Dynamic modeling and robust control of a 3-PRC translational parallel kinematic machine

The dynamic modeling and robust control for a three-prismatic-revolute-cylindrical (3-PRC) parallel kinematic machine (PKM) with translational motion have been investigated in this paper. By introducing a mass distribution factor, the simplified dynamic equations have been derived via the virtual work principle and validated on a virtual prototype with the ADAMS software package. Based upon the established model, three dynamics controllers have been attempted on the 3-PRC PKM. The intuitive co-simulations with the combination of MATLAB/Simulink and ADAMS show that the control performance of neither inverse dynamics control nor robust inverse dynamics control is satisfactory in the presence of parametric uncertainties in PKM dynamics. On the contrary, the controller based on the passivity-based robust control scheme is more suitable for tracking control of the PKM in terms of both control performances and controller design procedures. The results presented in the paper provide a sound base for both the mechanical system design and control system design of a 3-PRC PKM.     

Relaxing the stability limit of adaptive control systems in the presence of unmodelled dynamics

It is known that a closed-loop dynamical system subject to an adaptive controller remains stable either if there does not exist significant unmodelled dynamics or the effect of system uncertainties is negligible. This implies that these controllers cannot tolerate large system uncertainties even when the unmodelled dynamics satisfy a set of conditions. In this paper, we present an adaptive control architecture such that the proposed adaptive controller is augmented with an adaptive robustifying term. Unlike standard adaptive controllers, the proposed architecture allows the closed-loop dynamical system to remain stable in the presence of large system uncertainties when the unmodelled system dynamics satisfy a set of conditions. A numerical example is provided to demonstrate the efficacy of the proposed approach.     

On adaptive inverse dynamics for free-floating space manipulators

This paper is devoted to the investigation of adaptive inverse dynamics for free-floating space manipulators (FFSMs) suffering from parameter uncertainties/variations. To overcome the nonlinear parametric problem of the dynamics of FFSMs, we introduce a new regressor matrix called the generalized dynamic regressor. Based on this regressor, and with Lyapunov stability analysis tools, we obtain a new parameter adaptation law and show that the closed-loop system is stable, and that the joint tracking errors converge asymptotically to zero. Simulation results are provided to illustrate the performance of the proposed adaptive algorithm. Furthermore, we conduct a comparative study between adaptive inverse dynamics, prediction error based adaptation, and passivity based adaptation.     

Adaptive tracking control of manipulators: Theory and experiments

This paper considers the trajectory tracking problem for uncertain robot manipulators and proposes two adaptive controllers as solutions to this problem. The first controller is derived under the assumption that the manipulator state is measurable, while the second strategy is developed for those applications in which only position measurements are available. The adaptive schemes are very general and computationally efficient since they do not require knowledge of either the mathematical model or the parameter values of the manipulator dynamics, and are implemented without calculation of the robot inverse dynamics or inverse kinematic transformation. It is shown that the control strategies ensure uniform boundedness of all signals in the presence of bounded disturbances, and that the ultimate size of the tracking errors can be made arbitrarily small. Experimental results are presented for a PUMA 560 manipulator and demonstrate that accurate and robust trajectory tracking can be achieved by using the proposed controllers.     

Robust adaptive control for a nonholonomic mobile robot with unknown parameters

A robust adaptive controller for a nonholonomic mobile robot with unknown kinematic and dynamic parameters is proposed. A kinematic controller whose output is the input of the relevant dynamic controller is provided by using the concept of backstepping. An adaptive algorithm is developed in the kinematic controller to approximate the unknown kinematic parameters, and a simple single-layer neural network is used to express the highly nonlinear robot dynamics in terms of the known and unknown parameters. In order to attenuate the effects of the uncertainties and disturbances on tracking performance, a sliding mode control term is added to the dynamic controller. In the deterministic design of feedback controllers for the uncertain dynamic systems, upper bounds on the norm of the uncertainties are an important clue to guarantee the stability of the closed-loop system. However, sometimes these upper bounds may not be easily obtained because of the complexity of the structure of the uncertainties. Thereby, simple adaptation laws are proposed to approximate upper bounds on the norm of the uncertainties to address this problem. The stability of the proposed control system is shown through the Lyapunov method. Lastly, a design example for a mobile robot with two actuated wheels is provided and the feasibility of the controller is demonstrated by numerical simulations.     

Autonomous mobile robots navigation using RBF neural compensator

This paper presents an approach to adaptive trajectory tracking of mobile robots which combines a feedback linearization based on a nominal model and a RBF-NN adaptive dynamic compensation. For a robot with uncertain dynamic parameters, two controllers are implemented separately: a kinematics controller and an inverse dynamics controller. The uncertainty in the nominal dynamics model is compensated by a neural adaptive feedback controller. The resulting adaptive controller is efficient and robust in the sense that it succeeds to achieve a good tracking performance with a small computational effort. The analysis of the RBF-NN approximation error on the control errors is included. Finally, the performance of the control system is verified through experiments.     

基于自适应动态规划的移动装弹机械臂轨迹控制

针对移动装弹机械臂系统非线性、强耦合、受多种不确定因素影响的问题,本文基于自适应动态规划方法,提出了仅包含评价网络结构的轨迹跟踪控制方法,有效减小了系统跟踪误差.首先,考虑到系统非线性特性、变量间强耦合作用及重力因素的影响,通过拉格朗日方程建立了移动装弹机械臂的动力学模型.其次,针对系统存在不确定性上界未知的问题,建立单网络评价结构,通过策略迭代算法,求解哈密顿–雅可比–贝尔曼方程,基于李雅普诺夫稳定性理论,设计了自适应动态规划轨迹跟踪控制方法.最后,通过仿真实验将该控制方法与自适应滑模控制方法进行了对比,进一步检验了所设计控制方法的有效性.     

Dynamics and control of a novel 3-DOF parallel manipulator with actuation redundancy

This paper deals with the dynamics and control of a novel 3-degrees-of-freedom （DOF） parallel manipulator with actuation redundancy. According to the kinematics of the redundant manipulator, the inverse dynamic equation is formulated in the task space by using the Lagrangian formalism, and the driving force is optimized by utilizing the minimal 2-norm method. Based on the dynamic model, a synchronized sliding mode control scheme based on contour error is proposed to implement accurate motion tracking control. Additionally, an adaptive method is introduced to approximate the lumped uncertainty of the system and provide a chattering-free control. The simulation results indicate the effectiveness of the proposed approaches and demonstrate the satisfactory tracking performance compared to the conventional controller in the presence of the parameter uncertainties and un-modelled dynamics for the motion control of manipulators.     

Robust control of robot manipulators with fast load adaptation

Many adaptive robot controllers have been proposed in the literature to solve manipulator trajectory tracking problems for high-speed operations in the presence of parameter uncertainties. However, most of these controllers stem from the applications of the existing adaptive control theory, which is traditionally focused on tracking slowly time-varying parameters. In fact, manipulator dynamics have fast transient processes for high-speed operations and load changes are abrupt. These observations motivate the present research to incorporate change detection techniques into self-tuning schemes for tracking abrupt load variations and achieving fast load adaptation. To this end, a robustly global stabilizing controller for a robot model with parametric and non-parametric uncertainies is developed based on the Lyapunov second method, and it is then made adaptive via the self-tuning regulator concept. The two-model approach to online change detection in load is used and the estimation algorithm is reinitialized once load changes are detected. This allows a much faster adaptive identification of load parameters than the ordinary forgetting factor approach. Simulation results demonstrate that the proposed controller achieves better tracking accuracy than the existing adaptive and non-adaptive controllers.     

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.     

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.     

Adaptive Dynamic Surface control of An electrohydraulic Actuator with Friction Compensation

In this paper, an adaptive nonlinear control scheme with a friction observer for position control of an electrohydraulic actuator is proposed. The observer based on the LuGre friction model is employed to compensate for the friction. Adaptation laws are used to handle parameter uncertainties in the actuator and friction model. The control law including dynamics of the observer is developed through a backstepping‐like dynamic surface control (DSC) technique. Experimental results have illustrated the success of the control scheme. The results also show that the adaptive DSC controller has better tracking performance than an adaptive backstepping and conventional PI controllers.     

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。     

Trajectory Tracking Control of Omnidirectional Wheeled Mobile Manipulators: Robust Neural Network-Based Sliding Mode Approach

This paper addresses the robust trajectory tracking problem for a redundantly actuated omnidirectional mobile manipulator in the presence of uncertainties and disturbances. The development of control algorithms is based on sliding mode control (SMC) technique. First, a dynamic model is derived based on the practical omnidirectional mobile manipulator system. Then, a SMC scheme, based on the fixed large upper boundedness of the system dynamics (FLUBSMC), is designed to ensure trajectory tracking of the closed-loop system. However, the FLUBSMC scheme has inherent deficiency, which needs computing the upper boundedness of the system dynamics, and may cause high noise amplification and high control cost, particularly for the complex dynamics of the omnidirectional mobile manipulator system. Therefore, a robust neural network (NN)-based sliding mode controller (NNSMC), which uses an NN to identify the unstructured system dynamics directly, is further proposed to overcome the disadvantages of FLUBSMC and reduce the online computing burden of conventional NN adaptive controllers. Using learning ability of NN, NNSMC can coordinately control the omnidirectional mobile platform and the mounted manipulator with different dynamics effectively. The stability of the closed-loop system, the convergence of the NN weight-updating process, and the boundedness of the NN weight estimation errors are all strictly guaranteed. Then, in order to accelerate the NN learning efficiency, a partitioned NN structure is applied. Finally, simulation examples are given to demonstrate the proposed NNSMC approach can guarantee the whole system's convergence to the desired manifold with prescribed performance.     

移动机械手鲁棒自适应模糊控制

基于旋量理论建立了非完整移动机械手系统的动力学模型,通过反步控制技术,应用非线性参数化模糊逻辑系统设计了移动机械手的鲁棒自适应模糊控制器.该控制器放松了移动机械手控制器设计中斜对称性的要求,对移动机械手系统中存在的参数或外界扰动等不确定性具有较强的鲁棒性和自适应能力.理论证明和仿真结果表明,所设计的控制器是有效的.     

Inverse optimal sliding mode control of spacecraft with coupled translation and attitude dynamics

This paper proposes two robust inverse optimal control schemes for spacecraft with coupled translation and attitude dynamics in the presence of external disturbances. For the first controller, an inverse optimal control law is designed based on Sontag-type formula and the control Lyapunov function. Then a robust inverse optimal position and attitude controller is designed by using a new second-order integral sliding mode control method to combine a sliding mode control with the derived inverse optimal control. The global asymptotic stability of the proposed control law is proved by using the second method of Lyapunov. For the other control law, a nonlinear H_∞ inverse optimal controller for spacecraft position and attitude tracking motion is developed to achieve the design conditions of controller gains that the control law becomes suboptimal H_∞ state feedback control. The ultimate boundedness of system state is proved by using the Lyapunov stability theory. Both developed robust inverse optimal controllers can minimise a performance index and ensure the stability of the closed-loop system and external disturbance attenuation. An example of position and attitude tracking manoeuvres is presented and simulation results are included to show the performance of the proposed controllers.     

Robust adaptive multi-task tracking control of redundant manipulators with dynamic and kinematic uncertainties and unknown disturbances

In this paper, a novel adaptive multi-priority controller for redundant manipulators is proposed to accomplish the multi-task tracking when kinematic/dynamic uncertainties and unknown disturbances exist. Prioritized redundancy resolution in kinematic level is incorporated into this passivity-based control framework. The kinematic and dynamic parameter adaptations are driven by both tracking error and prediction error. Moreover, the tracking information from both primary and subtasks are all utilized to accelerate the parameter estimation when the tasks are independent, whereas the inevitable tracking error of the subtasks due to algorithmic singularities is properly eliminated in the adaptation laws when the tasks are dependent. Potential ill-conditioned solution of the pseudoinverse is avoided using an improved singularity-robust inverse of the projected Jacobian. Along with the improvement of the multi-task tracking performance, smoothness of the commanded torques is still guaranteed for easy application. Measurements of the noisy joint acceleration and task velocity are avoided. The controller is mathematically derived based on Lyapunov stability analysis. Simulation results of the two cases are presented to verify the effectiveness and superiority of the proposed controller.     

Simulation of a SCARA robot with PD and learning controllers

In this study, a SCARA robot manipulator is simulated under PD and learning based controllers. The trajectory following performance of the robot is studied against these controllers. The adaptive/learning hybrid controller scheme and learning controller method are utilized as learning based controllers. The results of simulations show that, learning algorithm based controllers reduce the position tracking error effectively. The hybrid adaptive/learning controller has similar performance as the learning controller although it uses partial state information and compensates both mechanical and electrical dynamics, whereas the learning controller needs both position and velocity measurements neglecting electrical dynamics.     

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.     

Adaptive neural network tracking control for manipulators with uncertain kinematics, dynamics and actuator model

A neural-network-based adaptive controller is proposed for the tracking problem of manipulators with uncertain kinematics, dynamics and actuator model. The adaptive Jacobian scheme is used to estimate the unknown kinematics parameters. Uncertainties in the manipulator dynamics and actuator model are compensated by three-layer neural networks. External disturbances and approximation errors are counteracted by robust signals. The actuator controller is designed based on the backstepping scheme. Compared with the existing work, the proposed method considers the manipulator kinematics uncertainty, does not need the “linearity-in-parameters” assumption for the uncertain terms in the dynamics of manipulator and actuator, and guarantees the tracking error to be as small as desired. Finally, the performance of the proposed approach is illustrated by the simulation example.