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     

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.     

Adaptive control of manipulators using uncalibrated joint-torque sensing

The application of joint-torque sensory feedback (JTF) in robot control has been proposed in the past that, unlike the model-based controllers, does not require the dynamic model of the robot links. JTF, however, assumes precise measurement of joint torque and accurate friction model of the joints. This paper presents an adaptive JTF control algorithm that does not rely on these assumptions. First, the robot dynamics with JTF is presented in a standard form with a minimum number of parameters, where the inertia matrix appears symmetric and positive definite. Second, an adaptive JTF control law is developed that requires only incorporation of uncalibrated joint-torque signals, i.e., the gains and offsets of multiple sensors are unknown. Also, all physical parameters of the joints including inertia of the rotors, link twist angles, and friction parameters are assumed to be unknown to the controller. The stability analysis of the control system is presented. Experimental results demonstrating the tracking performance of the proposed adaptive JTF controller are presented.     

Boundary control of flexible aircraft wings for vibration suppression

In this paper, we propose a boundary control strategy for vibration suppression of two flexible wings. As a basic approach, Hamilton's principle is used to ascertain the system dynamic model, which includes governing equations – four partial differential equations and boundary conditions – several ordinary differential equations. Considering the coupled bending and torsional deformations of flexible wings, boundary control force and torque act on the fuselage to regulate unexpected deformations of flexible wings. Then, we present the stability analysis of the closed-loop system through Lyapunov's direct method. Simulations are carried out by using finite difference method. The simulation experimental results illustrate the significant effect of the developed control strategies.     

Experimental two-axis vibration suppression and control of a flexible robot arm

This article focuses on the implementation of a dual-mode controller for the maneuver of a two-axis flexible robotic arm. The joint angle trajectory tracking is accomplished by proportional and derivative and feedforward controllers. Based on the pole placement technique, a linear stabilizer is designed for elastic mode stabilization in the plane perpendicular to each joint axis. The stabilizer is switched on when the trajectory reaches the vicinity of the terminal state. The effect of switching time of the stabilizer and varying payload on arm vibration are investigated. With the proposed control system, accurate joint angle tracking and elastic mode stabilization can be accomplished. © 1993 John Wiley & Sons, Inc.     

Distributed structural identification and control of shells using distributed piezoelectrics: Theory and finite element analysis

Distributed dynamic identification and vibration control of high-performance flexible structures has drawn much attention in recent years. This article presents an analytical and finite-element study on a distributed piezoelectric sensor and distributed actuator coupled with flexible shells and plates. The integrated piezoelectric sensor/actuator can monitor the oscillation as well as actively control the structural vibration by the direct/converse piezoelectric effects, respectively. Based on Maxwell's equations and Love's assumptions, new theories on distributed sensing and active vibration control of a generic shell using the distributed piezoelectrics are derived. These theories can be easily simplified to account for plates, cylinders, beams, etc. A new piezoelectric finite element is also formulated using the variational principle and Hamilton's principle. A piezoelectric micropositioning device was first studied; analytical solutions are compared closely with experimental and finite-element results. Distributed vibration identification and control of a zero-curvature shell-a plate-are also investigated.     

Adaptive control of flexible link manipulators using a pseudolink dynamic model

This paper presents a novel adaptive control scheme for a lightweight manipulator arm governed by electric motors. The controller design is based on the dynamic model of the arm in a quasi-static approximation which consists of the transports subsystem and the motor equations corrected for the elastic compliance of the plant. A passivity property of the flexible electromechanical system is established and an adaptive motor controller is developed which contains the rigid manipulator controller as a part. The motor controller updates all unknown rigid manipulator parameters as well as elastic parameters and ensures global asymptotic stability of the tracking errors with all signals in the system remaining bounded. Projecting of parameter estimates is used in the update law to avoid possible singularities when generating control input. Simulation results for a single-link elastic arm confirm the validity and demonstrate advantages of the proposed method.     

Feedback control design with vibration suppression for flexible air-breathing hypersonic vehicles

This paper investigates the problem of feedback control design with vibration suppression for a flexible air-breathing hypersonic vehicle （FAHV）. FAHV includes intricate coupling between the engine and flight dynamics, as well as complex interplay between flexible and rigid modes, which results in an intractable system for the control design. In this paper, a longitudinal model, which is described by a coupled system of ordinary differential equations （ODEs） and partial differential equations （PDEs）, is adopted. Firstly, a linearized ODE model for the rigid part is established around the trim condition, while vibration of the fuselage is described by PDEs. Secondly, based on the Lyapunov direct method, a control law via ODE state feedback and PDE boundary output feedback is designed for the system such that the closed-loop exponential stability is ensured. Finally, simulation results are given to illustrate the effectiveness of the proposed design method.     

Controller design for flexible structure vibration suppression with robustness to contacts

Model-based feedback control of vibration in flexible structures can be complicated by the possibility that interaction with an external body occurs. If not accounted for, instability or poor performance may result. In this paper, a method is proposed for achieving robust vibration control of flexible structures under contact. The method uses robust linear state feedback, coupled with a state estimation scheme utilizing contact force measurement. Uncertain contact characteristics are modelled by a sector-bounded non-linear function, such that state feedback gains can be synthesized using a matrix inequality formulation of the Popov stability criterion. A separation theorem is used to establish a robust H₂ cost bound for the closed loop system. Experimental results from a multi-mode flexible structure testbed confirm that vibration attenuation and stability can be maintained over a broad range of contact characteristics, in terms of compliance and clearance.     

Dynamic active impedance for vibration suppression of Large Space Structures

This paper approaches the control of Large Space Structures (LSS) by modulating the impedance of a joint to obtain desired vibration suppression. The suppression of several vibration modes cannot be done efficiently with a constant gain control system, i.e. a constant joint impedance. A dynamic active impedance controller is required and is proposed herein for this purpose. The method is applied to a flexible beam which is modelled by the Euler-Bernoulli equation. The experimental set-up and its operation can emulate a typical slew manoeuvre about a fixed axis. The boundary conditions for the beam in this case are defined for a servomotor at one end and a free condition at the other end. The beam parameters are experimentally identified for the first three modes of vibration. Active impedances are determined separately for the rigid mode and the first three modes of vibration using a pole placement method. The four different active impedances are realized using gain scheduling while transitions between gains follow a cubic polynomial of time. The duration of application of each impedance is determined based on their respective settling time. Preliminary experiments establish the minimum duration for each transition from one active impedance to another in suppressing beam vibrations.     

基于DSP/FPGA的反步法阻抗控制柔性关节机械臂

针对柔性关节机械臂与环境接触时的柔顺控制问题,提出一种反步法阻抗控制方法,并基于李雅普诺夫稳定性理论证明了控制器的稳定性.该方法是在建立柔性关节机器人模型的基础上,将李雅普诺夫函数选取与控制器设计相结合的一种回归设计方法.它从系统的最低阶次微分方程开始,逐步设计满足要求的虚拟控制,最终设计出真正的控制器.轨迹跟踪和阻抗控制实验结果表明,该方法是有效而可行的.     

Adaptive input shaping for single-link flexible manipulators using an algebraic identification

This work proposes an adaptive control scheme applied to single link-flexible manipulators, which combines a feedback controller of the joint angle with an adaptive input shaper updated by an algebraic non-asymptotic identification. The feedback controller is designed to guarantee trajectory tracking of the joint angle, simplifying thus the input shaper, which can be designed for the arm dynamics only. The input shaper is updated by an algebraic identification of the natural frequency corresponding to the first vibration mode of the arm. In addition, the influence of the assumptions adopted to derive the algebraic identification on the performance of the estimation is studied. Finally, the proposed adaptive control strategy is implemented in practice.     

MEMS-based multi-modal vibration energy harvesters for ultra-low power autonomous remote and distributed sensing

Microsystem Technologies - In this contribution, we discuss the implementation of a novel microelectromechanical-systems (MEMS)-based energy harvester (EH) concept within the technology platform...     

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.     

Integrated topology optimization and optimal control for vibration suppression in structural design

This paper presents a topology design methodology for structures with active vibration control. The methodology takes into account the structural effect of the control forces and includes the modal control design. Location points for the actuation forces are chosen a priori. Structural topology optimization is used for distributing material on a fixed domain, using continuum finite element discretization for the static and free vibration analyses. Optimal control for transient response in modal space is used to derive the control force. The cost function for the optimization combines the strain energy and the control energy. Results of the numerical simulations validates the proposed methodology.     

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     

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.