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.     

Control of flexible mobile manipulators: positioning and vibration reduction using an eye-in-hand range camera

In this paper, the positioning of a long flexible manipulator on a moving platform is investigated. The problem is to position the gripper at a requested relative distance in front of an object with unknown location. For this purpose, the gripper is equipped with a range camera giving the distance to surrounding objects within, ∼1% and with a sampling rate above 1 kHz. The range measurements are used in combination with internal angle measurements from joint encoders to estimate both the flexibility in the mechanical construction and the relative distance from gripper to object. This is solved satisfactorily by an extended Kalman filter (EKF). For the motion control of the manipulator, a time-scaled feedback controller is suggested. A fast inner loop is used to damp out oscillations and reject disturbances, both from the platform and the manipulator. An outer control loop, with a lower closed-loop bandwidth, then steers the gripper, based on the range measurements, to the requested final position in front of the object. This loop assumes a stationary and rigid platform and a rigid manipulator. At this moment, only simulations of a flexible manipulator on a rigid platform have been studied. However, the results show that the flexibility can be estimated from indirect measurements of the range to the object and the joint angles. Also, good damping and disturbance rejection are achieved, as long as the bandwidth of the actuators is sufficiently high compared to the oscillation. The use of range measurements of the surrounding objects makes the positioning task very robust against an uncertain platform position.     

Control of constrained manipulators with flexible joints

This paper presents results on control design of constrained manipulators with flexible joints. It will be assumed that such manipulators are under gravity and contact reaction effects. It is also assumed that measurable joint variables are limited to rotor angles and its velocities. A simple biased proportional and derivative feedback controller is shown to be able to drive the manipulator to a desired configuration specified in link angles with desired contact force specified in the direction normal to the constraint surface at the desired position. A sufficient condition for global stability will be established by using a Lyapunov function which is constructed taking into account the spring stiffness, gravity factors and constraint functions. An example is studied and computer simulation results are presented to show closed-loop performance. Editor: M. Corless     

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.     

Low-level flexible planning for mobile manipulators: a distributed perception approach

The paper proposes a method to improve flexibility of the motion planning process for mobile manipulators. The approach is based on the exploitation of perception data available only from simple proximity sensors distributed on the robot. Such data are used to correct pre-planned motions to cope with uncertainties and dynamic changes of the scene at execution time. The algorithm computes robot motion commands aimed at fulfilling the mission by combining two tasks at the same time, i.e. following the planned end-effector path and avoiding obstacles in the environment, by exploiting robot redundancy as well as handling priorities among tasks. Moreover, a technique to smoothly switch between the tasks is presented. To show the effectiveness of the method, four experimental case studies have been presented consisting in a place task executed by a mobile manipulator in an increasingly cluttered scene.     

Control of linear systems with multiparameter singular perturbations

The singular perturbation theory is extended to systems with several small parameters which can change the system order. Difficulties arising in testing the boundary layer stability in multiparameter linear problems are discussed. The theory is applied to linear quadratic optimal control and Nash game problems.     

Active damping of flexible structures via saturating actuators

The active damping aspect is treated of the spacecraft control laboratory experiment (SCOLE). A continuum model, rather than a finite element model, is used. First, a group of rather weak sufficient conditions for strong stabilizability is presented. Structural passive damping is no longer required to be positive definite and, in fact, can even be zero, while strong stabilizability can still be achieved by active damping. Then, the mode excitation problem is studied for both linear and (saturating) nonlinear active damping. The popular notions of ‘characteristic equation’ and ‘root locus’ in feedback control are extended to our distributed parameter system, which is a feature of this work. The root locus provides an insight into the nature of active damping     

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.     

Two-time-scale distributions and singular perturbations

Two-time-scale (TTS) distributions are introduced. For a class of stable systems, it is shown that every TTS distribution has a two-frequency-scale (TFS) Laplace transform. Conversely, it is shown that the impulse response of any stable TFS transfer function, and hence any stable (standard) singularly perturbed system, can be characterized in terms of a stable TTS distribution. A time domain decomposition for TTS distributions is obtained which parallels the slow and fast decomposition of singularly perturbed systems and also the frequency domain decomposition of TFS transfer functions. It is shown that every stable TTS distribution can be decomposed in terms of two simpler distributions represented in two different time scales. A composite distribution is constructed from these two which approximates the TTS distribution arbitrarily closely in the L ₁ norm.     

Robust damping control of mobile manipulators

A novel robust control technique, robust damping control (RDC), is introduced. An RDC controller is further developed for the motion control of a mobile manipulator subject to kinematic constraints. The knowledge of dynamic parameters of the mobile manipulator is assumed to be completely unknown. The proposed RDC controller is capable of disturbance-rejection in the presence of unknown bounded disturbance, without requiring the knowledge of its bound. The stability of the closed-loop system is guaranteed. The controller has a simple structure and can be easily implemented in applications. Experimental tests on a 2-DOF robotic manipulator illustrate that the proposed control is significantly better than conventional robust control.     

Remarks on order reduction for a robustly suboptimal controller via singular perturbations

It is shown that under a generic assumption the suboptimally robust controller constructed according to Glover and McFarlane (1989) leads to a singularly perturbed system, which may be reduced in the usual way, avoiding thus the difficulties mentioned by Habets (1991). The reduced controller obtained by this procedure is in fact optimal.     

柔性机械臂的双时间尺度组合控制

本文研究柔性机械臂的轨迹跟踪和振动抑制问题. 首先, 利用Lagrange法和假设模态法建立柔性机械臂的动态模型, 进而利用奇异摄动理论得到柔性机械臂的双时间尺度模型. 然后, 基于慢时间尺度模型利用滑模控制理论设计轨迹跟踪控制器; 借助于快时间尺度模型利用自适应动态规划设计参数不精确已知情况下的最优振动抑制控制器; 将二者相结合, 构造双时间尺度组合控制器, 利用奇异摄动理论证明闭环系统稳定. 最后, 在Matlab/Simulink环境下进行实验, 与现有方法相比, 本文设计的控制器对柔性振动具有更好的振动抑制效果, 跟踪精度更高.     

Distributed structural dynamics control of flexible manipulators —I. Structural dynamics and distributed viscoelastic actuator

Reducing structural dead weight has become of increasing importance in the design of new generation lightweight and high-speed robot manipulators. However, due to the nature of structural flexibility, the dynamic oscillation associated with robot structures can affect the operation accuracy and precision. This work, in two parts, presents a study on the vibration control of elastic or flexible robot structures. Effects of distributed passive (Part I) and active (in Part II) actuators on elastic robot structures are studied. The proposed distributed passive viscoelastic actuator (in Part I) is a layer (or layers) of viscoelastic polymer directly attached to the flexible robot element, the oscillation of which is to be controlled. The passive actuator is activated by the oscillation of the robot structure and it automatically dissipates vibration energy and constrains the undesirable motion to eliminate the disturbance and to maintain a precise robot trajectory. A finite element program capable of analyzing flexible links is developed. Results obtained from the finite element simulation are presented.     

柔性臂协调运动系统的动态反馈镇定

研究柔性臂协调运动系统分布参数模型的镇定问题.基于系统能量关系和正实引理,提出一种构造性的设计方法.所设计的控制器由前馈和动态反馈两部分构成,其中动态反馈部分的传递函数是严格正实的.通过线性算子半群理论和LaSalle不变集原理,证明了闭环系统是渐近稳定的.     

Control of singular problem via differentiation of a Min-Max

For Ω a smooth domain in Rⁿ with boundary Λ = Λ₀Λ₁, we are concerned with the wave equation y″ − Δy = S in Q_T =]0, T[ × Ω with = ∂/∂t, at source term satisfying S, S′ ε L¹(0, T L² (Ω)). A Dirichlet condition is imposed on Λ₀ and we consider an absorbing condition ∂y/∂n + uy′ = 0 in [0, T] × gL₁ where u is the control.parameter. We introduce the cost function. and using the Min-Max formulation of J we by-pasas the sensitivity analysis of u → y and obtain the gradient of J with a usual adjoint problem. We first present an abstract frame for this kind of problems. using the differentiability results of a Min-Max [1,2], which we very shortly deduce here, we show that the well posedness of the adjoint equation implies differentiability of the cost function governed by a linear well posed problem.     

Stability and singular perturbations in constrained Markov decisionproblems

Constrained Markov decision problems (CMDPs) with the average cost criterion and a single ergodic chain, or the discounted cost with a general multichain structure, are considered. Conditions for stability of the optimal value and control to changes of the parameters of the problem, such as immediate costs, transition probabilities, and the discount factor, are established. Singular constrained problems, for which the optimal value and controls exhibit discontinuities, are studied     

Robustness of exponential stability to singular perturbations and delays

Singularly perturbed nonlinear differential equations with small time delays in the slow variables are considered. Averages of the fast variables are used in order to obtain a sufficient condition under which the exponential stability of the slow subsystem is robust to singular perturbations and delays.     

A review on vision-based control of flexible manipulators

In this review, recent developments in the field of flexible robot arm control using visual servoing are reviewed. In comparison to rigid robots, the end-effector position of flexible links cannot be obtained precisely enough with respect to position control using kinematic information and joint variables. To solve the task here the use of a vision sensor (camera) system, visual servoing is proposed to realize the task of control flexible manipulators with improved quality requirements. The paper is organized as follows: the visual servoing architectures will be reviewed for rigid robots first. The advantages, disadvantages, and comparisons between different approaches of visual servoing are carried out. The using of visual servoing to control flexible robot is addressed next. Open problems such as state variables estimation as well as the combination of different sensor properties as well as some application-oriented points related to flexible robot are discussed in detail.     

双臂柔性机械手的终端滑模控制

提出一种用于双臂柔性机械手系统的终端滑模控制方法，以解决其非最小相位控制问题．重新定义了柔性机械手系统的输出，通过输入输出线性化，将系统分解为输入输出子系统和内部子系统．设计逆动态终端滑模控制策略，使输入输出子系统在有限时间内收敛到零；选择适当的控制器参数，使零动态子系统在平衡点附近渐近稳定，从而保证整个系统的渐近稳定．仿真结果证明了该设计方法的有效性．