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.     

Nonlinear asymptotic attitude tracking control of an underactuated 3-degree-of-freedom helicopter using neural network feedforward term

This paper proposes a new asymptotic attitude tracking controller for an underactuated 3-degree-of-freedom (DOF) laboratory helicopter system by using a nonlinear robust feedback and a neural network (NN) feedforward term. The nonlinear robust control law is developed through a modified inner-outer loop approach. The application of the NN-based feedforward is to compensate for the system uncertainties. The proposed control design strategy requires very limited knowledge of the system dynamic model, and achieves good robustness with respect to system parametric uncertainties. A Lyapunov-based stability analysis shows that the proposed algorithms can ensure asymptotic tracking of the helicopter’s elevation and travel motion, while keeping the stability of the closed-loop system. Real-time experiment results demonstrate that the controller has achieved good tracking performance.     

Adaptive Control of a Two-Link Robot Using Batch Least-Square Identifier

We design a regulation-triggered adaptive controller for robot manipulators to efficiently estimate unknown parameters and to achieve asymptotic stability in the presence of coupled uncertainties.Robot manipulators are widely used in telemanipulation systems where they are subject to model and environmental uncertainties.Using conventional control algorithms on such systems can cause not only poor control performance,but also expensive computational costs and catastrophic instabilities.Therefore,system uncertainties need to be estimated through designing a computationally efficient adaptive control law.We focus on robot manipulators as an example of a highly nonlinear system.As a case study,a 2-DOF manipulator subject to four parametric uncertainties is investigated.First,the dynamic equations of the manipulator are derived,and the corresponding regressor matrix is constructed for the unknown parameters.For a general nonlinear system,a theorem is presented to guarantee the asymptotic stability of the system and the convergence of parameters'estimations.Finally,simulation results are discussed for a two-link manipulator,and the performance of the proposed scheme is thoroughly evaluated.     

基于期望轨迹补偿的机器人鲁棒自适应控制

针对机器人存在的参数不确定性和外扰的问题,提出了一种基于期望轨迹补偿和自适应控制的方法,在传统自适应控制方法的基础上,结合变结构控制方法,设计了一种新的控制策略.该方法采用期望轨迹补偿,离线计算回归矩阵,可以有效节约控制系统在线计算的时间,实时性好,并利用变结构思想补偿非线性摩擦和外界干扰,利用lyapunov直接法分...     

Adaptive feedback linearizing control of nonholonomic wheeled mobile robots in presence of parametric and nonparametric uncertainties

In this paper, the integrated kinematic and dynamic trajectory tracking control problem of wheeled mobile robots (WMRs) is addressed. An adaptive robust tracking controller for WMRs is proposed to cope with both parametric and nonparametric uncertainties in the robot model. At first, an adaptive nonlinear control law is designed based on input–output feedback linearization technique to get asymptotically exact cancellation of the parametric uncertainty in the WMR parameters. The designed adaptive feedback linearizing controller is modified by two methods to increase the robustness of the controller: (1) a leakage modification is applied to modify the integral action of the adaptation law and (2) the second modification is an adaptive robust controller, which is included to the linear control law in the outer loop of the adaptive feedback linearizing controller. The adaptive robust controller is designed such that it estimates the unknown constants of an upper bounding function of the uncertainty due to friction, disturbances and unmodeled dynamics. Finally, the proposed controller is developed for a type (2, 0) WMR and simulations are carried out to illustrate the robustness and tracking performance of the controller.     

具有H_∞跟踪性能的机器人自适应PID控制

针对非线性不确定机器人系统的轨迹跟踪控制问题,提出一种鲁棒自适应PID控制算法.该控制器由主控制器和监督控制器组成.主控制器以常规PID控制为基础,基于滑模控制思想设计PID参数的自适应律,根据误差实时修正PID参数.基于Lyapunov函数设计的监督控制器补偿自适应PID控制器与理想控制器之间的差异,使系统具有设定的H_∞的跟踪性能.最后,两关节机器人的仿真实验结果表明了算法的有效性.

Abstract：

A robust adaptive PID control algorithm is proposed for trajectory tracking of robot manipulators with nonlinear uncertainties.The controller is composed of a main controller and a supervisory controller.The main controller is designed based on the traditional PID controller.The parameters of the PID controller are updated online according to the system running errors with the adaptation law based on the sliding mode control.The supervisory controller is proposed to compensate the error between the adaptive PID controller and the ideal controller in the sense of the Lyapunov function with the specified H_∞ tracking performance.Finally, the simulation results based on a two-joint robot manipulator show the effectiveness of the presented controller.     

基于不确定逼近的机械手间接自适应鲁棒预测控制

为了使机械手系统在含有模型不确定项时具有良好的跟踪性能和较强的抗干扰能力,提出了一种间接自适应鲁棒预测控制。首先,针对机械手模型设计出非线性鲁棒预测控制器;然后,基于三次样条函数逼近控制律中因模型不确定性产生的未知项,并在控制律中引入一个D-控制项抑制外部干扰。理论证明了所设计的控制器能够使跟踪误差收敛到原点。仿真验证了所提方法的有效性。     

Robust adaptive control for mobile manipulators

This paper addresses the trajectory tracking control of a nonholonomic wheeled mobile manipulator with parameter uncertainties and disturbances. The proposed algorithm adopts a robust adaptive control strategy where parametric uncertainties are compensated by adaptive update techniques and the disturbances are suppressed. A kinematic controller is first designed to make the robot follow a desired end-effector and platform trajectories in task space coordinates simultaneously. Then, an adaptive control scheme is proposed, which ensures that the trajectories are accurately tracked even in the presence of external disturbances and uncertainties. The system stability and the convergence of tracking errors to zero are rigorously proven using Lyapunov theory. Simulations results are given to illustrate the effectiveness of the proposed robust adaptive control law in comparison with a sliding mode controller.     

Neural network robust control of a 3-DOF hydraulic manipulator with asymptotic tracking

Multiaxial hydraulic manipulators are complicated systems with highly nonlinear dynamics and various modeling uncertainties, which hinders the development of high-performance controller. In this paper, a neural network feedforward with a robust integral of the sign of the error (RISE) feedback is proposed for high precise tracking control of hydraulic manipulator systems. The established nonlinear model takes three-axis dynamic coupling, hydraulic actuator dynamics, and nonlinear friction effects into consideration. A radial basis function neural network (RBFNN) is synthesized to approximate the uncertain system dynamics and external disturbance, which can greatly reduce the dependence on accurate system model. In addition, a continuous RISE feedback law is judiciously integrated to deal with the residual unknown dynamics. Since the major unknown dynamics can be estimated by the RBFNN and then compensated in the feedforward design, the high-gain feedback issue in RISE feedback control will be avoided. The proposed RISE-based neural network robust controller theoretically guarantees an excellent semi-global asymptotic stability. Comparative simulation is performed on a 3-DOF hydraulic manipulator, and the obtained results verify the effectiveness of the proposed controller.     

A robust constrained control approach for flexible air‐breathing hypersonic vehicles

This article investigates the robust adaptive control system design for the longitudinal dynamics of a flexible air‐breathing hypersonic vehicle (FAHV) subject to parametric uncertainties and control input constraints. A combination of back‐stepping and nonlinear disturbance observer (NDO) is utilized for exploiting an adaptive output‐feedback controller to provide robust tracking of velocity and altitude reference trajectories in the presence of flexible effects and system uncertainties. The dynamic surface control is introduced to solve the problem of “explosion of terms.” A new NDO is developed to guarantee the proposed controller's disturbance attenuation ability and to performance robustness against uncertain aerodynamic coefficients. To deal with the problem of actuator saturation, a novel auxiliary system is exploited to compensate the desired control laws. The stability of the presented NDO and controller is analyzed. Simulation results are given to demonstrate the effectiveness of the presented control strategy.     

Parameterizing robust manipulator controllers under approximate inverse dynamics: A double‐Youla approach

We consider the goal of ensuring robust stability when a given manipulator feedback control law is modified online, for example, to safely improve the performance by a learning module. To this end, the factorization approach is applied to both the plant and controller models to characterize robustly stabilizing controllers for rigid‐body manipulators under approximate inverse dynamics control. Outer‐loop controllers to stabilize the nonlinear uncertain loop that results from approximate inverse dynamics are often derived by lumping uncertainty in a single term and subsequent analysis of the error system. Here, by contrast, the well‐known norm bounds of these uncertain dynamics are first recast into a generalized plant configuration that preserves the characteristic uncertainty structure. Then, the overall loop uncertainty is expressed with respect to the nominal outer‐loop feedback controller by means of an uncertain dual‐Youla operator. Therefore, using the dual‐Youla parameterization, we provide a novel way to rigorously quantify permissible perturbations of robot manipulator feedforward/feedback controllers. The method proposed in this paper does not constitute another robust control law for rigid‐body manipulators, but rather a characterization of a set of robustly stabilizing controllers. The resulting double‐Youla parameterization for the control of robot manipulators is amenable to numerous advanced design methods. The result is thoroughly discussed by a planar elbow manipulator and exemplified with a six‐degree‐of‐freedom robot scenario with varying payload.     

A globally stable saturated desired compensation adaptive robust control for linear motor systems with comparative experiments

The recently proposed saturated adaptive robust controller is integrated with desired trajectory compensation to achieve global stability with much improved tracking performance. The algorithm is tested on a linear motor drive system which has limited control effort and is subject to parametric uncertainties, unmodeled nonlinearities, and external disturbances. Global stability is achieved by employing back-stepping design with bounded (virtual) control input in each step. A guaranteed transient performance and final tracking accuracy is achieved by incorporating the well-developed adaptive robust controller with effective parameter identifier. Signal noise that affects the adaptation function is alleviated by replacing the noisy velocity signal with the cleaner position feedback. Furthermore, asymptotic output tracking can be achieved when only parametric uncertainties are present.     

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.     

指数稳定的机器人鲁棒跟踪控制

本文提出了一种用于控制具有参数不确性机器人轨迹踊跃的鲁棒控制策略，该控制器的设计根据Ｌｙａｐｕｎｏｖ理论，由一个基于Ｓｌｏｔｉｎｅ方法的标称控制器和一个非线性连续反馈补偿器组成。     

Observer‐based adaptive robust control of a class of nonlinear systems with dynamic uncertainties

In this paper, a discontinuous projection‐based adaptive robust control (ARC) scheme is constructed for a class of nonlinear systems in an extended semi‐strict feedback form by incorporating a nonlinear observer and a dynamic normalization signal. The form allows for parametric uncertainties, uncertain nonlinearities, and dynamic uncertainties. The unmeasured states associated with the dynamic uncertainties are assumed to enter the system equations in an affine fashion. A novel nonlinear observer is first constructed to estimate the unmeasured states for a less conservative design. Estimation errors of dynamic uncertainties, as well as other model uncertainties, are dealt with effectively via certain robust feedback control terms for a guaranteed robust performance. In contrast with existing conservative robust adaptive control schemes, the proposed ARC method makes full use of the available structural information on the unmeasured state dynamics and the prior knowledge on the bounds of parameter variations for high performance. The resulting ARC controller achieves a prescribed output tracking transient performance and final tracking accuracy in the sense that the upper bound on the absolute value of the output tracking error over entire time‐history is given and related to certain controller design parameters in a known form. Furthermore, in the absence of uncertain nonlinearities, asymptotic output tracking is also achieved. Copyright © 2001 John Wiley & Sons, Ltd.     

A Robust Tracking Controller for Electrically Driven Robot Manipulators: Stability Analysis and Experiment

 In this paper, a robust controller for electrically driven robotic systems is developed. The controller is designed in a backstepping manner. The main features of the controller are: 1) Control strategy is developed at the voltage level and can deal with both mechanical and electrical uncertainties. 2) The proposed control law removes the restriction of previous robust methods on the upper bound of system uncertainties. 3) It also benefits from global asymptotic stability in the Lyapunov sense. It is worth to mention that the proposed controller can be utilized for constrained and nonconstrained robotic systems. The effectiveness of the proposed controller is verified by simulations for a two link robot manipulator and a four-bar linkage. In addition to simulation results, experimental results on a two link serial manipulator are included to demonstrate the performance of the proposed controller in tracking a given trajectory.     

A Robust Control Law with Estimated Perturbation Compensation for Robot Manipulators

By considering the dynamic response of a robot manipulator as characterized by the sliding function, a technique is proposed to estimate the perturbation in the robot control system. Perturbation compensation is then incorporated in the design of a robust control law to cancel the effects of system parametric uncertainties and external disturbances. A normalized power rate component is introduced to replace the discontinuous control that is usually associated with variable structure system. The suggested robust control law ensures that the robot control system reaches an user specified neighbourhood of the sliding manifold in finite time and with prescribed transient behaviour. Explicit estimates of the bounds on modelling errors and external disturbances are not required while signal measurement uncertainties can be accommodated. Furthermore, using the equivalent control concept, a very simple expression is derived to estimate the system perturbation signal. Detailed computer simulation results are presented to demonstrate the effectiveness of the proposed control law.     

A Novel Robust Flight Controller Design for an Air-Breathing Hypersonic Vehicle

A novel robust flight control design method is proposed for a generic air-breathing hypersonic vehicle based on a state-dependent Riccati equation technique and a nonlinear disturbance observer. The highly nonlinear dynamics of the hypersonic vehicle are firstly brought to a linear structure having a state-dependent coefficient form. And then a state-dependent Riccati equation is solved at each sampling moment to obtain a nonlinear feedback optimal control law. In order to enhance robustness of the closed-loop system, a nonlinear disturbance observer is introduced to estimate the uncertainty caused by parametric variations and external disturbances. The resulting composite controller achieves not only promising robustness and disturbance rejection performance but also flexible adjustment in the response time. Compared to a Kriging controller, the proposed controller has great advantages in the system response time and robustness. The feasibility of the proposed method is validated by simulation results.     

Robust parametric CMAC with self-generating design for uncertain nonlinear systems

In this paper, a robust parametric cerebellar model articulation controller (RP-CMAC) with self-generating design, called RPCSGD, is proposed for uncertain nonlinear systems. The proposed controller consists of two parts: one is the parametric CMAC with self-generating design (PCSGD), which is utilized to approximate the ideal controller and the other is the robust controller, which is designed to achieve a specified H^∞ robust tracking performance of the system. The corresponding memory size of the proposed controller can be suitably constructed via the self-generating design. Thus, the useless or untrained memories will not take possession of the space. Besides, the concept of sliding-mode control (SMC) is adopted so that the proposed controller has more robustness against the approximated error and uncertainties. The stability of the system can be guaranteed surely due to the derivations of the adaptive laws of the proposed RPCSGD based on the Lyapunov function. Finally, the proposed controller is applied to the second-order chaotic system and the one-link rigid robotic manipulator. The tracking performance and effectiveness of the proposed controller are verified by simulations of the computer.