The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do not possess sharply defined boundaries, e.g., the “class of bald men,” or the “class of numbers which are much greater than 10,” or the “class of adaptive systems,” etc. A basic concept which makes it possible to treat fuzziness in a quantitative manner is that of a fuzzy set, that is, a class in which there may be grades of membership intermediate between full membership and non-membership. Thus, a fuzzy set is characterized by a membership function which assigns to each object its grade of membership (a number lying between 0 and 1) in the fuzzy set. After a review of some of the relevant properties of fuzzy sets, the notions of a fuzzy system and a fuzzy class of systems are introduced and briefly analyzed. The paper closes with a section dealing with optimization under fuzzy constraints in which an approach to...

Fuzzy sets and systems

A two-link robotic manipulator is a Multi-Input Multi-Output (MIMO), highly nonlinear and coupled system. Therefore, designing an efficient controller for this system is a challenging task for the control engineers. In this paper, the Fractional Order Fuzzy Proportional-Integral-Derivative (FOFPID) controller for a two-link planar rigid robotic manipulator for trajectory tracking problem is investigated. Robustness testing of FOFPID controller for model uncertainties, disturbance rejection and noise suppression is also investigated. To study the effectiveness of FOFPID controller, its performance is compared with other three controllers namely Fuzzy PID (FPID), Fractional Order PID (FOPID) and conventional PID. For tuning of parameters of all the controllers, Cuckoo Search Algorithm (CSA) optimization technique was used. Two performance indices namely Integral of Absolute Error (IAE) and Integral of Absolute Change in Controller Output (IACCO) having equal weightage for both the links are considered for minimization. Numerical simulation results clearly indicate the superiority of FOFPID controller over the other controllers for trajectory tracking, model uncertainties, disturbance rejection and noise suppression.

Performance analysis of fractional order fuzzy PID controllers applied to a robotic manipulator

The master–slave control design problem is considered for the networked teleoperation system with friction and external disturbances. A new finite-time synchronization control method is proposed with the help of adaptive fuzzy approximation. We develop a new nonsingular fast terminal sliding mode (NFTSM) to provide faster convergence and higher precision than the linear hyperplane-sliding mode and the classic terminal-sliding mode (TSM). Then, the adaptive fuzzy-logic system is employed to approximate the system uncertainties, and the corresponding adaptive fuzzy NFTSM controller is designed. By constructing Lyapunov function, the stability and finite-time synchronization performance are proved with the new controller in the presence of system uncertainties and external disturbances. Compared with the traditional teleoperation design method, the new control scheme achieves better transient-state performance and steady-state performance. Finally, the simulations are performed and the comparisons are shown among the proposed method, the P+d method, the PD+d method, the DFF method, and the classic TSM FTSM. The simulation results further demonstrate the effectiveness of the proposed method.

Adaptive Fuzzy Finite-Time Coordination Control for Networked Nonlinear Bilateral Teleoperation System

This paper introduces a novel and general real-time adaptive motion planning (RAMP) approach suitable for planning trajectories of high-DOF or redundant robots, such as mobile manipulators, in dynamic environments with moving obstacles of unknown trajectories. The RAMP approach enables simultaneous path and trajectory planning and simultaneous planning and execution of motion in real time. It facilitates real-time optimization of trajectories under various optimization criteria, such as minimizing energy and time and maximizing manipulability. It also accommodates partially specified task goals of robots easily. The approach exploits redundancy in redundant robots (such as locomotion versus manipulation in a mobile manipulator) through loose coupling of robot configuration variables to best achieve obstacle avoidance and optimization objectives. The RAMP approach has been implemented and tested in simulation over a diverse set of task environments, including environments with multiple mobile manipulators. The results (and also the accompanying video) show that the RAMP planner, with its high efficiency and flexibility, not only handles a single mobile manipulator well in dynamic environments with various obstacles of unknown motions in addition to static obstacles, but can also readily and effectively plan motions for each mobile manipulator in an environment shared by multiple mobile manipulators and other moving obstacles.

Real-Time Adaptive Motion Planning (RAMP) of Mobile Manipulators in Dynamic Environments With Unforeseen Changes

This paper addresses the robust trajectory tracking problem for a redundantly actuated omnidirectional mobile manipulator in the presence of uncertainties and disturbances. The development of control algorithms is based on sliding mode control (SMC) technique. First, a dynamic model is derived based on the practical omnidirectional mobile manipulator system. Then, a SMC scheme, based on the fixed large upper boundedness of the system dynamics (FLUBSMC), is designed to ensure trajectory tracking of the closed-loop system. However, the FLUBSMC scheme has inherent deficiency, which needs computing the upper boundedness of the system dynamics, and may cause high noise amplification and high control cost, particularly for the complex dynamics of the omnidirectional mobile manipulator system. Therefore, a robust neural network (NN)-based sliding mode controller (NNSMC), which uses an NN to identify the unstructured system dynamics directly, is further proposed to overcome the disadvantages of FLUBSMC and reduce the online computing burden of conventional NN adaptive controllers. Using learning ability of NN, NNSMC can coordinately control the omnidirectional mobile platform and the mounted manipulator with different dynamics effectively. The stability of the closed-loop system, the convergence of the NN weight-updating process, and the boundedness of the NN weight estimation errors are all strictly guaranteed. Then, in order to accelerate the NN learning efficiency, a partitioned NN structure is applied. Finally, simulation examples are given to demonstrate the proposed NNSMC approach can guarantee the whole system's convergence to the desired manifold with prescribed performance.

Trajectory Tracking Control of Omnidirectional Wheeled Mobile Manipulators: Robust Neural Network-Based Sliding Mode Approach

A computed torque controller for uncertain robotic manipulator systems: Fuzzy approach

This paper addresses the robust trajectory tracking problem for a general class of nonholonomic systems with velocity constraints in the presence of uncertainties. The development of the proposed algorithm is based on sliding mode control technique. First, for the purpose of designing controllers, the conservative upper-bounded function of dynamics model of nonholonomic systems is derived based on the dynamics structure properties. Then, a sliding mode control scheme is presented to guarantee trajectory tracking of closed-loop system. The asymptotical or exponential stability is obtained in the Lyapunov sense. Finally, simulation examples are given to demonstrate the proposed approach.

Robust motion control for nonholonomic constrained mechanical systems: sliding mode approach

A control system for the movable manipulator system consisting of movable platform, manipulator and visual system is composed of primary control computer, display, single-chip microprocessor, servo motor and its driver, photoelectric encoder, step motor and its driver, two movement control cards, camera head, image acquisition card, infrared sensor, ultrasonic sensor, power supply and PCI bus

Controlling system of movable manipulator

The utility model discloses a system for controlling a travelling manipulator, which can be used for the parallel and coordinating working for modules such as mobile platforms, manipulators, a visual system, etc. The travelling manipulator system comprises the mobile platforms and the manipulators. The controlling system comprises a main control computer, a displayer, a single chip computer, a servo motor, a servo motor driver, a photoelectric encoder, a stepper motor, a stepper motor driver, a motion control board, a camera, an image grabber, an infrared sensor, an ultrasonic sensor, the power supply, and a PCI bus; according to pre-execution task and the current locations of the mobile platform and the manipulator, main control computer conducts the motion planning for the mobile platform and the manipulator; operators can issue the command for the main control computer by means of the displayer and control the travelling manipulator system for implementing the operating task for the travelling. The utility model can complete the task under the complicated and unknown environment for implementing the coordination control for the mobile platform, the manipulator, and the visual system with the optimal synthesis performance of the system.

System for controlling travelling manipulator

Tracking control problem of mobile manipulators with dynamical uncertainties is addressed in this paper. The controller is designed based on model of mobile manipulators consisting of two cascaded subsystems: a chained-like kinematical model without uncertainties and a dynamical model with uncertainties. The proposed control law can ensure that full states of closed-loop system can track given trajectories in presence of dynamical uncertainties. A globally asymptotic stability is obtained in Lyapunov sense. Simulation studies show feasibility and effectiveness of the proposed approach.

Xinchun Li

Papers

A computed torque controller for uncertain robotic manipulator systems: Fuzzy approach

Robust motion control for nonholonomic constrained mechanical systems: sliding mode approach

Controlling system of movable manipulator

System for controlling travelling manipulator

Tracking control of mobile manipulator with dynamical uncertainties