Trajectory control of a non-linear one-link flexible arm

The trajectory-tracking control problem is considered for a one-link flexible arm described by a non-linear model. Two meaningful system outputs are chosen; namely, the joint angle and the angular position of a suitable point along the link. The common goal is to stiffen the behaviour of the flexible link with respect to the chosen output. Based on the input-output inversion algorithm, a state-feedback control law is designed that enables exact tracking of any smooth trajectory specified for the output. In the closed loop an unobservable dynamics naturally arises, related to the variables describing the arm's distributed flexibility. Joint-based design is shown to be always stable, whereas in the link-point design the closed-loop dynamics may become unstable depending on the location of the output along the link. Open- versus closed-loop strategies are developed and compared. Extensive simulation results are included.     

Force control and exponential stabilisation of one-link flexible arm

In this paper, we discuss a force control problem for a constrained one-link flexible arm. To solve the force control problem, we propose a simple boundary feedback controller that consists of the bending moment at the root of the flexible arm and its time derivative. The striking point is that information about the force and the rotational angle of the motor is not necessary for the implementation of the controller, and thus we do not need a force sensor or encoder in the construction of the controller. The exponential stability of the closed-loop system is then provided using the energy multiplier method. We describe several experiments carried out to investigate the performance of the proposed controller.     

Experiments in load-adaptive control of a very flexible one-link manipulator

An adaptive control algorithm based on the Self-Tuning Regulator concept has been experimentally demonstrated on a very flexible one-link robotic manipulator. The very lightly-damped structural resonances of the manipulator coupled with the use of a primary sensor separated from the actuator by flexible structure (non-collocated sensor and actuator) to give good accuracy in tip positioning make high-performance controllers very sensitive to modeling error. The adaptive controller is able to maintain precise tip position control despite wide variations in end effector load. An identification algorithm is employed which estimates the mass of the tip load. It makes use of a simple parameterization of system transfer functions which is a linear-fractional expression in the mass of the load. The Linear Quadratic Gaussian synthesis procedure is used for control design, a polynomial interpolation to a precalculated table of controller gains is made on-line to implement a controller appropriate to the identified value of load mass. Rate of convergence of the identification algorithm is such that the system is able to adapt to a 40% change in moment of inertia during a single commanded step change in position.     

Feedback control of one-link flexible manipulator with gear train

This article reports experimental results in control of a one-link flexible manipulator. A d.c. drive with gear train rotates the link with a tip-mass in the horizontal plane. A “stiff” hardware servo-system tracks the commanded drive velocity. We describe the experimental setup and develop a dynamic model for the one-mode flexible vibration control. We design and experimentally test controllers for active damping of the vibrations and stabilization of the link-tip position. Results for continuous control implemented with an analog computer and a sampled-data, digital-computer control are reported. A high control performance is achieved despite the gear-train friction influence. In addition, sampled-data digital controllers for tracking control of the link reference motion are designed and tested.     

Direct adaptive control of a one-link flexible arm with tracking

A robust tracking controller for a one-link flexible arm based on a model reference adaptive control approach is proposed. In order to satisfy the model matching conditions, the reference model is chosen to be the optimally controlled linearized model of the system. The resulting controller overcomes the fundamental limitation in previously published research on direct adaptive control of flexible robots that required additional actuators solely to control the flexible degrees of freedom. The nominal trajectory is commanded by means of a tracking control. Simulation results for the prototype in the laboratory show improvements obtained with the outer adaptive feedback loop compared to a pure optimal regulator control. Robustness is tested by varying the payload mass.     

A robust constrained control approach for flexible air‐breathing hypersonic vehicles

This article investigates the robust adaptive control system design for the longitudinal dynamics of a flexible air‐breathing hypersonic vehicle (FAHV) subject to parametric uncertainties and control input constraints. A combination of back‐stepping and nonlinear disturbance observer (NDO) is utilized for exploiting an adaptive output‐feedback controller to provide robust tracking of velocity and altitude reference trajectories in the presence of flexible effects and system uncertainties. The dynamic surface control is introduced to solve the problem of “explosion of terms.” A new NDO is developed to guarantee the proposed controller's disturbance attenuation ability and to performance robustness against uncertain aerodynamic coefficients. To deal with the problem of actuator saturation, a novel auxiliary system is exploited to compensate the desired control laws. The stability of the presented NDO and controller is analyzed. Simulation results are given to demonstrate the effectiveness of the presented control strategy.     

On tracking control of flexible robot arms

A controller for solving the tracking problem of flexible robot arms is presented. In order to achieve this goal, the desired trajectory for the link (flexible) coordinates is computed from the dynamic model of the robot arm and is guaranteed to be bounded, and the desired trajectory for the joint (rigid) coordinates can be assigned arbitrarily. The case of no internal damping is also considered, and a robust control technique is used to enhance the damping of the system     

受时变约束柔性臂鲁棒RBF神经网络力/位置控制

研究了受时变约束的柔性臂系统，建立了分布参数模型，通过奇异摄动方法将该模型划分为表征系统刚性运动的集中参数子系统和表征系统振动的分布参数子系统．设计了集中参数子系统的鲁棒RBF神经网络力／位置控制算法和分布参数子系统的鲁棒自适应振动抑制控制算法．理论分析及仿真结果验证了该方法的有效性．     

Observer-based control of discrete-time Lipschitzian non-linear systems: application to one-link flexible joint robot

The problem of designing asymptotic observers along with observer-based feedbacks for a class of discrete-time non-linear systems is considered. We assume that the system non-linearity is globally Lipschitz and the system is supposed to be stabilizable by a linear controller. Sufficient linear matrix inequality condition is derived to ensure the stability of the considered system under the action of feedback control based on the reconstructed states. A numerical example of a single-link flexible joint robot is presented to illustrate the efficacy of the theoretical developments.     

Superposition in efficient robust constrained predictive control

A stabilizing control method, which does not require on-line optimizations, is developed for linear systems with polytopic model uncertainties and hard input constraints. This work is motivated by the constrained robust MPC (CRMPC) approach (IEEE Trans. Automat. Control 45 (2000a) 1765) which adopts the dual mode prediction strategy (i.e. free control moves and invariant set) and minimizes a worst case performance criterion. Based on the observation that, a feasible control sequence for a particular state can be found as a linear combination of feasible sequences for other states, we suggest a stabilizing control algorithm providing sub-optimal and feasible control sequences using pre-computed optimal sequences for some canonical states. The on-line computation of the proposed method reduces to simple matrix multiplication.     

Implementation of robust impedance and force control

In this paper, we discuss the problem of implementing impedance control in the presence of model uncertainties and its application to robot force control. We first propose a sliding mode-based impedance controller. The implementation of the targeted impedance, and the preservation of stability in the presence of model uncertainties, are the key issues in the proposed approach. Using sliding mode control, a simple and robust algorithm is obtained so that the targeted impedance can be accurately implemented without the exact model of the robot. The controller is designed in terms of the task space coordinates. The chattering in the sliding mode control is eliminated by using a continuous function. The problem of force control is also addressed for the impedance controlled robot. An off-line estimation method of the environment model is suggested and used in the force control scheme. The proposed impedance and force control schemes have been experimentally verified on a two degree-of-freedom direct-drive robot arm. The experimental results are presented in this paper.     

Dynamic stability analysis of a one-link force-controlled flexible manipulator

This study analyzes the effects of link flexibility on the dynamic stability of a force-controlled flexible manipulator. The closed-loop dynamic equation for a l-link manipulator is first derived explicitly using the modal representation technique. Stability analysis is then carried out by computing the system eigenvalues. Results show that the link flexibility is one of the causes of dynamic instability of motion of the flexible robotic arm.     

Inversion techniques for trajectory control of flexible robot arms

A general framework is given for computing the torques that are needed for moving a flexible arm exactly along a given trajectory. This torque computation requires a dynamic generator system, as opposed to the rigid case, and can be accomplished both in an open- or in a closed-loop fashion. In the open-loop case, the dynamic generator is the full or reduced order inverse system associated to the arm dynamics and outputs. In order to successfully invert the arm dynamics, the torque generator should be a stable system. The stability properties depend on the chosen system output, that is on the robot variables (e.g., joint or end-effector) to be controlled. The same inversion technique can be applied for closed-loop trajectory control of flexible robots. A simple but meaningful nonlinear dynamic model of a one-link flexible arm is used to illustrate different feasible control strategies. Simulation results are reported that display the effects of the system output choice on the closed-loop stability and on the overall tracking performance.     

Modeling and control of two constrained manipulators

The coordinated control of two manipulators in the presence of environment constraints is studied in this paper. Such a control method is needed in applications in which the two manipulators grasp a common object whose motion is constrained by environments. The two manipulators are not only constrained with each other, but also constrained by the environment in their workspace. It is realized that the motion and constraint equations obtained directly from mechanics are not suitable for the control purpose. A set of equivalent equations are derived, which are in the standard form of the nonlinear system representation with clear state equations and output equations. A nonlinear feedback is found which exactly linearizes and decouples the dynamic nonlinear system of the two constrained manipulators. The coordinated controller design is then carried out based on the linearized system by using linear system theory.     

Stability analysis of position and force control for robot arms

Stability issues involving the control of a robot arm under the influence of external forces are discussed. Several different scenarios are considered: position control with the external force as an unmodeled disturbance, compliant control for a bounded external force in some subspace, and compliant control for a force due to the interaction with an environment whose dynamical behavior can be modeled. In each of these cases, a stability analysis using the Lyapunov method is presented. An explanation of instability is suggested in the case that the environment has flexibility and the gains are inappropriately chosen. When the environment is stiff in the force control subspace, robust (in time delay) stability can be achieved via the integral force feedback. However, the integral feedback gain should be chosen sufficiently small to account for possible flexibility in the system     

Virtual passive control of flexible arms with collocated and noncollocated feedback

A novel approach to the control of flexible manipulators is proposed. The controller includes both joint‐variable and tip‐deflection feedback. It is shown that tip‐deflection feedback transforms the original structure into new system in which the structure parameters are virtually scaled up or down. The new system can hence be easily stabilized via a strictly passive feedback law. A co‐hub, lumped‐parameter structure with multiple massless links is first investigated and stability conditions are developed. The results are then applied to a distributed‐parameter flexible arm, which is decomposed into an equivalent lumped‐parameter structure via a set of modal functions normalized in a particular way. Tip‐deflection feedback is shown to be capable of enhancing control performance on a flexible arm, and stability is ensured as long as the gain associated with the noncollocated feedback satisfies a simple inequality. The stability criteria re valid independent of high‐order flexible modes. © 2001 John Wiley & Sons, Inc.     

复杂约束下的挠性航天器姿态参考管理控制

本文提出了一种基于显式参考管理与模态观测器的挠性航天器姿态机动控制方法. 首先, 采用改进的罗德里格斯参数建立了航天器的运动学和动力学模型, 分析了存在的控制约束和角速度约束. 在此基础上, 设计了基于显式参考管理的约束挠性航天器姿态重定向控制算法. 由于挠性模态不能直接测量, 内层设计了模态观测器, 并将观测器观测得到的模态坐标作为内层无约束控制器的输入. 随后, 外层导航模块根据所需满足的约束条件设计了相应的动态路径, 该路径可以根据当前状态以合适的速率收敛到最终状态, 通过跟踪该路径, 航天器姿态就可以在满足约束的情况下快速到达期望位置. 通过构造合适的李雅普诺夫函数, 严格证明了该挠性航天器显式参考管理姿态控制算法的稳定性. 最后, 仿真结果进一步验证所设计算法的约束处理效果与振动抑制能力.     

Adaptive robust attitude control of a flexible spacecraft

A new attitude control strategy for rotational manoeuvre of an elastic spacecraft is presented. Adaptive sliding mode control with hybrid sliding surface (HSS) is used to minimize the effects of uncertainties, disturbances and the difficulties arising from measurement of flexible dynamic co‐ordinates. The model of the spacecraft considered as rigid central hub and two elastic appendages. Collocated actuators and sensors are placed on the rigid central hub. Stability proof of the overall closed‐loop system is given via Lyapunov analysis. Numerical simulations show that the attitude manoeuvres can be performed precisely and the elastic deformations of the flexible substructures are suppressed as well. Copyright © 2006 John Wiley & Sons, Ltd.     

Modeling and robust adaptive iterative learning control of a vehicle‐based flexible manipulator with uncertainties

In this brief, this paper deals with a robust adaptive iterative learning control (ILC) problem for a flexible manipulator attached to a moving vehicle with uncertainties. To begin with, considering the infinite dimensionality of the flexible distributed parameter system, a coupled ordinary differential equation and partial differential equation model is established without any discretization. Then, it is followed by a presentation of an adaptive ILC strategy, which can drive the vehicle and joint to the desired positions based on a proportional‐derivative feedback structure with unmodeled dynamics and external disturbances. The deformation of the flexible manipulator can also be suppressed simultaneously under the proposed control laws. By using Lyapunov's direct method, the stability of the closed‐loop system is demonstrated. The simulation results are provided to illustrate the effectiveness of the proposed control laws.     

Sliding-mode motion/force control of constrained robots

A sliding-mode controller is proposed for the simultaneous position and force control of constrained robot manipulators with parametric uncertainties. Based on this controller, the trajectories of the closed-loop system can reach a stable sliding surface in finite time. Under this condition, the asymptotic convergence of the motion error and force error can be successfully ensured with improved results compared to previous studies