An estimation method of end-point impedance based on bilateral control system

ABSTRACT

This paper aims at developing an estimation method of end-point impedance. Human operators are constantly changing their end-point impedance for adapting to the surrounded environment and executing some complicated tasks, and it is highly meaningful to investigate these variations for the further understanding of human motion. Most of the conventional researches, however, have considered non-contact-point impedance or tasks that is only holding the vibrated sticks due to the experimental constraints. This paper proposes the estimation method of end-point impedance by using bilateral control system. The extra signal is added to the force controller for the impedance estimation. In addition, the effect of the bilateral controller is estimated and removed from the impedance estimation process for securing the applicability of moving tasks. The proposed method was validated through simulations and an experiment. The experimental result showed that the end-point stiffness can be estimated properly even if the operator robot was moving and changed its end-point impedance.     

Multi-point impedance control for redundant manipulators

This paper proposes an impedance control method called the multi-point impedance control (MPIC) for redundant manipulators. The method can not only control end-effector impedance, but also regulate impedances of several points on the links of the manipulator, which are called virtual end-point impedances, utilizing arm redundancy. Two approaches for realizing the MPIC are presented. In the first approach, controlling the end-effector impedance and the virtual end-point impedances are considered as the tasks with the same level, and the joint control law developed in this approach can realize the closest impedances of the multiple points, including the end-effector and the virtual end-points to the desired ones in the least squared sense. On the other hand, in the second approach, controlling the end-effector impedance is considered the most important task, and regulating the impedances of the virtual end-points is considered as a sub-task. Under the second approach, the desired end-effector impedance can be always realized since the joint control torque for the regulation of the virtual end-point impedances is designed in such a way that it has no effect on the end-effector motion of the manipulator. Simulation experiments are performed to confirm the validity and to show the advantages of the proposed method.     

Online learning of virtual impedance parameters in non-contact impedance control using neural networks

Impedance control is one of the most effective methods for controlling the interaction between a manipulator and a task environment. In conventional impedance control methods, however, the manipulator cannot be controlled until the end-effector contacts task environments. A noncontact impedance control method has been proposed to resolve such a problem. This method on only can regulate the end-point impedance, but also the virtual impedance that works between the manipulator and the environment by using visual information. This paper proposes a learning method using neural networks to regulate the virtual impedance parameters according to a given task. The validity of the proposed method was verified through computer simulations and experiments with a multijoint robotic manipulator.     

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.     

Optimal impedance via model predictive control for robot-aided rehabilitation

This paper proposes an optimal impedance controller for robot-aided rehabilitation of walking, aiming to increase the patient’s activity during the therapy. In an online procedure, the joint torques produced by the patient during the gait is estimated using the generalized momenta-based disturbance observer and the Extended Kalman filter algorithm. At the same time, a model predictive control is performed to obtain the instantaneous optimal stiffness parameters of the robot’s impedance controller, trying to maximize the patient’s active participation by increasing his/her joint torques. In this feasibility study, experiments with a healthy subject, considering a modular lower limb exoskeleton and a set of user’s behaviors, are performed to evaluate the proposed controller. The results show the robot stiffness converges to a value which increases the user’s active participation.     

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.     

Direct adaptive impedance control of robot manipulators

This article presents an adaptive scheme for controlling the end-effector impedance of robot manipulators. The proposed control system consists of three subsystems: a simple “filter” that characterizes the desired dynamic relationship between the end-effector position error and the end-effector/environment contact force, an adaptive controller that produces the Cartesian-space control input required to provide this desired dynamic relationship, and an algorithm for mapping the Cartesian-space control input to a physically realizable joint-space control torque. The controller does not require knowledge of either the structure or the parameter values of the robot dynamics and is implemented without calculation of the robot inverse kinematic transformation. As a result, the scheme represents a general and computationally efficient approach to controlling the impedance of both nonredundant and redundant manipulators. Furthermore, the method can be applied directly to trajectory tracking in free-space motion by removing the impedance filter. Computer simulation results are given for a planar four degree-of-freedom redundant robot under adaptive impedance control. These results demonstrate that accurate end-effector impedance control and effective redundancy utilization can be achieved simultaneously by using the proposed controller.     

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.     

基于无模型自适应的外骨骼式上肢康复机器人主动交互训练控制方法

设计了一种基于无模型自适应的外骨骼式上肢康复机器人主动交互训练控制方法.在机器人与人体上肢接触面安装力传感器采集人机交互力矩信息作为量化的主动运动意图,设计了一种无模型自适应滤波算法使交互力矩变得平滑而连贯;以人机交互力矩为输入,综合考虑机器人末端点与参考轨迹的相对位置和补偿力的信息,设计了人机交互阻抗控制器,用于调节各关节的给定目标速度;设计了将无模型自适应与离散滑模趋近律相结合的速度控制器完成机器人各关节对目标速度的跟踪.仿真结果表明,该控制方法可以实现外骨骼式上肢康复机器人辅助患者完成主动交互训练的功能.通过调节人机交互阻抗控制器的相应参数,机器人可以按照患者的运动意图完成不同的主动交互训练任务,并在运动出现偏差时予以矫正.控制器在设计实现过程中不要求复杂准确的动力学建模和参数识别,并有一定的抗干扰性和通用性.     

Adaptive impedance control of a variable stiffness actuator

This paper proposes an optimal impedance control method for a variable stiffness actuator (VSA), in which a variable stiffness mechanism and an actuator are aligned in series. First, we introduce a circuit expression of the robotic system and provide a unified framework to determine an optimal index of robots driven by VSAs, irrespective of the presence or absence of the environment. Next, we design a torque controller for a one-degree-of-freedom (DOF) robot and find the optimal condition of the stiffness in the VSA for a given task. Then, we design a stiffness control law for the VSA exploiting the intrinsic indivisible property between motion and passive impedance. This stiffness control law adaptively tunes the passive stiffness to minimize the energy consumption without defining any explicit desired impedance, which is usually required in impedance controllers. The stability of the closed loop system is proved using Lyapunov’s analysis. Simulations and experimental results validate the effectiveness of the proposed method and the robustness in response to parameter changes.     

Extended impedance control of redundant manipulators based on weighted decomposition of joint space

In this work, impedance control approach based on an extended task space formulation is addressed to control the kinematically redundant manipulators. By defining a weighted inner product in joint space, a minimal parameterization of the null space is achieved, and we can visualize the null space motion explicitly. Moreover, it is shown that careful choice of the weighting matrix gives physically consistent and inertially decoupled dynamics. By augmenting this minimal null motion parameter with a forward kinematic relation, a new extended task space formulation can be obtained. Based on this formulation, we propose two control methods, a kinematically decomposed impedance controller and an inertially decoupled impedance controller, to control the motion of the end-effector as well as the internal motion expanding the conventional impedance control. We also show the relationship with the previous dynamic controllers of a redundant manipulator. Some numerical simulations are given to demonstrate the performance of the proposed control methods. © 1998 John Wiley & Sons, Inc.     

Model reference adaptive impedance control for physical human-robot interaction

This paper presents a novel enhanced human-robot interaction system based on model reference adaptive control. The presented method delivers guaranteed stability and task performance and has two control loops. A robot-specific inner loop, which is a neuroadaptive controller, learns the robot dynamics online and makes the robot respond like a prescribed impedance model. This loop uses no task information, including no prescribed trajectory. A task-specific outer loop takes into account the human operator dynamics and adapts the prescribed robot impedance model so that the combined human-robot system has desirable characteristics for task performance. This design is based on model reference adaptive control, but of a nonstandard form. The net result is a controller with both adaptive impedance characteristics and assistive inputs that augment the human operator to provide improved task performance of the human-robot team. Simulations verify the performance of the proposed controller in a repetitive point-to-point motion task. Actual experimental implementations on a PR2 robot further corroborate the effectiveness of the approach.     

Whole-body impedance control of wheeled mobile manipulators

Humanoid service robots in domestic environments have to interact with humans and their surroundings in a safe and reliable way. One way to manage that is to equip the robotic systems with force-torque sensors to realize a physically compliant whole-body behavior via impedance control. To provide mobility, such robots often have wheeled platforms. The main advantage is that no balancing effort has to be made compared to legged humanoids. However, the nonholonomy of most wheeled systems prohibits the direct implementation of impedance control due to kinematic rolling constraints that must be taken into account in modeling and control. In this paper we design a whole-body impedance controller for such a robot, which employs an admittance interface to the kinematically controlled mobile platform. The upper body impedance control law, the platform admittance interface, and the compensation of dynamic couplings between both subsystems yield a passive closed loop. The convergence of the state to an invariant set is shown. To prove asymptotic stability in the case of redundancy, priority-based approaches can be employed. In principle, the presented approach is the extension of the well-known and established impedance controller to mobile robots. Experimental validations are performed on the humanoid robot Rollin’ Justin. The method is suitable for compliant manipulation tasks with low-dimensional planning in the task space.     

Robust impedance control of robot manipulators using differential equations as universal approximator

This paper presents a robust impedance controller for robot manipulators using function approximation techniques (FATs). Recently, some FAT-based robust impedance control approaches have been presented using Fourier series expansion or Legendre polynomials for uncertainty estimation. However, the dimensions of regressor matrices in these approaches are relatively large. This problem becomes hypersensitive especially for higher degree of freedom robot manipulators. In this paper, a simpler and less computational FAT-based robust controller is presented without considering discontinuous nonlinearities. It is assumed that the lumped uncertainty can be modelled by a linear differential equation with unknown coefficients. Then, using the Stone–Weierstrass theorem, it is verified that these differential equations are universal approximators. The advantage of the proposed controller in comparison with previous related works is reducing the dimensions of regressor matrices. Simulation results on a Puma560 robot manipulator indicate the efficiency of the proposed method.     

Impedance control of industrial robots

Manipulation fundamentally requires the manipulator to be mechanically coupled to the object being manipulated. A consideration of the physical constraints imposed by dynamic interaction shows that control of a vector quantity such as position or force is inadequate and that control of the manipulator impedance is necessary. Techniques for planning and control of manipulator behavior are presented which result in a unified approach to target acquisition, obstable avoidance, kinematically constrained motion, and dynamic interaction. A feedback control algorithm for implementing a cartesian end-point impedance on a nonlinear manipulator is presented. The modulation of end-point impedance independent of feedback is also considered. A method for choosing the impedance appropriate to a task using optimization theory is discussed.     

Cooperative modalities in robotic tele-rehabilitation using nonlinear bilateral impedance control

A nonlinear model reference adaptive bilateral impedance controller is proposed that can accommodate various cooperative tele-rehabilitation modes for patient–therapist interaction using a multi-DOF tele-robotic system. In this controller, two reference impedance models are implemented for the master and slave robots using new model reference adaptive control laws for the nonlinear bilateral teleoperation system. “Hand-over-hand” and “adjustable-flexibility” are two modes of patient–therapist cooperation that are realized using the proposed strategy. The Lyapunov-based stability proof guarantees the patient’s and the therapist’s safety during the cooperation and interaction with robots, even in the presence of modeling uncertainties of the multi-DOF teleoperation system. The performance of the proposed bilateral impedance controller is experimentally investigated for upper-limb tele-rehabilitation in the two mentioned cooperation modes.     

Variable stiffness control for SEAs in rehabilitation training

ABSTRACT

Series Elastic Actuator (SEA) with both security and high performance is used extensively for rehabilitation robots with physical interaction. Human joints applied for motion therapy show variable stiffness properties during the process of rehabilitation training. When using robot to do motion therapy, impedance control is one of the most popular methods for rehabilitation works. However, impedance control with constant stiffness usually produces rigidity in the body due to natural changes of muscle tension. It may seriously restrict the achievement of excellent training effect and may even cause harm to patients. In this study, a novel real-time parallel variable stiffness control method is proposed based on cascade impedance controller. First, an SEA joint is analyzed and the limit factor of the impedance frequency is discussed. Subsequently, cascade impedance controller scheme with stiffness adjustment regulator is utilized to achieve the stiffness and the passivity of the controller is proved. Based on the scheme, a novel stiffness self-adjustment algorithm is presented which can regulate the stiffness by impedance approximation. Finally, simulation and experimental results are provided to validate the stiffness adjustment method during the rehabilitation process.     

Robot impedance control and passivity analysis with inner torque and velocity feedback loops

Impedance control is a well-established technique to control interaction forces in robotics. However, real implementations of impedance control with an inner loop may suffer from several limitations. In particular, the viable range of stable stiffness and damping values can be strongly affected by the bandwidth of the inner control loops (e.g., a torque loop) as well as by the filtering and sampling frequency. This paper provides an extensive analysis on how these aspects influence the stability region of impedance parameters as well as the passivity of the system. This will be supported by both simulations and experimental data. Moreover, a methodology for designing joint impedance controllers based on an inner torque loop and a positive velocity feedback loop will be presented. The goal of the velocity feedback is to increase (given the constraints to preserve stability) the bandwidth of the torque loop without the need of a complex controller.     

Impact reduction for redundant manipulators using augmented impedance control

In this article, the problem of controlling redundant manipulators to reduce collision impact effects is considered, and an augmented kinematics and impedance control scheme is proposed for its solution. The proposed scheme achieves satisfactory performance by minimizing the magnitudes of impulsive forces as well as reducing rebound effects of the end-effector. In the proposed control scheme, kinematic redundancy is resolved using an augmented kinematics approach where the augmentation of the Jacobian matrix is based on an impact model derived using the Cartesian-space dynamic model of the manipulator. The proposed impact controller uses a simplified impedance control scheme aimed at reducing impulsive forces as well as rebound effects. The performance of the proposed controller is illustrated by computer simulations. © 2995 John Wiley & Sons, Inc.     

Planning and controlling cooperating robots through distributed impedance

This article presents distributed impedance as a new approach for multiple robot system control. In this approach, each cooperating manipulator is controlled by an independent impedance controller. In addition, along selected degrees of freedom, force control is achieved through an external loop, to improve control of the object's internal loading. Extensive stability analysis is performed, based on a realistic model that includes robot impedance and object dynamics. Experiments are performed using two cooperating industrial robots holding an object through point contacts. Force and position control actions are suitably dispatched to achieve both internal loading control and object position control. Individual impedance parameters are specified according to the theoritical stability criterion. The performance of the system is demonstrated for transportation and contact tasks. © 2002 Wiley Periodicals, Inc.