Distributed structural dynamics control of flexible manipulators—II. Distributed sensor and active electromechanical actuator

Structural oscillation of lightweight robot arms can degrade the accuracy and precision of a robot's high-demanding performance. This paper is the second of two on vibration control of elastic or flexible robot structure. The proposed electromechanical device has both sensing and control capabilities. Effects of active damping treatment on elastic robot arms are discussed. The proposed active distributed sensor and controller is a layer, or multi-layer, of piezoelectric polymer directly attached to the flexible component which is required to be monitored and controlled. By utilizing direct and converse piezoelectric characteristics, respectively, the integrated piezeoelectric sensor/controller can monitor the vibration due to induced mechanical stress/strain in the polymer; and it can also actively and directly constrain the undesirable vibration of flexible component by injecting high voltages. Experimental results and finite element simulations of the electromechanical sensor/actuator are presented and discussed.     

On the robust control of robot manipulators including actuator dynamics

A robust nonlinear control law that incorporates the manipulator dynamics as well as dynamics of actuators is developed in this article. The inertial parameters of the manipulator and the electrical parameters of the actuators are considered to be of uncertain values. In contrast to the known methods, the presented design procedure is based on less restrictive assumptions regarding the characteristics of uncertainties. We just assume that unknown parameters are bounded, which is evidently true for any robotic system. Exponential stability of the developed controller is proved by the Lyapunov method. © 1996 John Wiley & Sons, Inc.     

performance control of robot manipulators with kinematics,dynamics and actuator uncertainties

This paper deals with the task‐space trajectory tracking control problem of robot manipulators. An improved adaptive backstepping controller is proposed to deal with the uncertainties in kinematics, dynamics, and actuator modeling. To avoid the explosion of computation in conventional backstepping techniques, a modified dynamic surface control algorithm is proposed, which guarantees the asymptotic convergence rather than the uniformly ultimately boundedness of tracking errors in conventional dynamic surface control methods. Furthermore, the expression of the norm of tracking errors is explicitly derived in relation to the controller parameters, which provides instructions on tuning controller parameters to adjust the system performance. Moreover, the passivity structure of the designed adaptation law is thoroughly analyzed. Simulation of a free‐floating space robot is used to verify the effectiveness of the proposed control strategy in comparison with the conventional tracking control schemes. Copyright © 2016 John Wiley & Sons, Ltd.     

Inverse dynamics of spatial open-chain flexible manipulators with lumped and distributed actuators

This article addresses the problem of inverse dynamics for three-dimensional flexible manipulators with both lumped and distributed actuators. A recursive procedure is presented for computing the lumped inverse dynamic torques and the distributed piezoelectric actuator inputs for simultaneously tracking a prescribed end-point trajectory and reducing induced vibrations in the manipulator. The procedure sequentially solves for the non-causal inverse dynamic torques and piezoelectric voltages applied to each link in the manipulator, starting from the last element in the chain and proceeding to the base element. The method allows trajectory tracking wherein controllability of the structural vibrations is assured in all possible configurations through the use of only one motor at each intermediate joint and three motors at the ground. Numerical simulation shows that the elastic vibrations can be reduced significantly through the use of distributed actuators while at the same time satisfying the trajectory tracking requirement through the use of inverse dynamics. © 1994 John Wiley & Sons, Inc.     

On the dynamics and control of flexible joint space manipulators

Space manipulator systems are designed to have lightweight structure and long arms in order to achieve reduction of fuel consumption and large reachable workspaces, respectively. Such systems are subject to link flexibilities. Moreover, space manipulator actuators are usually driven by harmonic gear mechanisms which lead to joint flexibility. These types of flexibility may cause vibrations both in the manipulator and the spacecraft making the positioning of the end-effector very difficult. Here, both types of flexibilities are lumped at the joints and the dynamic equations of a general flexible joint space manipulator are derived. Their internal structure is highlighted and similarities and differences with fixed-base robots are discussed. It is shown that one can exploit the derived dynamic structure in order to design a static feedback linearization control law and obtain an exact linearization and decoupling result. The application of such controllers is desired in space applications due to their small computational effort. In case of fixed-base manipulators, the effective use of a static feedback controller is feasible only if a simplified model is considered. Then, the proposed static feedback linearization control law is applied to achieve end-effector precise trajectory tracking in Cartesian space maintaining a desirable non-oscillatory motion of the spacecraft. The application of the proposed controller is illustrated by a planar seven degrees of freedom (dof) system.     

Neural-network-based two-loop control of robotic manipulators including actuator dynamics in task space

A neural-network-based motion controller in task space is presented in this paper. The proposed controller is addressed as a two-loop cascade control scheme. The outer loop is given by kinematic control in the task space. It provides a joint velocity reference signal to the inner one. The inner loop implements a velocity servo loop at the robot joint level. A radial basis function network （RBFN） is integrated with proportional-integral （PI） control to construct a velocity tracking control scheme for the inner loop. Finally, a prototype technology based control system is designed for a robotic manipulator. The proposed control scheme is applied to the robotic manipulator. Experimental results confirm the validity of the proposed control scheme by comparing it with other control strategies.     

Synchronized adaptive control for coordinating manipulators with time‐varying actuator constraint and uncertain dynamics

This paper addresses the control issue for cooperative visual servoing manipulators on strongly connected graph with communication delays, in which case that the uncertain robot dynamics and kinematics, uncalibrated camera model, and actuator constraint are simultaneously considered. An adaptive cooperative image‐based approach is established to overcome the control difficulty arising from nonlinear coupling between visual model and robot agents. To estimate the coupled camera‐robot parameters, a novel adaptive strategy is developed and its superiority mainly lies in the containment of both individual image‐space errors and the synchronous errors among networked robots; thus, the cooperative performance is significantly strengthened. Moreover, the proposed cooperative controller with a Nussbaum‐type gain is implemented to both globally stabilize the closed‐loop systems and realize the synchronization control objective under the existence of unknown and time‐varying actuator constraint. Finally, simulations are carried out to validate the developed approach.     

Nonlinear dynamics of viscoelastic flexible structural systems by finite element method

This article presents a nonlinear displacement based finite elements model to study and analyze the nonlinear dynamic response of flexible double wishbone structural vehicle suspension system considering damping effect which was not previously discussed elsewhere. Due to large deflection and moderate rotation encountered during passing over road bumps, the kinematic nonlinearity is included through von Kármán strain component. Elastic undamped as well as viscous and viscoelastic damping mechanism are considered and compared. Considering the viscoelastic damping mechanism, the viscoelastic damping mechanism is modeled based on the integral constitutive form, which is recast into an incremental form suitable for finite element implementation. Additionally, the revolute joint element is adopted to incorporate the joint flexibility in the double wishbone system. The plane frame element is adopted to model the suspension links by using Timoshenko beam theory. The developed nonlinear finite element equations of motion are solved through the incremental iterative Newmark technique. The developed procedure is verified by comparing the obtained results with analytical solution and excellent agreement is observed. The applicability of the developed procedure is demonstrated by conducting parametric studies to show the effects of the road irregularities profiles, the vehicle speed, and the material damping coefficients on the nonlinear vibrations response of the double wishbone suspension systems. The obtained results are supportive in the design and manufacturing processes of these structural systems.

     

基于分布参数机械臂协调操作柔性负载双时标控制

基于分布参数系统理论,建立机械臂协调操作柔性负载系统的动力学模型.利用奇异摄动方法,对动力学模型进行双时标分解,得到一个表征系统大范围刚性运动的集中参数慢变子系统和表征系统弹性振动的分布参数快变子系统.分别设计了自适应模糊滑模慢变控制器和振动反馈快变控制器,并通过分析快变子系统主算子及其生成C_O半群的特性,证明了分布参数闭环子系统的渐近稳定性.最后,通过仿真实验验证了所提出方法的有效性.     

Integrated distributed sensing and active vibration suppression of flexible manipulators using distributed piezoelectrics

Structural oscillation of flexible robot manipulators would severely hamper their operation accuracy and precision. This article presents an integrated distributed sensor and active distributed vibration actuator design for elastic or flexible robot structures. The proposed distributed sensor and actuator is a layer, or multilayer of piezoelectric material directly attached on the flexible component needed to be monitored and controlled. The integrated piezoelectric sensor/actuator can monitor the oscillation as well as actively and directly constrain the undesirable oscillation of the flexible robot manipulators by direct/converse piezoelectric effects, respectively. A general theory on the distributed sensing and active vibration control using the piezoelectric elements is first proposed. An equivalent finite element formulation is also developed. A physical model with distributed sensor/actuator is tested in laboratory; and a finite element model with the piezoelectric actuator is simulated. The distributed sensing and control effectiveness are studied.     

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.     

Gain-scheduled ℓ-optimal control for boiler-turbine dynamics with actuator saturation

This paper presents a gain-scheduled approach for boiler-turbine controller design. The objective of this controller design is to achieve tracking performance in the power output and drum pressure while regulating water level deviation. Also, the controller needs to take into account the magnitude and rate saturation constraints on actuators. The nonlinear boiler-turbine dynamics is brought into a linear parameter varying (LPV) form which is a parameter-dependent state-space realization. The LPV form of the boiler-turbine dynamics is characterized by nonlinear dependence on drum pressure, which is naturally the scheduling variable. The controller is designed by utilizing the set-valued method for l¹- optimization, which explicitly addresses state constraints and controller saturations in the design process. The overall gain-scheduled design is augmented by a reference governor to avoid performance degradation in the presence of large tracking commands.     

Hybrid force and motion control of flexible joint parallel manipulators using inverse dynamics approach

An inverse dynamics control algorithm is developed for hybrid motion and contact force trajectory tracking control of flexible joint parallel manipulators. First, an open-tree structure is considered by the disconnection of adequate number of unactuated joints. The loop closure constraint equations are then included. Elimination of the joint reaction forces and the other intermediate variables yield a fourth-order relation between the actuator torques and the end-effector position and contact force variables, showing that the control torques do not have an instantaneous effect on the end-effector contact forces and accelerations because of the flexibility. The proposed control law provides simultaneous and asymptotically stable control of the end-effector contact forces and the motion along the constraint surfaces by utilizing the feedback of positions and velocities of the actuated joints and rotors. A two degree of freedom planar parallel manipulator is considered as an example to illustrate the effectiveness of the method.     

An inverse dynamics control strategy for tip position tracking of flexible multi-link manipulators

In this article, we present an inverse dynamics control strategy to achieve small tracking errors for a class of multi-link structurally flexible manipulators. This is done by defining new outputs near the end points of the arms as well as by augmenting the control inputs by terms that ensure stable operation of the closed loop system under specific conditions. The controller is designed in a two-step process. First, a new output is defined such that the zero dynamics of the original system are stabilized. Next, to ensure stable asymptotic tracking, the control input is modified such that stable asymptotic tracking of the new output or approximate tracking of the actual output may be achieved. This is illustrated for the case of single- and two-link flexible manipulators. ©1997 John Wiley & Sons, Inc.     

Control of flexible manipulators via singular perturbations and distributed vibration damping

A composite control strategy for a two-link flexible manipulator is analyzed which combines hub actuation with distributed vibration control. The hub actuation is based upon an integral manifold approach in which the system dynamics are approximately linearized to any order of a small parameter E representing stiffness of the robot arms. A polymer film is proposed as a distributed actuator to dampen vibrations due to elasticity in the links. Simulation results are provided which show that the addition of the distributed actuator significantly reduces the displacement and velocity of the first flexible mode in each link compared to hub actuation alone. Editor: T. Vincent     

基于PMAC的航空结构件柔性工装分布式控制系统设计

航空结构件是航空飞行器中的重要组成部分,航空结构件的自动化柔性工装质量直接影响航空飞行器的飞行安全水平。为降低系统位置和姿态控制误差,减小航空结构件的磨损面积,设计了基于PMAC的航空结构件柔性工装分布式控制系统。采用PMAC运动控制器,接收电子部件的反馈信号,控制步进电机、直流电机和交流电机。结合工控机、定位器、伺服电机和分布式通信网络,完成硬件系统的设计。根据航空结构件柔性工装操作设备的组成结构和工作原理,构建相应模型。确定航空结构件在目标曲面上的柔性工装位置,从移动位置和装配力两个方面,计算柔性工装控制量。在PMAC控制器的作用下,通过位姿的调整实现系统的航空结构件柔性工装分布式控制功能。系统测试结果表明,设计分布式控制系统的位置和姿态控制误差分别降低了13cm和0.32°,且设计系统控制下航空结构件的磨损面积较小。     

Robust adaptive tracking control of distributed delay systems with actuator and communication failures

This paper is concerned with the robust adaptive fault‐tolerant tracking control problem for a class of distributed delay systems against faulted and perturbed actuators and communications. As all the faults on actuators and communications, network delays in control and communication channels, and perturbations in communications and exogenous disturbances are unknown, some adaptation schemes are developed to adjust controller parameters in real‐time for constructing a class of distributed compensation controllers based on the delayed signals. Then, according to the information from the adaptive mechanism, the effect of each actuator and communication fault, network delay, channel perturbation and exogenous disturbance can be eliminated completely by using the proposed distributed adaptive‐state feedback controllers. Furthermore, asymptotic tracking results of the distributed closed‐loop systems can be achieved based on Lyapunov stability theory. An example is provided to further illustrate the effectiveness of the proposed direct adaptive design technique. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Backstepping boundary control of Burgers’ equation with actuator dynamics

In this paper, we propose a backstepping boundary control law for Burgers’ equation with actuator dynamics. While the control law without actuator dynamics depends only on the signals u(0,t) and u(1,t), the backstepping control also depends on u_x(0,t), u_x(1,t), u_xx(0,t) and u_xx(1,t), making the regularity of the control inputs the key technical issue of the paper. With elaborate Lyapunov analysis, we prove that all these signals are sufficiently regular and the closed-loop system, including the boundary dynamics, is globally H³ stable and well posed.     

Distributed adaptive control and stability verification for linear multiagent systems with heterogeneous actuator dynamics and system uncertainties

The contribution of this paper is a control synthesis and stability verification framework for linear time-invariant multiagent systems with heterogeneous actuator dynamics and system uncertainties. In particular, we first propose a distributed adaptive control architecture in a leader-follower setting for this class of high-order multiagent systems. The proposed architecture uses a hedging method, which alters the ideal reference model dynamics of each agent in order to ensure correct adaptation in the presence of heterogeneous actuator dynamics of these agents. We then use Lyapunov stability theory and linear matrix inequalities to analyse the proposed architecture. This analysis reveals a stability condition, where evaluation of this condition with respect to a given graph topology allows stability verification of the controlled multiagent system. From a practical point of view, this condition also shows a fundamental tradeoff between heterogeneous agent actuation capabilities and unknown parameters in agent dynamics. Several illustrative numerical examples are also provided to demonstrate the efficacy of the proposed architecture.