基于干扰观测器的机械臂广义模型预测轨迹跟踪控制

为实现对多自由度机械臂关节运动精确轨迹跟踪,提出一种基于非线性干扰观测器的广义模型预测轨迹跟踪控制方法。针对机械臂轨迹跟踪运动学子系统,采用广义预测控制（Generalized Predictive Control,GPC）方法设计期望的虚拟关节角速度。对于机械臂轨迹跟踪动力学子系统,考虑机械臂的参数不确定性和未知外界扰动,利用GPC方法设计关节力矩控制输入,基于非线性干扰观测器方法实时估计和补偿系统模型中的不确定性。在李雅普诺夫稳定性理论框架下证明了机械臂关节角位置和角速度的跟踪误差最终收敛于零的小邻域。数值仿真验证了所提出控制方法的有效性和优越性。     

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.     

空间机器人最优能耗捕获目标的自适应跟踪控制

提出了一种能够引导末端执行器以期望速度跟踪目标的轨迹规划方法。该方法可以实现避障并满足关节限制要求。基于轨迹规划方法,设计了一种利用自由飘浮空间机器人跟踪与捕获章动自旋卫星的自适应控制策略。此外,该控制策略还考虑了最优能耗、测量误差和优化误差。首先,为了使执行器的跟踪误差和机械臂的能耗最小,将空间机器人的控制策略描述为一个关于关节速度、力矩和避障距离的不等式约束优化问题。然后,推导出一个系数为下三角矩阵的显式状态方程,并对目标函数进行解耦和线性化。设计了一种关节速度和力矩分段优化方法去代替传统的凸二次规划方法求解最优问题,这种方法具有较高的计算效率。最后,利用李雅普诺夫稳定性理论验证了所提控制方法的收敛性。     

Learning Control of Robot Manipulators in Task Space

Two important properties of industrial tasks performed by robot manipulators, namely, periodicity (i.e., repetitive nature) of the task and the need for the task to be performed by the end‐effector, motivated this work. Not being able to utilize the robot manipulator dynamics due to uncertainties complicated the control design. In a seemingly novel departure from the existing works in the literature, the tracking problem is formulated in the task space and the control input torque is aimed to decrease the task space tracking error directly without making use of inverse kinematics at the position level. A repetitive learning controller is designed which “learns” the overall uncertainties in the robot manipulator dynamics. The stability of the closed‐loop system and asymptotic end‐effector tracking of a periodic desired trajectory are guaranteed via Lyapunov based analysis methods. Experiments performed on an in‐house developed robot manipulator are presented to illustrate the performance and viability of the proposed controller.     

Backstepping control of flexible joint manipulator based on hyperbolic tangent function with control input and rate constraints

In this paper, we investigate the trajectory tracking problems of the link angle and angle speed of the flexible joint manipulator model based on external disturbance, the control input and rate constraints. The controller of the flexible joint manipulator model is designed using the backstepping control scheme. To achieve this objective, the smooth hyperbolic tangent function is used to solve the problems of control input and rate constraints, and the stability is proved using Lyapunov function in the design procedure of the backstepping control scheme. Finally, the effectiveness of the proposed backstepping controller is verified by numerical simulation.     

Adaptive neural network output feedback control for flexible multi-link robotic manipulators

In this paper, a novel approach for adaptive control of flexible multi-link robots in the joint space is presented. The approach is valid for a class of highly uncertain systems with arbitrary but bounded dimension. The problem of trajectory tracking is solved through developing a stable inversion for robot dynamics using only joint angles measurement; then a linear dynamic compensator is utilised to stabilise the tracking error for the nominal system. Furthermore, a high gain observer is designed to provide an estimate for error dynamics. A linear in parameter neural network based adaptive signal is used to approximate and eliminate the effect of uncertainties due to link flexibilities and vibration modes on tracking performance, where the adaptation rule for the neural network weights is derived based on Lyapunov function. The stability and the ultimate boundedness of the error signals and closed-loop system is demonstrated through the Lyapunov stability theory. Computer simulations of the proposed robust controller are carried to validate on a two-link flexible planar manipulator.     

考虑关节柔性的绳驱动空中机械臂关节空间鲁棒控制

空中机械臂在外部环境交互作业方面表现出很强的研究和应用价值,但当前系统位姿控制性能较弱、负载能力不足以及续航时间短的问题严重制约其作业能力的提升.鉴于此,设计一种带有绳驱动机械臂的新型空中机械臂系统,并将引入绳驱动机制带来的柔性效应等价到关节处,建立考虑关节柔性的刚柔耦合动力学模型.首先,针对系统在集总干扰下的关节空间轨迹跟踪控制,采用线性扩张状态观测器对集总干扰进行估计和补偿,并采用超螺旋算子和分数阶非奇异终端滑模以保证系统在到达阶段和滑模阶段均有较好的控制性能;然后,在Lyapunov稳定性框架下验证所设计控制器的稳定性;最后,通过可视化仿真和地面实验对所设计控制器的有效性进行验证.实验结果表明,所设计的鲁棒控制器比其他两种现有的控制器具有更快的响应速度、更强的抗干扰能力以及更高的跟踪精度,能够满足绳驱动空中机械臂的控制需求.     

Intelligent tracking control for robot manipulator including actuator dynamics via TSK-type fuzzy neural network

In this paper, a Takagi-Sugeno-Kang-type fuzzy-neural-network control (T-FNNC) scheme is constructed for an n-link robot manipulator to achieve high-precision position tracking. According to the concepts of mechanical geometry and motion dynamics, the dynamic model of an n-link robot manipulator including actuator dynamics is introduced initially. However, it is difficult to design a suitable model-based control scheme due to the uncertainties in practical applications, such as friction forces, external disturbances and parameter variations. In order to cope with this problem, a T-FNNC system without the requirement of prior system information and auxiliary control design is investigated to the joint position control of an n-link robot manipulator for periodic motion. In this model-free control scheme, a five-layer fuzzy-neural-network is utilized for the major control role, and the adaptive tuning laws of network parameters are established in the sense of projection algorithm and Lyapunov stability theorem to ensure the network convergence as well as stable control performance. In addition, experimental results of a two-link robot manipulator actuated by dc servomotors are provided to verify the effectiveness and robustness of the proposed T-FNNC methodology.     

基于PMSM驱动的柔性关节空间机械臂轨迹跟踪控制方法

针对目前柔性关节空间机械臂轨迹跟踪控制方法忽略了不同重力影响下的机械臂驱动力变化,导致柔性关节空间机械臂轨迹跟踪控制效果较差的问题,提出了基于PMSM驱动的柔性关节空间机械臂轨迹跟踪控制方法。基于构建PMSM驱动数学模型,采用PMSM的矢量控制方法,分析驱动力矩矢量。根据驱动力矩矢量分析结果,分析不同重力环境下有、无摩擦时的驱动力矩。构建柔性关节模型,分析其在不同重力环境下遇到的重力释放问题,使用自适应反演滑膜控制方法,设计控制率,保证机械臂能够按照既定的方向运动,使机械臂具有鲁棒性。根据柔性关节空间机械臂动力学特性,分析不同重力环境下基于PMSM驱动力矩,确定重力项是随之发生改变的。设计控制器,构建动力学模型,确保空间阶段能够最大限度跟踪运动轨迹。实验结果表明,所提方法X轴、Y轴的末端跟踪结果均与实际运动轨迹一致,误差为0。关节控制力矩在时间为3s时,出现了最大为0.5N.m的误差,说明所提方法的跟踪控制效果较好。     

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.     

Mutual Synchronization of Multiple Robot Manipulators with Unknown Dynamics

In this paper, we investigate the mutual synchronization control problem of multiple robot manipulators in the case that the desired trajectory is only available to a portion of the team members, and the dynamics and the external disturbances of the manipulators are unknown. Treating the weighted average of the outputs of the neighbors as the reference trajectory, an adaptive neural network (NN) tracking control is designed for each manipulator. Based on the Lyapunov analysis, rigid mathematical proof is provided for the proposed algorithm for both state feedback and output feedback cases. It is shown that, under the proposed adaptive NN control, the tracking error of each manipulator converges to an adjustable neighborhood of the origin. Simulations are provided to demonstrate the effectiveness of the proposed approach.     

考虑柔性关节的机械臂自适应运动控制策略研究

具有柔性关节的轻型机械臂因其自重轻、响应迅速、操作灵活等优点,取得了广泛应用;针对具有柔性关节的机械臂系统的关节空间轨迹跟踪控制系统动力学参数不精确的问题,提出一种结合滑模变结构设计的自适应控制器算法;通过自适应控制的思想对系统动力学参数进行在线辨识,并采用Lyapunov方法证明了闭环系统的稳定性;仿真结果表明,该控制策略保证了机械臂系统对期望轨迹的快速跟踪,具有良好的跟踪精度,系统具有稳定性。     

Adaptive backstepping control for an n-degree of freedom robotic manipulator based on combined state augmentation

The aim of this paper is to improve the tracking performance of a robotic manipulator by designing an adaptive controller and implementing it on the system. The proposed controller guarantees the system stability as well as good tracking performance in existence of nonlinearity and parameter uncertainties. The requirement to decrease the system response overshoot and steady state error as well as increasing speed of tracking for manipulators is essential to many manufacturers. To this mean, in this paper, the tracking error equations for an n-DOF manipulator are derived and the response characteristics are improved by augmenting a new state to the system equations. The stability of the closed-loop system is guaranteed based on the Lyapunov theory via backstepping control approach. The robotic manipulator model contains parametric uncertainties and many of the parameter values are unknown. To solve the problem, an adaption law is proposed via adaptive backstepping mechanism. Different experiments are carried out for a 2-DOF manipulator to show the effectiveness of the proposed approach and the results are compared with four of the recently revealed researches on control. Experimental results present the superiority of the state augmented adaptive backstepping in tracking the desired joint angles. Moreover, in order to present the industrial application of the proposed control method, it is simulated for a large industrial Scara manipulator.     

Robust tracking control of a unicycle-type wheeled mobile manipulator using a hybrid sliding mode fuzzy neural network

This article presents a robust tracking controller for an uncertain mobile manipulator system. A rigid robotic arm is mounted on a wheeled mobile platform whose motion is subject to nonholonomic constraints. The sliding mode control (SMC) method is associated with the fuzzy neural network (FNN) to constitute a robust control scheme to cope with three types of system uncertainties; namely, external disturbances, modelling errors, and strong couplings in between the mobile platform and the onboard arm subsystems. All parameter adjustment rules for the proposed controller are derived from the Lyapunov theory such that the tracking error dynamics and the FNN weighting updates are ensured to be stable with uniform ultimate boundedness (UUB).     

并联机器人的非线性 P I D 控制

采用分散控制策略和非线性PID控制算法，实现6自由度并联机器人的商精度轨迹最踪控制。该非线性PID控制器由两个二阶非线性微分最踪器提供高质量的微分信号，并采用非线性组合形成控制作用，从而确保了高控制性能的实现。实验结果验证了非线性控制方案的有效性。     

Adaptive control of free-floating space manipulators using dynamically equivalent manipulator model

In this paper, adaptive control of free-floating space manipulators is considered. The dynamics based on the momentum conservation law for the free-floating space manipulator has non-linear parameterization properties. Therefore, the adaptive control based on a linear parameterization model cannot be used in this dynamics. In this paper, the dynamics of the free-floating space manipulator system are derived using the Dynamically Equivalent Model (DEM) approach. The DEM is a fixed-base manipulator system and allows us to linearly parameterize the dynamic equations. Using this linearly parameterized dynamic equation, an adaptive control method is developed to control the system in joint space. Parameter identification and torque calculations are done using the DEM dynamics. Simulations show that the tracking errors of the manipulator joints to a given desired trajectory become zero when the calculated torques act on the joints of the space manipulator system.     

机械手的神经网络稳定自适应控制

本文针对机械手轨迹跟随控制问题，提出了一种稳定的神经网络自适应控制器设计方法，这里机械的非线性动力学假设是未知的，提出方法是神经网络方法和扇区自适应变结构控制方法的集成，扇区变结构控制的作用有两个，其一是在系统神经网络控制失灵的情形下提供闭环系统的全局稳定性；其二是在神经网络的近似域内改进系统的跟随性能，本文采用李雅普诺夫稳定理论给出了的稳定性和跟随误差收敛性的证明，并且通过数字仿真验证了提出方法     

Robust nonlinear control of a planar 2-DOF parallel manipulator with redundant actuation

A new robust nonlinear controller is presented and applied to a planar 2-DOF parallel manipulator with redundant actuation. The robust nonlinear controller is designed by combining the nonlinear PD (NPD) control with the robust dynamics compensation. The NPD control is used to eliminate the trajectory disturbances, unmodeled dynamics and nonlinear friction, and the robust control is used to restrain the model uncertainties of the parallel manipulator. The proposed controller is proven to guarantee the uniform ultimate boundedness of the closed-loop system by the Lyapunov theory. The trajectory tracking experiment with the robust nonlinear controller is implemented on an actual planar 2-DOF parallel manipulator with redundant actuation. The experimental results are compared with the augmented PD (APD) controller, and the proposed controller shows much better trajectory tracking accuracy.     

Dynamic Modeling and Tracking Control of a Nonholonomic Wheeled Mobile Manipulator with Dual Arms

This paper presents methodologies for dynamic modeling and trajectory tracking of a nonholonomic wheeled mobile manipulator (WMM) with dual arms. The complete dynamic model of such a manipulator is easily established using the Lagrange’s equation and MATHEMATICA. The structural properties of the overall system along with its subsystems are also well investigated and then exploited in further controller synthesis. The derived model is shown valid by reducing it to agree well with the mobile platform model. In order to solve the path tracking control problem of the wheeled mobile manipulator, a novel kinematic control scheme is proposed to deal with the nonholonomic constraints. With the backstepping technique and the filtered-error method, the nonlinear tracking control laws for the mobile manipulator system are constructed based on the Lyapunov stability theory. The proposed control scheme not only achieves simultaneous trajectory and velocity tracking, but also compensates for the dynamic interactions caused by the motions of the mobile platform and the two onboard manipulators. Simulation results are performed to illustrate the efficacy of the proposed control strategy.     

Type-2 fuzzy sliding mode control without reaching phase for nonlinear system

A new sliding mode control (SMC) algorithm for the nth order nonlinear system suffering from parameters uncertainty and subjected to an external perturbation is proposed. The algorithm employs a time-varying switching plane. At the initial time t=t₀, the plane passes through the point determined by the system initial conditions in the error state space. Afterwards, the plane moves to the origin of the state space. Since the nonlinear system is sensible to the perturbations and uncertainties during the reaching phase, the elimination of such phase yields in a considerable amelioration of system robustness. Switching plane is chosen such that: (1) the reaching phase is eliminated, (2) the nonlinear system is insensitive to the external disturbance and the model uncertainty from the initial time (3) the convergence of the tracking error to zero. Furthermore, a Type-2 fuzzy system is used to approximate system dynamics (assumed to be unknown) and to construct the equivalent controller such that: (1) all signals of closed-loop system are uniformly ultimately bounded, (2) the problems related to adaptive fuzzy controllers like singularity and constraints on the control gain are resolved. To ensure the robustness of the overall closed-loop system, analytical demonstration using Lyapunov theorem is considered. Finally, a robot manipulator is considered as a real time system in order to confirm the efficiency of the proposed approach. The experimentation is done for both regulation and tracking control problems.