Adaptive backstepping integral control of a small‐scale helicopter for airdrop missions

This paper presents an adaptive Lyapunov‐based controller with integral action for small‐scale helicopters carrying out airdrop missions. The proposed controller is designed via adaptive backstepping. Unlike the approximate modeling approaches, where the coupling effect of the helicopter is neglected, the proposed method is developed according to a complete dynamic model such that the closed‐loop helicopter system is guaranteed to be globally ultimately bounded. Two numerical simulations with airdrops are conducted to exemplify the merits of the proposed controller. Through simulation results, the proposed control method is shown to outperform the well‐known controller in Mahony and Hamel, Int. J. Robust Nonlinear Control, Vol. 14, No. (12), pp. 1035–1059 (2004). Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust control of robot manipulators based on uncertainty and disturbance estimation

In this work, uncertainty and disturbance estimation (UDE) based robust trajectory tracking controller for rigid link manipulators was proposed. The UDE was employed to estimate the composite uncertainty that comprises the effects of system nonlinearities, external disturbances, and parametric uncertainties. A feedback linearization based controller was designed for trajectory tracking, and the same was augmented by the UDE‐estimated uncertainties to achieve robustness. The resulting controller however required measurement of joint velocities apart from the joint positions. To address the issue, an observer that employed the UDE‐estimated uncertainties for robustness was proposed, giving rise to the UDE‐based controller–observer structure. Closed‐loop stability of the overall system was established. The notable feature of the proposed design was that it neither required accurate plant model nor any information about the uncertainty. Also, the design needed only joint position measurements for its implementation. To demonstrate the effectiveness, simulation results of the proposed approach as applied to the trajectory tracking control of two‐link robotic manipulator and comparison of its performance with some of the well‐known existing controllers were presented. Lastly, hardware implementation of the proposed design for trajectory control of Quanser's single‐link flexible joint module was carried out, and it was shown that the proposed strategy offered a viable approach for designing implementable robust controllers for robots. Copyright © 2011 John Wiley & Sons, Ltd.     

Tracking control of a closed-chain five-bar robot with two degrees of freedom by integration of an approximation-based approach and mechanical design

The trajectory tracking problem of a closed-chain five-bar robot is studied in this paper. Based on an error transformation function and the backstepping technique, an approximation-based tracking algorithm is proposed, which can guarantee the control performance of the robotic system in both the stable and transient phases. In particular, the overshoot, settling time, and final tracking error of the robotic system can be all adjusted by properly setting the parameters in the error transformation function. The radial basis function neural network (RBFNN) is used to compensate the complicated nonlinear terms in the closed-loop dynamics of the robotic system. The approximation error of the RBFNN is only required to be bounded, which simplifies the initial "trail-and-error" configuration of the neural network. Illustrative examples are given to verify the theoretical analysis and illustrate the effectiveness of the proposed algorithm. Finally, it is also shown that the proposed approximation-based controller can be simplified by a smart mechanical design of the closed-chain robot, which demonstrates the promise of the integrated design and control philosophy.     

Robust Tracking Control of Helicopters Using Backstepping with Disturbance Observers

This paper addresses the robust and accurate trajectory tracking problem for unmanned helicopters in the presence of model uncertainties and external disturbances. First, the helicopter's model is simplified to a six‐degrees‐of‐freedom rigid body augmented with a simplified rotor dynamic model, with the model uncertainties and the external disturbances being treated as lumped unknown disturbances. Second, a nonlinear disturbance observer is designed to estimate this lumped disturbance. Then, a backstepping controller with disturbance compensation is designed to ensure robust and highly trajectory tracking. After that, the theoretical analysis of the efficiency of the designed disturbance observer‐based backstepping controller (Backstepping+DO) is shown by the Lyapunov theory. Finally, simulation results and conclusions are presented and discussed.     

State Space Constrained Iterative Learning Control for Robotic Manipulators

Real‐life work operations of industrial robotic manipulators are performed within a constrained state space. Such operations most often require accurate planning and tracking a desired trajectory, where all the characteristics of the dynamic model are taken into consideration. This paper presents a general method and an efficient computational procedure for path planning with respect to state space constraints. Given a dynamic model of a robotic manipulator, the proposed solution takes into consideration the influence of all imprecisely measured model parameters, making use of iterative learning control (ILC). A major advantage of this solution is that it resolves the well‐known problem of interrupting the learning procedure due to a high transient tracking error or when the desired trajectory is planned closely to the state space boundaries. The numerical procedure elaborated here computes the robot arm motion to accurately track a desired trajectory in a constrained state space taking into consideration all the dynamic characteristics that influence the motion. Simulation results with a typical industrial robot arm demonstrate the robustness of the numerical procedure. In particular, the results extend the applicability of ILC in robot motion control and provide a means for improving the overall trajectory tracking performance of most robotic systems.     

An Adaptive Neural Sliding Mode Controller for MIMO Systems

Here, a novel adaptive neural sliding mode controller (ANSMC) is proposed to handle the coupling and dynamic uncertainty of MIMO systems. The structure of this model-free new controller is based on a radial basis function neural network (RBFNN) which is derived from Lyapunov stability theory and relaxing Kalman–Yacubovich lemma to monitor the system for tracking a user-defined reference model. The weights of RBFNN can be initialized at zero, then, a novel online tuning algorithm is developed based on Lyapunov stability theory. A boundary layer function is introduced into the updating law to cover the parameter errors and modeling errors, and to guarantee the state errors converge into a specified error bound. An e-modification is added into the updating law to release the assumption of persistent excitation and obtain the appropriate values of the connecting weights of a RBFNN. To evaluate the control performance of the proposed controller, a two-link robot system is chosen as the simulation case. The numerical simulations results show that this novel controller has very good tracking accuracy, stability and robustness.     

干扰下的无人直升机自适应反步法鲁棒跟踪控制

针对无人直升机干扰下的鲁棒轨迹跟踪问题,设计了一种自适应反步控制方法.鉴于作用在直升机上的干扰是产生跟踪误差的主要原因,该方法的主要思想是寻求一种方法来补偿这种干扰.首先,将未建模动态如外部阵风干扰、配平误差、机身、垂尾、平尾以及其他可忽略的动态产生的力和力矩看成一种组合干扰,从而建立了一个方便反步法控制器设计的简化模型.当设计好反步法控制器后,设计了一个非线性自适应律来估计这种组合干扰,并通过将干扰估计值整合到反步控制器中,使得闭环跟踪系统的鲁棒稳定性得到了保证,即基于李雅普诺夫稳定性理论证明了所设的控制器对于干扰主动阻隔,特别是低频干扰的主动阻隔是有效的.最后,两个仿真研究验证了该方法是优于常规反步法和积分反步法的.     

Fixed‐time adaptive sliding mode trajectory tracking control of uncertain mechanical systems

An adaptive fixed‐time trajectory tracking controller is proposed for uncertain mechanical systems in this study. The polynomial reference trajectory is planned for trajectory tracking error. Fractional power of linear sliding mode is applied to design the nonlinear controller, adaptive laws are used to adjust controller parameters. Trajectory planning and fractional power are combined to ensure the tracking‐error convergence in a fixed time. The boundary layer technique is used to suppress the model uncertainties and decrease the chattering phenomenon. The closed‐loop system stability is proved strictly in the Lyapunov framework to show that the trajectory tracking errors and adaptive parameters tend to zero in a fixed time set in advance. Numerical simulation results of robotic manipulators illustrate the effectiveness of the proposed controller.     

Motion Control of a Nonholonomic Mobile Manipulator in Task Space

In this paper, the motion control of a mobile manipulator subjected to nonholonomic constraints is investigated. The control objective is to design a computed‐torque controller based on the coupled dynamics of the mobile manipulator. The proposed controller achieves the capability of simultaneous tracking of a reference velocity for the mobile base and a reference trajectory for the end‐effector. The aforementioned reference velocity and trajectory are defined in the task space, such task setting imitates the actual working conditions of a mobile manipulator and thus makes the control problem practical. To solve this tracking problem, a steering velocity is firstly designed based on the first‐order kinematic model of the nonholonomic mobile base via dynamic feedback linearization. The main merit of the proposed steering velocity design is that it directly utilizes the reference velocity set in the task space without requiring the knowledge of a reference orientation. A torque controller is subsequently developed based on a proposed Lyapunov function which explicitly considers the coupled dynamics of the mobile manipulator to ensure the mobile base and end‐effector track the reference velocity and trajectory respectively. This proposed computed‐torque controller is able to realize asymptotic stability of both the base velocity tracking error and the end‐effector motion tracking error. Simulations are conducted to demonstrate the effectiveness of the proposed controller.     

Spatial Trajectory Tracking Control of a Fully Actuated Helicopter in Known Static Environment

In this paper, we consider the control problem of tracking a 3D spatial trajectory for a fully actuated helicopter in static known environment, which is predefined to avoid obstacles and collisions considering the distance, fuel consumption and other related constraints. For this purpose, a nonlinear controller using the radial basis function neural network (RBFNN) is designed. Based on Lyapunov analysis, the proposed adaptive neural network control succeeds in tracking the desired trajectory robustly to a small neighborhood of zero, and guarantees the boundedness of all the closed-loop signals at the same time. Extensive numerical results are given to illustrate the effectiveness of the designed controller.     

Robust adaptive fuzzy sliding mode trajectory tracking control for serial robotic manipulators

The ever increasingly stringent performance requirements of industrial robotic applications highlight significant importance of advanced robust control designs for serial robots that are generally subject to various uncertainties and external disturbances. Therefore, this paper proposes and investigates the design and implementation of a robust adaptive fuzzy sliding mode controller in the task space for uncertain serial robotic manipulators. The sliding mode control is well known for its robustness to system parameter variations and external disturbances, and is thus a highly desirable and cost-effective approach to achieve high precision control task for serial robots. The proposed controller is designed based on a fuzzy logic approximation to accomplish trajectory tracking with high accuracy and simultaneously attenuate effects from uncertainties. In the controller, the high-frequency uncertain term is approximated by using a fuzzy logic system while the low-frequency term is adaptively updated in real time based on a parametric adaption law. The control efficacy and effectiveness of the proposed control algorithm are comparatively verified against a recently proposed conventional controller. The test results demonstrate that the proposed controller has better trajectory tracking performances and is more robust against large disturbances than the conventional controller under the same operating conditions.     

基于不确定逼近的机械手自适应鲁棒预测控制

针对具有参数不确定性和未知外部干扰的机械手轨迹跟踪问题提出了一种多输入多输出自适应鲁棒预测控制方法. 首先根据机械手模型设计非线性鲁棒预测控制律, 并在控制律中引入监督控制项; 然后利用函数逼近的方法逼近控制律中因模型不确定性以及外部干扰引起的未知项. 理论证明了所设计的控制律能够使机械手无静差跟踪期望的关节角轨迹. 仿真验证了本文设计方法的有效性.     

An Evolutionary Radial Basis Function Neural Network with Robust Genetic-Based Immunecomputing for Online Tracking Control of Autonomous Robots

This paper presents an evolutionary radial basis function neural network with genetic algorithm and artificial immune system (GAAIS-RBFNN) for tracking control of autonomous robots. Both the GAAIS-RBFNN computational intelligence and online tracking controller are implemented in one field-programmable gate array (FPGA) chip to cope with the optimal control problem of real-world mobile robotics. The hybrid GAAIS paradigm incorporated with Taguchi quality method is employed to determine the optimal structure of RBFNN. The control parameters of tracking controller are online tuned by minimizing the performance index using the proposed GAAIS-RBFNN to achieve trajectory tracking. Experimental results and comparative works are conducted to show the effectiveness and merit of the proposed FPGA-based GAAIS-RBFNN tracking controller using system-on-a-programmable-chip technology. This FPGA-based online hybrid GAAIS-RBFNN intelligent controller outperforms the existing bio-inspired RBFNN controllers using individual GA and AIS algorithms.     

Sliding mode-based adaptive tube model predictive control for robotic manipulators with model uncertainty and state constraints

In this paper, the optimal tracking control for robotic manipulatorswith state constraints and uncertain dynamics is investigated, and a sliding mode-based adaptive tube model predictive control method is proposed. First, utilizing the high-order fully actuated system approach, the nominal model of the robotic manipulator is constructed as the predictive model. Based on the nominal model, a nominal model predictive controller with the sliding mode is designed, which relaxes the terminal constraints, and realizes the accurate and stable tracking of the desired trajectory by the nominal system. Then, an auxiliary controller based on the node-adaptive neural networks is constructed to dynamically compensate nonlinear uncertain dynamics of the robotic manipulator. Furthermore, the estimation deviation between the nominal and actual states is limited to the tube invariant sets. At the same time, the recursive feasibility of nominal model predictive control is verified, and the ultimately uniformly boundedness of all variables is proved according to the Lyapunov theorem. Finally, experiments show that the robotic manipulator can achieve fast and efficient trajectory tracking under the action of the proposed method.     

System identification and improved internal model control for yaw of unmanned helicopter

The sea breeze is a low-frequency disturbance that severely damages the stability of small unmanned helicopters operating over the sea, especially for the yaw control, which is highly sensitive to disturbance. General internal model control is an appropriate method for dealing with this kind of operation conditions, whereas conventional internal model control cannot eliminate the tracking errors between a nominal model and a real model. In coping with unknown dynamics and low-frequency gust disturbances for small helicopters, this paper proposes a novel robust controller constructed with system identification and integrator-based improved general internal model. As a refinement of the conventional frame, the proposed control scheme extends the applicable scope of a controlled plant from a priori known dynamic to an unknown dynamic. Furthermore, under the proposed controller, it is guaranteed that the tracking error between the actual model and the nominal model converges to zero asymptotically. Finally, the effectiveness and advantage of the proposed control scheme are verified through comparative practical flight tests.     

基于径向基函数神经网络的机器人滑模控制

尽管滑模控制响应快,对系统参数和外部扰动呈不变性,但在保证系统的渐进稳定性上却存在很强的抖动缺点.因此,在一般滑模控制的基础上,引入了径向基函数神经网络(RBFNN).利用滑模控制的特点设定目标函数,将切换函数作为RBFNN的输入,滑模控制量作为其输出.利用RBF神经网络的在线学习功能,消除了控制的抖动,同时使系统具有很强的鲁棒性.对两连杆机械手进行了仿真研究,其结果表明,在存在模型误差和外部扰动的情况下,该方案既能达到高精度快速跟踪的目的,又能消除滑模控制的抖动问题.     

Recursive Direct Learning of Control Efforts for Trajectories with Different Magnitude Scales

Direct learning control (DLC) schemes have been developed recently to address non‐repeatable trajectory tracking problems. Unlike conventional iterative learning schemes, DLC schemes learn a set of unknown basis function vectors which can be used to generate the desired control profile of a new trajectory. DLC schemes use all available trajectory tracking information to obtain the unknown basis function vectors in a Least Squares and pointwise manner. A drawback of DLC is that the inverse matrix calculation is inevitable, which is time consuming and may result in singularities due to the batch processing nature. A Recursive Direct Learning Control method is proposed which learns the basis function vectors meanwhile overcomes the implementation difficulties in DLC schemes. The focus of this paper is on learning the control profile of trajectories with same operation period but different magnitude scales. The recursive learning method makes use of one trajectory information at a time, thus avoids the batch processing. The scheme is first developed for a class of nonlinear time varying systems and then extended to cover more general classes of nonlinear systems including robotic manipulator dynamics. Extensive simulation results on a two‐link robotic model are provided to confirm the features of the proposed algorithm.     

Robust control of 3-DOF parallel robot driven by PMAs based on nominal stiffness model

This paper deals with an efficient implementation of robust controller on 3-DOF parallel robot driven by pneumatic muscle actuators (PMAs). PMA is a new flexible pneumatic actuator with relatively complex mathematical model. For the purpose of controlling robot, a new method to establish mathematical model of PMA is proposed. Based on analysis of stiffness characteristics of PMA, the concept of nominal stiffness coefficient is put forward and applied to establishment of mathematical model of PMA. According to 3-DOF robotic decoupling property, two rotational freedom of X, Y-axis are controlled by robust controller. Based on the dynamics, trajectory tracking control in simulation performs well under the circumstances of different interference via robust controller. Experimental results show that robust controller has satisfactory tracking performance and the characteristic of high real time. Its maximum tracking errors around X–Y axis are not more than 0.4°. Due to its less interference in motion around Z-axis, controlling Z-axis also has good tracking performance via computed torque method.     

Model‐assisted extended state observer and dynamic surface control–based trajectory tracking for quadrotors via output‐feedback mechanism

In this paper, an output‐feedback trajectory tracking controller for quadrotors is presented by integrating a model‐assisted extended state observer (ESO) with dynamic surface control. The quadrotor dynamics are described by translational and rotational loops with lumped disturbances to promote the hierarchical control design. Then, by exploiting the structural property of the quadrotor, a model information–assisted high‐order ESO that relies only on position measurements is designed to estimate not only the unmeasurable states but also the lumped disturbances in the rotational loop. In addition, to account for the problem of “explosion of complexity” inherent in hierarchical control, the output feedback–based trajectory tracking and attitude stabilization laws are respectively synthesized by utilizing dynamic surface control and the corresponding estimated signals provided by the ESO. The stability analysis is given, showing that the output‐feedback trajectory tracking controller can ensure the ultimate boundedness of all signals in the closed‐loop system and make the tracking errors arbitrarily small. Finally, flight simulations with respect to an 8‐shaped trajectory command are performed to verify the effectiveness of the proposed scheme in obtaining the stable and accurate trajectory tracking using position measurements only.