control <s> In this paper, the interval type-2 fuzzy proportional–integral–derivative controller (IT2F-PID) is proposed for controlling an inverted pendulum on a cart system with an uncertain model. The proposed controller is designed using a new method of type-reduction that we have proposed, which is called the simplified type-reduction method. The proposed IT2F-PID controller is able to handle the effect of structure uncertainties due to the structure of the interval type-2 fuzzy logic system (IT2-FLS). The results of the proposed IT2F-PID controller using a new method of type-reduction are compared with the other proposed IT2F-PID controller using the uncertainty bound method and the type-1 fuzzy PID controller (T1F-PID). The simulation and practical results show that the performance of the proposed controller is significantly improved compared with the T1F-PID controller. <s> BIB004 </s> Underactuated robotics: A review <s> a. Fuzzy PID composite control <s> The ballbot is a human-sized dynamically stable mobile robot that balances on a single ball. Unlike statically stable mobile robots, the ballbot is tall and narrow with a high center of gravity and a small footprint. Moreover, its dynamic stability enables it to be physically interactive. These characteristics make it better suited to navigate and interact in cluttered human environments. This paper presents the evolved hardware design of the ballbot with a four-wheel inverse mouse-ball drive to actuate the ball, and a yaw drive mechanism that enables unlimited rotation about its vertical axis. The ballbot also has a triad of legs that provide static stability when powered down. This paper presents a detailed description of the ballbot's control architecture, and it presents several experimental results that demonstrate its balancing and locomotion capabilities. This paper also presents a trajectory planning algorithm that plans for body lean motions, which, when tracked, result in the desired rest-to-rest motions of the robot. Finally, the paper illustrates some interesting human-robot physical interaction behaviors that can be achieved as a result of the ballbot's dynamic stability. <s> BIB005 </s> Underactuated robotics: A review <s> a. Fuzzy PID composite control <s> This paper presents the design of an optimized Interval Type 2 Fuzzy Proportional Derivative Controller (IT2F-PDC) in cascade form for Rotary Inverted Pendulum (RIP) system. The parameters of the IT2F-PDC are optimised by using Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). The goal is to balance the pendulum in upright unstable equilibrium position. The IT2F-PDC which is the extended version of conventional type 1 fuzzy logic controller, improves the control strategy by using the advantage ::: of its footprint of uncertainty for the fuzzy membership ::: function. The performance characteristics considered for the controller are steady state error, settling time, rise time, maximum overshoot, and control energy. Experimental and simulation results indicated that the effectiveness and robustness of the proposed GA- and PSO-based controllers on the RIP with respect to load disturbances, parameter variation, and noise effects have been improved over state-of-the-art method. However, the comparative results for simulation and experiment based on cascade IT2F-PDC indicate that GA-based IT2F-PDC has lower steady state error while PSO-based IT2F-PDC has lower overshoot, settling time, and control energy, but both have almost the same rise time. The proposed control strategy can be regarded as a promising strategy for controlling different unstable and nonlinear systems. <s> BIB006 </s> Underactuated robotics: A review <s> a. Fuzzy PID composite control <s> This paper addresses a three-dimensional (3D) path following control problem for underactuated autonomous underwater vehicle (AUV) subject to both internal and external uncertainties. A two-layered framework synthesizing the 3D guidance law and heuristic fuzzy control is proposed to achieve robust adaptive following along a predefined path. In the first layer, a 3D guidance controller for underactuated AUV is presented to guarantee the stability of path following in the kinematics stage. In the second layer, a heuristic adaptive fuzzy algorithm based on the guidance command and feedback linearization Proportional-Integral-Derivative (PID) controller is developed in the dynamics stage to account for the nonlinear dynamics and system uncertainties, including inaccuracy modelling parameters and time-varying environmental disturbances. Furthermore, the sensitivity analysis of the heuristic fuzzy controller is presented. Against most existing methods for 3D path following, the proposed robust fuzzy control scheme reduces the design and implementation costs of complicated dynamics controller, and relaxes the knowledge of the accuracy dynamics modelling and environmental disturbances. Finally, numerical simulation results validate the effectiveness of the proposed control framework and illustrate the outperformance of the proposed controller as well. HighlightsA two-layered framework synthesizing the guidance and control is proposed for 3D AUV path following.Robust and heuristic fuzzy path following algorithm is adopted to account for the system uncertainties.Proposed control scheme reduces the design and implementation cost with regard to most existing methods.Case study and quantitative comparison explicitly show the effectiveness of the proposed framework. <s> BIB007
Fuzzy proportional-integral-derivative (PID) composite control is a combination of fuzzy technology and conventional PID control algorithm to achieve higher control accuracy. Fuzzy control is used when the temperature deviation is large. It has the characteristics of fast response and good dynamic performance. PID control is used when the temperature deviation is small. It has good static performance and meets system control accuracy. Therefore, it has better control performance than a single fuzzy controller and a single PID regulator. In the control of the UR system, the mainstream PID control method has parallel PID and cascaded PID. There are four improved parallel PID control methods for fuzzy systems. First, the input set of the fuzzy system is obtained based on the PID control. Sanchez and Flores 175 introduced a new fuzzy PI þ PD controller, which includes a dynamic switching fuzzy system. This scheme is able to implement real-time swing-up control for the Pendubot, with a very good performance. Second, the PID control law is used as the output sets of the fuzzy system. Based on the novel idea of controlling and stabilizing the IP via vertical forces, Maravall et al. BIB001 studied the excellent effects of vertical forces on IP stability. They also demonstrated how the fuzzy control design method could be used to construct a hybrid fuzzy control system. The system incorporates PD control into the T-S fuzzy control structure to stabilize the IP by vertical force. Third, the PID control parameters are adjusted by the fuzzy system. Solihin et al.  proposed a fuzzy-tuned PID controller design for anti-swing gantry crane control. The proposed fuzzy-tuned PID controller has an advantage of robustness compared with original PID control. Xiang et al. BIB007 also adaptively adjusted the parameters of the PID controller using three fuzzy systems. A 3-D guidance controller for underactuated AUV is presented to guarantee the stability of path following in the kinematics stage. In the dynamics phase, a heuristic adaptive fuzzy algorithm based on the pilot command and feedback linearization PID controller is developed. The sensitivity analysis of the heuristic fuzzy controller is presented. El-Bardini and El-Nagar BIB004 proposed the interval type-2 fuzzy PID controller to control an IP on a cart system with an uncertain model. The two proposed controllers have been tested using four simulation tasks. The simulation and practical result shows that the performance of the proposed controller is significantly improved compared with the type-1 fuzzy PID controller. Omni-directionally balanced mobile robots are also controlled by cascaded PID methods. BIB005 BIB002 BIB003 Hamza et al. BIB006 presented the design of an optimized interval type-2 fuzzy PD controller in cascade form for rotary IP system. The proposed control strategy could be regarded as a promising strategy for controlling different unstable and nonlinear systems.