Finite‐time geometric control for underactuated aerial manipulators with unknown disturbances

In this article, the finite‐time geometric control for underactuated aerial manipulators is investigated. The dynamics of the aerial manipulator with unknown disturbances is analyzed first. The dynamics of the system is decomposed into the locked subsystem and shape subsystem. The finite‐time controller for the aerial manipulator is then designed based on the analyzed dynamics. In the controller, the attitude tracking error of the aircraft base is expressed from the rotation matrix, which makes the controller continuous and almost globally stable on SO(3). A continuous adaptive term is added in the controller to compensate for the unknown disturbances. Finite‐time filters are designed to ensure the smoothness of the commands on each loop. The convergence of the entire controlled system is strictly proved using Lyapunov theory and the definition of finite‐time stability. The results show that the tracking error and the disturbance bound estimation error of the entire system are finite‐time bounded near origin. Finally, comparative simulation results are presented to show the performance of the proposed controller.     

Command-filtered sensor-based backstepping controller for small unmanned aerial vehicles with actuator dynamics

In this study, a command-filtered sensor-based backstepping controller is proposed for small unmanned aerial vehicles (UAVs) with actuator dynamics. The command filter is introduced to prompt the virtual control law to be limited in a certain range and the corresponding state to subsequently be restricted to a certain area. When using the sensor-based backstepping recursive method, precise models of the UAVs are not required because the controller is not sensitive to the external disturbance. The actuator dynamics are compensated without prior knowledge of the mathematical model of the executing agency. Besides, a robust compensator is developed for the virtual control law of the first subsystem of the UAV, which shows strong robustness against the uncertainties of the aerodynamic coefficients and external disturbances. Moreover, the closed-loop system is proven stable in the sense that the signals are bounded. A numerical simulation is carried out to verify the effectiveness of the developed controller.     

Robust attitude control for tail‐sitter unmanned aerial vehicles in flight mode transitions

Tail‐sitter unmanned aerial vehicles (UAVs) can flight as rotorcrafts as well as fixed‐wing aircrafts, but it is hard to control the flight mode transition. The vehicle dynamics involves serious parametric uncertainties, highly nonlinear dynamics, and is easy to be affected by external disturbances, especially during the mode transition. This paper presents a robust control method for a kind of tail‐sitter UAVs to achieve the flight mode transition. The robust controller is proposed based on the state‐feedback control scheme and the robust compensation method. The proposed control method does not need to switch the coordinate system, the controller structure, or the controller parameters during the mode transitions. Theoretical analysis is given to guarantee the robustness stability of the designed flight control system. Numerical simulation results are presented to show the advantages of the proposed control method compared with the state‐feedback control method and the sliding mode control approach.     

悬挂伸缩刀具的树障清理空中机器人飞行控制方法

针对输电线路附近的树障进行清理问题,本文提出了一种新型的悬挂伸缩刀具的树障清理空中机器人并进行了仿真和实物验证.首先,对悬挂伸缩刀具的空中机器人进行了伸缩刀具重心变化下的动力学、运动学建模及接触建模.其次,为避免空中机器人接触作业时机器人倾翻的问题,设计了力估计器用于力感知和导纳控制器用于力控制.针对空中机器人非线性强耦合、伸缩刀具时参数摄动及作业时扰动的问题,设计了线性自抗扰控制(LADRC)的机器人位姿控制器.再次,数值仿真验证了导纳控制能有效避免空中机器人接触作业时产生倾翻的问题,以及基于LADRC控制器的位姿控制具有良好的稳定性和抗扰性.最后,通过实物飞行和接触作业测试,进一步验证了本文悬挂伸缩刀具的树障清理空中机器人及其控制方法的有效性.     

Active torque-based gait adjustment multi-level control strategy for lower limb patient–exoskeleton coupling system in rehabilitation training

This paper proposes an active torque-based gait adjustment multi-level control strategy for lower limb patient–exoskeleton coupling system (LLPECS) in rehabilitation training. The proposed controller has three levels of high, middle, and low sub-controllers: gait adjustment layer (high-level), interaction torque design layer (middle-level), and trajectory tracking layer (low-level). The high-level sub-controller uses an adaptive central pattern generator (ACPG) to adjust the desired gait for rehabilitation training according to the patient’s active torque. In the middle-level sub-controller, the desired interaction torque is designed with neural networks and the estimated muscle torque by utilizing nonlinear disturbance observer (NDO). In the low-level sub-controller, a time delay estimation-based prescribed performance model free control is designed for the accurate tracking performance of the exoskeleton, so as to make the actual interaction torque track the desired value. An exoskeleton virtual prototype, which is developed in SolidWorks, has been imported to MATLAB/Simulink to conduct co-simulations in the SimMechanics environment. The results of co-simulations demonstrate the effectiveness of the proposed control strategy when the patient’s muscle torque is at different recovery degrees.     

Decentralized overlapping control of a formation of unmanned aerial vehicles

Decentralized overlapping feedback laws are designed for a formation of unmanned aerial vehicles. The dynamic model of the formation with an information structure constraint in which each vehicle, except the leader, only detects the vehicle directly in front of it, is treated as an interconnected system with overlapping subsystems. Using the mathematical framework of the inclusion principle, the interconnected system is expanded into a higher dimensional space in which the subsystems appear to be disjoint. Then, at each subsystem, a static state feedback controller is designed to robustly stabilize the perturbed nominal dynamics of the subsystem. The design procedure is based on the application of convex optimization tools involving linear matrix inequalities. As a final step, the decentralized controllers are contracted back to the original interconnected system for implementation.     

Zero dynamics stabilisation and adaptive trajectory tracking for WIP vehicles through feedback linearisation and LQR technique

This paper presents a composite control strategy integrating adaptive sliding-mode control and the linear quadratic regulator (LQR) technology for a wheeled inverted pendulum (WIP) vehicle system. The system can be partitioned into an actuated rotational subsystem and an underactuated longitudinal subsystem based on the different control input in the mathematical model. In particular, the instability analysis of zero dynamic for the underactuated longitudinal subsystem is investigated in detail using the feedback linearisation technology. Then, an adaptive sliding-mode control is designed for the trajectory tracking, where an adaptive algorithm is developed to handle with the parameter uncertainties. In addition, the LQR technique is employed to guarantee zero dynamics stability so as to achieve simultaneously the vehicle body stabilisation at the upright position. Simulation results show the good performance and strong robustness of the proposed control schemes.     

Adaptive dynamic programming-based adaptive-gain sliding mode tracking control for fixed-wing unmanned aerial vehicle with disturbances

This article proposes an adaptive dynamic programming-based adaptive-gain sliding mode control (ADP-ASMC) scheme for a fixed-wing unmanned aerial vehicle (UAV) with matched and unmatched disturbances. Starting from the dynamic of fixed-wing UAV, the control-oriented model composed of attitude subsystem and airspeed subsystem is established. According to the different issues in two subsystems, two novel adaptive-gain generalized super-twisting (AGST) algorithms are developed to eliminate the effects of disturbances in two subsystems and make the system trajectories tend to the designed integral sliding manifolds in finite time. Then, based on the expected equivalent sliding-mode dynamics, the modified adaptive dynamic programming approach with actor-critic structure is utilized to generate the nearly optimal control laws and achieve the nearly optimal performance of the sliding-mode dynamics. Furthermore, through the Lyapunov stability theorem, the tracking errors and the weight estimation errors of two neural networks are all uniformly ultimately bounded. Finally, comparative simulations demonstrate the superior performance of the proposed control scheme for the fixed-wing UAV.     

Nonlinear control with integral sliding properties for circular aerial robot trajectory tracking: Real‐time validation

A nonlinear control algorithm for tracking dynamic trajectories using an aerial vehicle is developed in this work. The control structure is designed using a sliding mode methodology, which contains integral sliding properties. The stability analysis of the closed‐loop system is proved using the Lyapunov formalism, ensuring convergence in a desired finite time and robustness toward unknown and external perturbations from the first time instant, even for high frequency disturbances. In addition, a dynamic trajectory is constructed with the translational dynamics of an aerial robot for autonomous take‐off, surveillance missions, and landing. This trajectory respects the constraints imposed by the vehicle characteristics, allowing free initial trajectory conditions. Simulation results demonstrate the good performance of the controller in closed‐loop system when a quadrotor follows the designed trajectory. In addition, flight tests are developed to validate the trajectory and the controller behavior in real time.     

Towards a Smooth Human–Robot Interaction for Rehabilitation Robotic Systems

The goal of this work is to develop a control framework to provide assistance to the subjects in such a manner that the interaction between the subjects and a robot-assisted rehabilitation system is smooth during the rehabilitation therapy. In order to achieve smoothness of interaction, a control framework is designed in such a way that it can automatically adjust the control gains of the robot-assisted rehabilitation system to modify the interaction dynamics between the system and the subject. An artificial neural network (ANN)-based proportional–integral (PI) gain scheduling controller is proposed to automatically determine the appropriate control gains for each individual subject. The human arm model is integrated with the ANN-based PI gain scheduling controller where the ANN uses estimated human arm parameters to select the appropriate PI gains for each subject such that the resultant interaction dynamics between the subject and the robot-assisted rehabilitation system could result in smooth interaction. Experimental results involving unimpaired subjects on a PUMA robot-based rehabilitation system are presented to demonstrate the efficacy of the proposed ANN-based PI gain scheduling controller on unimpaired subjects.     

A hierarchical controller for miniature VTOL UAVs: Design and stability analysis using singular perturbation theory

This paper presents the design and the stability analysis of a hierarchical controller for unmanned aerial vehicles (UAV), using singular perturbation theory. Position and attitude control laws are successively designed by considering a time-scale separation between the translational dynamics and the orientation dynamics of a six degrees of freedom vertical take-off and landing (VTOL) UAV model. For the design of the position controller, we consider the case where the linear velocity of the vehicle is not measured. A partial state feedback control law is proposed, based on the introduction of a virtual state into the translational dynamics of the system. Results from simulation and from experiments on a miniature quadrirotor UAV are provided to illustrate the performance of the proposed control scheme.     

Projection operator-based robust adaptive control of an aerial robot with a manipulator

This paper describes a quadcopter manipulator system, an aerial robot with an extended workspace, its controller design, and experimental validation. The aerial robot is based on a quadcopter with a three degree of freedom robotic arm connected to the base of the vehicle. The work aims to create a stable airborne robot with a robotic arm that can work above and below the airframe, regardless of where the arm is attached. Integrating a robotic arm into an underactuated, unstable system like a quadcopter can enhance the vehicle's functionality while increasing instability. To execute a mission with accuracy and reliability during a real-time task, the system must overcome the inter-coupling effects and external disturbances. This work presents a novel design for a robust adaptive feedback linearization controller with a model reference adaptive controller and hardware implementation of the quadcopter manipulator system with plant uncertainties. The closed-loop stability of the aerial robot and the tracking error convergence with the robust controller is analyzed using Lyapunov stability analysis. The quadcopter manipulator system is custom developed in the lab with an off-the-shelf quadcopter and a 3D-printed robotic arm. The robotic system architecture is implemented using a Jetson Nano companion computer for autonomous onboard flight. Experiments were conducted on quadcopter manipulator system to evaluate the autonomous aerial robot's stability and trajectory tracking with the proposed controller.     

Robust Tracking Control For A Wheeled Mobile Manipulator With Dual Arms Using Hybrid Sliding‐Mode Neural Network

In this paper, a robust tracking controller is proposed for the trajectory tracking problem of a dual‐arm wheeled mobile manipulator subject to some modeling uncertainties and external disturbances. Based on backstepping techniques, the design procedure is divided into two levels. In the kinematic level, the auxiliary velocity commands for each subsystem are first presented. A sliding‐mode equivalent controller, composed of neural network control, robust scheme and proportional control, is constructed in the dynamic level to deal with the dynamic effect. To deal with inadequate modeling and parameter uncertainties, the neural network controller is used to mimic the sliding‐mode equivalent control law; the robust controller is designed to compensate for the approximation error and to incorporate the system dynamics into the sliding manifold. The proportional controller is added to improve the system's transient performance, which may be degraded by the neural network's random initialization. All the parameter adjustment rules for the proposed controller are derived from the Lyapunov stability theory and e‐modification such that uniform ultimate boundedness (UUB) can be assured. A comparative simulation study with different controllers is included to illustrate the effectiveness of the proposed method.     

无人驾驶飞行器姿态的非线性扰动抑制控制

本文研究了无人驾驶飞行器(unmanned aerial vehicle,UAV)的姿态跟踪控制问题.针对在飞行器姿态跟踪时存在的系统模型不确定性和外界扰动,提出了一种基于四元数的姿态跟踪控制方法,基于UAV的姿态误差模型分别设计系统的观测器和控制器.首先,以四元数为姿态参数建立系统的非线性误差模型;在此基础之上,设计一种非线性干扰观测器(nonlinear disturbance observer,NDOB)用以在线估计误差模型中的复合扰动,并在控制输入端进行相应的补偿.然后通过设计非线性广义预测控制律设镇定误差系统,实现姿态跟踪.最后基于频域理论分析了非线性干扰观测器的扰动抑制性能.仿真与实验结果表明本文提出的方法在系统存在复合扰动的情况下能使系统姿态有效的跟踪期望值.     

Nonlinear robust adaptive sliding mode control design for miniature unmanned multirotor aerial vehicle

This paper addresses the stability and tracking control problem of miniature unmanned multirotor aerial vehicle (MUMAV) in the presence of bounded uncertainty. The uncertainty may appear from unmodeled dynamics, underactuated property, input disturbance and flying environment. Nonlinear robust adaptive sliding mode control algorithm is designed by using Lyapunov function. Robust adaptation laws are designed to learn and compensate the bounded parametric uncertainty. Lyapunov analysis shows that the proposed algorithms can guarantee asymptotic stability and tracking control property of the linear and angular dynamics of MUMAV system. Compared with other existing control methods, the proposed design is very simple and easy to implement as it does not require multiple design steps, augmented auxiliary signals and exact bound of the uncertainty. Experimental results on a miniature unmanned quadrotor aerial vehicle are presented to illustrate of effectiveness of the proposed design for real-time applications.     

Adaptive discrete-time controller design with neural network for hypersonic flight vehicle via back-stepping

In this article, the adaptive neural controller in discrete time is investigated for the longitudinal dynamics of a generic hypersonic flight vehicle. The dynamics are decomposed into the altitude subsystem and the velocity subsystem. The altitude subsystem is transformed into the strict-feedback form from which the discrete-time model is derived by the first-order Taylor expansion. The virtual control is designed with nominal feedback and neural network (NN) approximation via back-stepping. Meanwhile, one adaptive NN controller is designed for the velocity subsystem. To avoid the circular construction problem in the practical control, the design of coefficients adopts the upper bound instead of the nominal value. Under the proposed controller, the semiglobal uniform ultimate boundedness stability is guaranteed. The square and step responses are presented in the simulation studies to show the effectiveness of the proposed control approach.     

Robust Control of a Two-Link Flexible Manipulator with Quasi-Static Deflection Compensation Using Neural Networks

A robust control method of a two-link flexible manipulator with neural networks based quasi-static distortion compensation is proposed and experimentally investigated. The dynamics equation of the flexible manipulator is divided into a slow subsystem and a fast subsystem based on the assumed mode method and singular perturbation theory. A decomposition based robust controller is proposed with respect to the slow subsystem, and H ^∞ control is applied to the fast subsystem. The overall closed-loop control is determined by the composite algorithm that combines the two control laws. Furthermore, a neural network compensation scheme is also integrated into the control system to compensate for quasi-static deflection. The proposed control method has been implemented on a two-link flexible manipulator for precise end-tip tracking control. Experimental results are presented in this paper along with concluding remarks.     

Fixed-time backstepping distributed cooperative control for multiple unmanned aerial vehicles

This paper proposes a fixed-time backstepping distributed cooperative control scheme based on fixed-time extended state observer (FxTESO) for multiple unmanned aerial vehicles (UAVs). A fixed-time ESO, which is convergent independently of initial conditions, is designed to estimate and compensate the external disturbances in tracking process. Moreover, to eliminate the “explosion of complexity” in the traditional backstepping architecture, a nonlinear first-order filter is adopted to construct the distributed fixed-time control scheme. Based on the local information of neighboring UAVs, a fixed-time backstepping cooperative controller is designed. The proposed formation algorithm can be shown practicable for the UAV control system by using of Lyapunov stability theory and graph theory. Simulation results are given to demonstrate the effectiveness of the proposed control scheme.     

基于神经滑模的柔性连杆机械手末端位置控制

：为了提高柔性机械手末端位置控制的鲁棒性和精度,提出了一种基于神经滑模的控制策略．首先采 用输入/输出线性化方法将动力学模型部分线性化,使之分成输入/输出子系统与内动态子系统．输入/输出子系统 采用神经滑模控制,内动态子系统采用状态反馈控制器镇定．随后,对控制系统内动态稳定性进行了分析,并在 两自由度柔性连杆机械手控制的仿真试验中得到了满意的结果．试验结果表明,在存在模型不确定性时,该控制 策略提高了控制系统的鲁棒性和控制精度．     

Decentralized adaptive fuzzy sliding mode control for reconfigurable modular manipulators

A stable decentralized adaptive fuzzy sliding mode control scheme is proposed for reconfigurable modular manipulators to satisfy the concept of modular software. For the development of the decentralized control, the dynamics of reconfigurable modular manipulators is represented as a set of interconnected subsystems. A first‐order Takagi–Sugeno fuzzy logic system is introduced to approximate the unknown dynamics of subsystem by using adaptive algorithm. The effect of interconnection term and fuzzy approximation error is removed by employing an adaptive sliding mode controller. All adaptive algorithms in the subsystem controller are derived from the sense of Lyapunov stability analysis, so that resulting closed‐loop system is stable and the trajectory tracking performance is guaranteed. The simulation results are presented to show the effectiveness of the proposed decentralized control scheme. Copyright © 2009 John Wiley & Sons, Ltd.