Underactuated robotics: A review <s> c. Hybrid fuzzy control <s> Ball and plate system is the extension of traditional ball and beam system. In this paper, a trajectory planning and tracking problem of ball and plate system is put forward to proof-test diverse control schemes. Firstly, we derive the mathematical model of the ball and plate system in detail. Then a hierarchical fuzzy control scheme is proposed to deal with this problem. Our scheme is composed of three levels. The lowest level is a TS type fuzzy tacking controller; the middle level is a fuzzy supervision controller that takes actions in extreme situations; and the top level is a fuzzy planning controller that determines the desired trajectory. In order to optimize the ball's moving trajectory, the genetic algorithm is introduced to adjust the output membership functions of the fuzzy planning controller. Simulation results have shown that the hierarchical fuzzy control scheme can control the ball from a point to another without hitting the obstacles and in the least time. <s> BIB001 </s> Underactuated robotics: A review <s> c. Hybrid fuzzy control <s> This paper introduces the design and implementation of a two-wheel inverted pendulum (TWIP) system with a fuzzy control scheme and the system-on-a-programmable-chip (SoPC) technology. The control scheme includes three kinds of fuzzy controls which are the fuzzy balanced standing control (FBSC), the fuzzy traveling and position control (FTPC), and the fuzzy yaw steering control (FYSC). Based on the Takagi-Sugeno fuzzy model of the TWIP, the FBSC is a structure of a parallel distributed compensator solved by the linear matrix inequality approach. Based on the motion characteristic of the TWIP, the FTPC and the FYSC are designed with Mamdani architecture if-then rules. Furthermore, the fuzzy control scheme for the real TWIP is implemented into an SoPC development board with an embedded reduced-instruction-set-computer soft-core processor and user intellectual property modules. Both the computer simulations and practical experiments demonstrate the effectiveness of the proposed control scheme. <s> BIB002 </s> Underactuated robotics: A review <s> c. Hybrid fuzzy control <s> Abstract In contrast with fully controllable systems, a super articulated mechanical system (SAMS) is a controlled underactuated mechanical system in which the dimensions of the configuration space exceed the dimensions of the control input space. The control of the cart–seesaw system is especially difficult since it is an underactuated mechanism (three degrees of freedom and only two inputs). This research develops a balancing approach for a novel SAMS model, called the cart–seesaw system, using fuzzy logic and fuzzy coordinator compensation to drive the sliding carts and keep the seesaw angle close to zero in the equilibrium state. Experimental results indicate that utilizing the proposed control methodology significantly enhances the performance. Moreover, the presentation of the fuzzy balancing controller is not considerably affected by changes in the environmental parameters, which demonstrates the effectiveness of the fuzzy controller in minimizing the seesaw tilt angle in the time domain, although the system is caused by unpredicted loading variation. Moreover, the experimental results indicate the usefulness and robustness of the proposed fuzzy control methodology. Furthermore, the proposed software/hardware platform can be beneficial for standardizing laboratory equipment and developing amusement apparatus. <s> BIB003 </s> Underactuated robotics: A review <s> c. Hybrid fuzzy control <s> In this paper, we propose synthesized design of a fuzzy logic controller (FLC) for control of an underactuated unicycle system. The FLC objective is velocity control of the wheel while keeping the pendulum upright, which is an unstable equilibrium. The synthesized design consists of three phases. First, the FLC structures including the number of rules, membership functions, inference and parametric relations are chosen based on heuristic knowledge about the unicycle. Second, on the basis of a linearized model and linear feedback, the FLC output parameters are determined quantitatively for stabilization of the unicycle. Third, the FLC output parameters are tuned using an iterative learning tuning (ILT) algorithm, which minimizes an objective function that specifies the desired unicycle performance. The rationale for the synthesized FLC design is full utilization of the available information, which is achieved by combining model-based and model-free designs, and hence improves the FLC performance. We minimize the number of FLC rules and fuzzy labels. Six rules are used for regulation or setpoint tasks, whereas 10 rules are used with extra integral control to eliminate steady-state errors induced by system uncertainties and disturbances. Only two fuzzy labels are adopted for each fuzzy variable. The ILT process consists of two phases, exploration for stabilization and exploitation for better performance. The effectiveness of the proposed FLC is validated using intensive simulations and comparisons. <s> BIB004
In order to combine the advantages of the Mamdani fuzzy system and the T-S fuzzy system, some researchers combined the Mamdani fuzzy system with the T-S fuzzy system to design a controller for the complex UR system. Since the ball plate system is an extension of the traditional ball and beam problem, Fan et al. BIB001 proposed the trajectory planning and tracking problem of the ball plate system. Based on this problem, this article proposes a hierarchical fuzzy control scheme. This solution is used to solve the trajectory planning and tracking problems of the ball and board system. The program consists of three levels. The lowest level is the T-S-type fuzzy positioning controller, the middle level is the fuzzy supervisory controller, and the top level is the fuzzy plan controller, which is used to determine the required trajectory. Huang et al. BIB002 introduced the design and implementation of a two-wheel IP Inference Engine system with a fuzzy control scheme and the system-on-aprogrammable-chip technology. The control scheme includes three kinds of fuzzy controls which are the fuzzy balanced standing control, the fuzzy traveling and position control, and the fuzzy yaw steering control. Lin et al. BIB003 developed a balancing approach for a novel super articulated mechanical system model, which called the cart-seesaw system, using fuzzy logic and fuzzy coordinator compensation to drive the sliding carts and keep the seesaw angle close to zero in the equilibrium state. Xu et al. BIB004 proposed synthesized design of an FLC for control of an underactuated unicycle system. The FLC objective is velocity control of the wheel while keeping the pendulum upright, which is an unstable equilibrium. Through the intensive simulations and comparisons, the effectiveness of the proposed FLC is validated. Fuzzy control based on traditional control.