A combined backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems

In this paper, a robust adaptive tracking control problem is discussed for a general class of strict-feedback uncertain nonlinear systems. The systems may possess a wide class of uncertainties referred to as unstructured uncertainties, which are not linearly parameterized and do not have any prior knowledge of the bounding functions. The Takagi-Sugeno type fuzzy logic systems are used to approximate the uncertainties. A unified and systematic procedure is employed to derive two kinds of novel robust adaptive tracking controllers by use of the input-to-state stability (ISS) and by combining the backstepping technique and generalized small gain approach. One is the robust adaptive fuzzy tracking controller (RAFTC) for the system without input gain uncertainty. The other is the robust adaptive fuzzy sliding tracking controller (RAFSTC) for the system with input gain uncertainty. Both algorithms have two advantages, those are, semi-global uniform ultimate boundedness of adaptive control system in the presence of unstructured uncertainties and the adaptive mechanism with minimal learning parameterizations. Four application examples, including a pendulum system with motor, a one-link robot, a ship roll stabilization with actuator and a single-link manipulator with flexible joint, are used to demonstrate the effectiveness and performance of proposed schemes.     

Observer-based adaptive control of robot manipulators: Fuzzy systems approach

This paper presents a fuzzy adaptive control suitable for motion control of multi-link robot manipulators with structured and unstructured uncertainties. When joint velocities are available, full state fuzzy adaptive feedback control is designed to ensure the stability of the closed loop dynamic. If the joint velocities are not measurable, an observer is introduced and an adaptive output feedback control is designed based on the estimated velocities. In the proposed control scheme, we need not derive the linear formulation of robot dynamic equation and tune the parameters. To reduce the number of fuzzy rules of the fuzzy controller, we consider the properties of robot dynamics and the decomposition of the uncertainties terms. The proposed controller is robust against uncertainties and external disturbance. Further, it is shown that required stability conditions, in both cases, can be formulated as LMI problems and solved using dedicated software. The validity of the control scheme is demonstrated by computer simulations on a two-link robot manipulator.     

Robust fuzzy tracking control for robotic manipulators

In this paper, a stable adaptive fuzzy-based tracking control is developed for robot systems with parameter uncertainties and external disturbance. First, a fuzzy logic system is introduced to approximate the unknown robotic dynamics by using adaptive algorithm. Next, the effect of system uncertainties and external disturbance is removed by employing an integral sliding mode control algorithm. Consequently, a hybrid fuzzy adaptive robust controller is developed such that the resulting closed-loop robot system is stable and the trajectory tracking performance is guaranteed. The proposed controller is appropriate for the robust tracking of robotic systems with system uncertainties. The validity of the control scheme is shown by computer simulation of a two-link robotic manipulator.     

A robust fuzzy logic controller for robot manipulators withuncertainties

Owing to load variation and unmodeled dynamics, a robot manipulator can be classified as a nonlinear dynamic system with structured and unstructured uncertainties. In this paper, the stability and robustness of a class of the fuzzy logic control (FLC) is investigated and a robust FLC is proposed for a robot manipulator with uncertainties. In order to show the performance of the proposed control algorithm, computer simulations are carried out on a simple two-link robot manipulator.     

Adaptive Fuzzy Neural Network Control Design via a T–S Fuzzy Model for a Robot Manipulator Including Actuator Dynamics

This paper focuses on the development of adaptive fuzzy neural network control (AFNNC), including indirect and direct frameworks for an $n$-link robot manipulator, to achieve high-precision position tracking. In general, it is difficult to adopt a model-based design to achieve this control objective due to the uncertainties in practical applications, such as friction forces, external disturbances, and parameter variations. In order to cope with this problem, an indirect AFNNC (IAFNNC) scheme and a direct AFNNC (DAFNNC) strategy are investigated without the requirement of prior system information. In these model-free control topologies, a continuous-time Takagi–Sugeno (T–S) dynamic fuzzy model with online learning ability is constructed to represent the system dynamics of an $n$-link robot manipulator. In the IAFNNC, an FNN estimator is designed to tune the nonlinear dynamic function vector in fuzzy local models, and then, the estimative vector is used to indirectly develop a stable IAFNNC law. In the DAFNNC, an FNN controller is directly designed to imitate a predetermined model-based stabilizing control law, and then, the stable control performance can be achieved by only using joint position information. All the IAFNNC and DAFNNC laws and the corresponding adaptive tuning algorithms for FNN weights are established in the sense of Lyapunov stability analyses to ensure the stable control performance. Numerical simulations and experimental results of a two-link robot manipulator actuated by dc servomotors are given to verify the effectiveness and robustness of the proposed methodologies. In addition, the superiority of the proposed control schemes is indicated in comparison with proportional–differential control, fuzzy-model-based control, T–S-type FNN control, and robust neural fuzzy network control systems.      

A Nonlinear Robust Control Using a Fuzzy Reasoning and Its Application to a Robot Manipulator

A simplified adaptive nonlinear robust controller (SANROC) has beenstudied in the literature. However, this is based on using the so-calledmatching condition. The present controller is not based on using such acondition. The estimate of an upper bound for uncertainties is usuallyincreased by using the adaptive mechanism, e.g., by consisting of amonotonically increased function. In this paper, instead of using such ananalytically adaptive mechanism, a fuzzy reasoning technique is alsoincorporated with the adaptive mechanism of SANROC. The proposed method isapplied to a pantagraph type robot manipulator. The effectiveness of thepresent method is illustrated by some experiments.     

Nonlinear robust adaptive Cartesian impedance control of UAVs equipped with a robot manipulator

In this paper, a new nonlinear robust adaptive impedance controller is addressed for Unmanned Aerial Vehicles (UAVs) equipped with a robot manipulator that physically interacts with environment. A UAV equipped with a robot manipulator is a novel system that can perform different tasks instead of human being in dangerous and/or inaccessible environments. The objective of the proposed robust adaptive controller is control of the UAV and its robotic manipulator’s end-effector impedance in Cartesian space in order to have a stable physical interaction with environment. The proposed controller is robust against parametric uncertainties in the nonlinear dynamics model of the UAV and the robot manipulator. Moreover, the controller has robustness against the bounded force sensor inaccuracies and bounded unstructured modeling (nonparametric) uncertainties and/or disturbances in the system. Tracking performance and stability of the system are proved via Lyapunov stability theorem. Using simulations on a quadrotor UAV equipped with a three-DOF robot manipulator, the effectiveness of the proposed robust adaptive impedance controller is investigated in the presence of the force sensor error, and parametric and non-parametric uncertainties.     

Adaptive tracking control for robot manipulator

In this study, an adaptive control system is proposed for the tracking control of an n-link robot manipulator to achieve high-precision position control. The presentation of the adaptive control system is divided into three parts: a feedforward controller, a state feedback controller and an uncertainty alleviator. All on-line tuning algorithms in the adaptive control system are derived in the sense of Lyapunov stability analysis, so that system-tracking stability can be guaranteed in the closed-loop system whether the uncertainties occur. It has learning ability similar to intelligent control, but with a simpler control framework. Computer simulations of a three-link SCARA robot manipulator verify the validity of the proposed control strategy in the possible presence of uncertainties. The merits of the proposed control scheme are that not only can the stability of the controlled system be guaranteed, but also no constrained conditions and prior knowledge of the controlled plant are required in the design process.     

Task-space control of robots using an adaptive Taylor series uncertainty estimator

An uncertainty estimation and compensation can improve the performance of control systems due to structured and unstructured uncertainty. This paper presents a robust task-space control approach using an adaptive Taylor series uncertainty estimator for electrically driven robot manipulators. It is worth noting that not only the lumped uncertainty is estimated and employed in the indirect form of robust controller, but also the upper bound of approximation error is estimated to form a robustifying term and the asymptotic convergence of tracking error and its time derivative are proven based on stability analysis. Finally, the effectiveness of the proposed controller is shown through simulation and comparison with two valuable control schemes applied on the Selective Compliance Assembly Robot Arm (SCARA) robot manipulator.     

Robust adaptive control of an underactuated free-flying space robot under a non-holonomic structure in joint space

This paper introduces a robust adaptive control scheme for an underactuated free-flying space robot under non-holonomic constraints. An underactuated robot manipulator is defined as a robot that has fewer joint actuators than the number of total joints. Because, if one of the joints is out of order, it is so hard to repair the joint, especially in space, the control of such a robot manipulator is important. However, it is difficult to control an underactuated robot manipulator because of the reduced dimension of the input space, i.e. the non-holonomic structure of the underactuated system. The proposed scheme does not need to assume that the exact dynamic parameters must be known. It is analysed in joint space to control the underactuated robot mounted on the space station under parametric uncertainties and external disturbances. The simulation results have shown that the proposed method is very feasible and robust for a two-link planar free-flying space robot with one passive joint.     

Repetitive control of electrically driven robot manipulators

This article presents a novel robust discrete repetitive control of electrically driven robot manipulators for tracking of a periodic trajectory. We propose a novel model, which presents the highly non-linear dynamics of robot manipulator in the form of linear discrete-time time-varying system. Based on the proposed model, we develop a two-term control law. The first term is an ordinary time-optimal and minimum-norm (TOMN) control by employing parametric controllers to guarantee stability. The second term is a novel robust control to improve the control performance in the face of uncertainties. The robust control estimates and compensates uncertainties including the parametric uncertainty, unmodelled dynamics and external disturbances. Performance of the proposed method is compared with two discrete methods, namely the TOMN control and an adaptive iterative learning (AIL) control. Simulation results confirm superiority of the proposed method in terms of the convergence speed and precision.     

Intelligent mobile manipulator navigation using adaptive neuro-fuzzy systems

The work presented in this paper deals with the problem of autonomous and intelligent navigation of mobile manipulator, where the unavailability of a complete mathematical model of robot systems and uncertainties of sensor data make the used of approximate reasoning to the design of autonomous motion control very attractive.A modular fuzzy navigation method in changing and dynamic unstructured environments has been developed. For a manipulator arm, we apply the robust adaptive fuzzy reactive motion planning developed in [J.B. Mbede, X. Huang, M. Wang, Robust neuro-fuzzy sensor-based motion control among dynamic obstacles for robot manipulators, IEEE Transactions on Fuzzy Systems 11 (2) (2003) 249-261]. But for the vehicle platform, we combine the advantages of probabilistic roadmap as global planner and fuzzy reactive based on idea of elastic band. This fuzzy local planner based on a computational efficient processing scheme maintains a permanent flexible path between two nodes in network generated by a probabilistic roadmap approach. In order to consider the compatibility of stabilization, mobilization and manipulation, we add the input of system stability in vehicle fuzzy navigation so that the mobile manipulator can avoid stably unknown and/or dynamic obstacles. The purpose of an integration of robust controller and modified Elman neural network (MENN) is to deal with uncertainties, which can be translated in the output membership functions of fuzzy systems.     

Variable Upper Bounding Approach for Adaptive-Robust Control in Robot Control

This paper presents a new adaptive-robust control law for robot manipulators with parametric uncertainty. Stability of the uncertain system has been guaranteed using the Lyapunov theory and the control law is derived by means of analytical approach. In this scheme, the manipulator parameters are determined with an estimation law, and both adaptive gain and additional control input are also updated as a function of the estimated value. The proposed adaptive control input includes a parameter estimation law as an adaptive controller and an additional control input vector as a robust controller. The developed approach has the advantages of both adaptive and robust control laws, and besides it eliminates the disadvantages of them.     

Robust Adaptive Dead Zone Technology for Fault-Tolerant Control of Robot Manipulators Using Neural Networks

In this paper, a multi-layered feed-forward neural network is trained on-line by robust adaptive dead zone scheme to identify simulated faults occurring in the robot system and reconfigure the control law to prevent the tracking performance from deteriorating in the presence of system uncertainty. Consider the fact that system uncertainty can not be known a priori, the proposed robust adaptive dead zone scheme can estimate the upper bound of system uncertainty on line to ensure convergence of the training algorithm, in turn the stability of the control system. A discrete-time robust weight-tuning algorithm using the adaptive dead zone scheme is presented with a complete convergence proof. The effectiveness of the proposed methodology has been shown by simulations for a two-link robot manipulator.     

Robust tracking enhancement of robot systems including motordynamics: a fuzzy-based dynamic game approach

A robust tracking control design of robot systems including motor dynamics with parameter perturbation and external disturbance is proposed in this study via adaptive fuzzy cancellation technique. A minimax controller equipped with a fuzzy-based scheme is used to enhance the tracking performance in spite of system uncertainties and external disturbance. The design procedure is divided into three steps. At first, a linear nominal robotic control design is obtained via model reference tracking with desired eigenvalue assignment. Next, a fuzzy logic system is constructed and then tuned to eliminate the nonlinear uncertainties as possibly as it can to enhance the tracking robustness. Finally, a minimax control scheme is specified to optimally attenuate the worst-case effect of both the residue due to fuzzy cancellation and external disturbance to achieve a minimax tracking performance. In addition, an adaptive fuzzy-based dynamic game theory is introduced to solve the minimax tracking problem. The proposed method is appropriate for the robust tracking design of robotic systems with large parameter perturbation and external disturbance. A simulation example of a two-link robotic manipulator driven by DC motors is also given to demonstrate the effectiveness of proposed design method's tracking performance     

基于自适应模糊补偿的机械臂复合控制策略

针对刚性机械臂存在摩擦和扰动等不确定因素给轨迹跟踪控制带来的困难,本文基于李亚普诺夫稳定性理论,给出了一种机械臂的自适应控制方案．该方案针对机械臂的标称部分,采用计算力矩的方法设计相应的控制量,在此基础上,构造模糊系统逼近摩擦得到补偿控制量,并针对随机扰动的上界设计反馈控制率,以克服扰动带来的影响,保证系统的稳定性．仿真结果表明,该复合控制对于具有不确定性摩擦以及扰动的机械臂轨迹跟踪问题效果良好．     

Adaptive robust fuzzy control for path tracking of a wheeled mobile robot

This paper proposes an adaptive robust fuzzy control scheme for path tracking of a wheeled mobile robot with uncertainties. The robot dynamics including the actuator dynamics is considered in this work. The presented controller is composed of a fuzzy basis function network (FBFN) to approximate an unknown nonlinear function of the robot complete dynamics, an adaptive robust input to overcome the uncertainties, and a stabilizing control input. The stability and the convergence of the tracking errors are guaranteed using the Lyapunov stability theory. When the controller is designed, the different parameters for two actuator models in the dynamic equation are taken into account. The proposed control scheme does not require the accurate parameter values for the actuator parameters as well as the robot parameters. The validity and robustness of the proposed control scheme are demonstrated through computer simulations. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

A robust neural controller for underwater robot manipulators

Presents a robust control scheme using a multilayer neural network with the error backpropagation learning algorithm. The multilayer neural network acts as a compensator of the conventional sliding mode controller to improve the control performance when initial assumptions of uncertainty bounds of system parameters are not valid. The proposed controller is applied to control a robot manipulator operating under the sea which has large uncertainties such as the buoyancy, the drag force, wave effects, currents, and the added mass/moment of inertia. Computer simulation results show that the proposed control scheme gives an effective path way to cope with those unexpected large uncertainties.     

A new robust observer-based adaptive type-2 fuzzy control for a class of nonlinear systems

In this paper, a novel robust observer-based adaptive controller is presented using a proposed simplified type-2 fuzzy neural network (ST2FNN) and a new three dimensional type-2 membership function is presented. Proposed controller can be applied to the control of high-order nonlinear systems and adaptation of the consequent parameters and stability analysis are carried out using Lyapunov theorem. Moreover, a new adaptive compensator is presented to eliminate the effect of the external disturbance, unknown nonlinear functions approximation errors and sate estimation errors. In the proposed scheme, using the Lyapunov and Barbalat's theorem it is shown that the system is stable and the tracking error of the system converges to zero asymptotically. The proposed method is simulated on a flexible joint robot, two-link robot manipulator and inverted double pendulums system. Simulation results confirm that in contrast to other robust techniques, our proposed method is simple, give better performance in the presence of noise, external disturbance and uncertainties, and has less computational cost.     

Robust tracking design based on adaptive fuzzy control of uncertain nonlinear MIMO systems with time delayed states

It is proposed here to use a robust tracking design based on adaptive fuzzy control technique to control a class of multi-input-multi-output (MIMO) nonlinear systems with time delayed uncertainty in which each uncertainty is assumed to be bounded by an unknown gain. This technique will overcome modeling inaccuracies, such as drag and friction losses, effect of time delayed uncertainty, as well as parameter uncertainties. The proposed control law is based on indirect adaptive fuzzy control. A fuzzy model is used to approximate the dynamics of the nonlinear MIMO system; then, two on-line estimation schemes are developed to overcome the nonlinearities and identify the gains of the delayed state uncertainties, simultaneously. The advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear system functions with an online update law. The adaptive fuzzy scheme uses a Variable Structure (VS) scheme to resolve the system uncertainties, time delayed uncertainty and the external disturbances such that H_∞ tracking performance is achieved. The control laws are derived based on a Lyapunov criterion and the Riccati-inequality such that all states of the system are uniformly ultimately bounded (UUB). Therefore, the effect can be reduced to any prescribed level to achieve H _∞ tracking performance. A two-connected inverted pendulums system on carts and a two-degree-of-freedom mass-spring-damper system are used to validate the performance of the proposed fuzzy technique for the control of MIMO nonlinear systems.