Noncontact impedance control for redundant manipulators

Proposes an impedance control method that can regulate a virtual impedance between a robot manipulator and external objects using visual information. The conventional impedance control method is not useful in some cases where no interaction force between the arm and its environment exists, although it is one of the most effective control methods for manipulators in contact with the environment. Using the proposed method, we can control the manipulator motion based on the virtual impedance before contact with the objects. The validity of the proposed method is verified through computer simulations and experiments using a direct-drive robot     

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.     

Neural network learning of robot arm impedance in operational space

Impedance control is one of the most effective control methods for the manipulators in contact with their environments. The characteristics of force and motion control, however, is determined by a desired impedance parameter of a manipulator's end-effector that should be carefully designed according to a given task and an environment. The present paper proposes a new method to regulate the impedance parameter of the end-effector through learning of neural networks. Three kinds of the feed-forward networks are prepared corresponding to position, velocity and force control loops of the end-effector before learning. First, the neural networks for position and velocity control are trained using iterative learning of the manipulator during free movements. Then, the neural network for force control is trained for contact movements. During learning of contact movements, a virtual trajectory is also modified to reduce control error. The method can regulate not only stiffness and viscosity but also inertia and virtual trajectory of the end-effector. Computer simulations show that a smooth transition from free to contact movements can be realized by regulating impedance parameters before a contact.     

Impedance control of a direct-drive manipulator without using force sensors

This research is concerned with impedance control of a manipulator which carries out stable contact tasks. The method controls the dynamic interaction between a robot and its environment by changing the apparent mechanical impedance of the manipulator. Conventional impedance control methods required force or torque sensors, which made the manipulator system very complex. In this paper a new method is proposed for controlling the impedance of a manipulator without using force or torque sensors. The angular velocity and angular acceleration of the manipulator joints are estimated, and by using a computer model of the manipulator, the necessary torque for each joint is calculated and applied to the joint to attain the desired impedance. The feasibility of the method is verified by surface-following experiments and collision experiments using a two-degree-of-freedom direct-drive manipulator.     

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.     

Extended impedance control using real and virtual sensors for redundant manipulators

Control of a redundant manipulator based on an impedance-control framework with multiple simultaneous control sources is described. Each control source provides a different behavior type. An application is decomposed into multiple simultaneous behaviors whose resultant behavior will provide the motion necessary to execute the task. The simultaneous control inputs are merged using impedance control to compute a resultant command to the manipulator. The task space of each behavior can have the dimensionality of the mechanism being controlled. Control of a seven-degree-of-freedom manipulator is described here with an available task space for each behavior of dimensionality seven.     

Nonlinear robust adaptive Cartesian impedance control of UAVs equipped with a robot manipulator

In this paper, a new nonlinear robust adaptive impedance controller is addressed for Unmanned Aerial Vehicles (UAVs) equipped with a robot manipulator that physically interacts with environment. A UAV equipped with a robot manipulator is a novel system that can perform different tasks instead of human being in dangerous and/or inaccessible environments. The objective of the proposed robust adaptive controller is control of the UAV and its robotic manipulator’s end-effector impedance in Cartesian space in order to have a stable physical interaction with environment. The proposed controller is robust against parametric uncertainties in the nonlinear dynamics model of the UAV and the robot manipulator. Moreover, the controller has robustness against the bounded force sensor inaccuracies and bounded unstructured modeling (nonparametric) uncertainties and/or disturbances in the system. Tracking performance and stability of the system are proved via Lyapunov stability theorem. Using simulations on a quadrotor UAV equipped with a three-DOF robot manipulator, the effectiveness of the proposed robust adaptive impedance controller is investigated in the presence of the force sensor error, and parametric and non-parametric uncertainties.     

Hierarchical control of end-point impedance and joint impedance forredundant manipulators

This paper proposes an impedance control method for redundant manipulators, which can control not only the end-point impedance using one of the conventional impedance control methods, but the joint impedance which has no effects on the end-point impedance. First, a sufficient condition for the joint impedance controller is derived. Then, the optimal controller for a given desired joint impedance is designed using the least squares method. Finally, computer simulations and experiments using a planar direct-drive robot are performed in order to confirm the validity of the proposed method     

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.     

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.     

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.     

Robot impedance control with nondiagonal stiffness

Impedance control is a widely adopted strategy to execute tasks involving interaction of a robot manipulator with the environment. The goal is to impose an end-effector dynamic behavior described by a mechanical impedance. A crucial point is the definition of the elastic contribution in the impedance equation according to the task requirements; this is achieved by a proper choice of the equivalent stiffness matrix. In the paper an energy based argument is used to derive the dynamic equation of a mechanical impedance characterized by a translational part and a rotational part. The adoption of unit quaternions to describe orientation displacements leads to a geometrically consistent definition of the stiffness in the impedance equation. Remarkably, off-diagonal elements in the equivalent stiffness matrix are considered; namely, coupling forces with orientation displacements and coupling moments with position displacements. The equilibrium and the stability of the impedance equation are discussed as well as the geometric properties of the stiffness matrix     

Impedance control with on-line neural-network compensator for robot contact tasks

In this paper, a force-tracking impedance controller with an on-line neural-network compensator is shown to be able to track a reference force in the presence of unknown environmental dynamics. The controller can be partitioned into three parts. The computed torque method is used to linearize and decouple the dynamics of a manipulator. An impedance controller is then added to regulate the mechanical impedance between the manipulator and its environment. In order to track a reference force signal, an on-line neural network is used to compensate the effect of unknown parameters of the manipulator and environment.     

Robust implementation of generalized impedance control for robot manipulators

Compliant manipulation requires the robot to follow a motion trajectory and to exert a force profile while making compliant contact with a dynamic environment. For this purpose, a generalized impedance in the task space consisting of a second-order function relating motion errors and interaction force errors is introduced such that force tracking can be achieved. Using variable structure model reaching control, the generalized impedance is realized in the presence of parametric uncertainties. The proposed control method is applied to a multi-d.o.f. robot for an assembly task of inserting a printed circuit board into an edge connector socket. It is suggested that an assembly strategy which involves a sequence of planned target generalized impedances can enable the task to be executed in a desirable manner. The effectiveness of this approach is illustrated through experiments by comparing the results with those obtained using a model-based control implementation.     

Haptic force control based on impedance/admittance control aided by visual feedback

This paper demonstrates a haptic device for interaction with a virtual environment. The force control is added by visual feedback that makes the system more responsive and accurate. There are two popular control methods widely used in haptic controller design. First, is impedance control when user motion input is measured, and then, the reaction force is fed back to the operator. The alternative method is admittance control, when forces exerted by user are measured and motion is fed back to the user. Both, impedance and admittance control are also basic ways for interacting with a virtual environment. In this paper, several experiments were performed to evaluate the suitability of force-impedance control for haptic interface development. The difference between conventional application of impedance control in robot motion control and its application in haptic interface development is investigated. Open loop impedance control methodology is implemented for static case and a general-purpose robot under open loop impedance control was developed as a haptic device, while a closed loop model based impedance control was used for haptic controller design in both static and dynamic case. The factors that could affect to the performance of a haptic interface are also investigated experimentally using parametric studies. Experimental results for 1 DOF rotational motion and 2 DOF planar translational motion systems are presented. The results show that the impedance control aided by visual feedback broaden the applicability of the haptic device and makes the system more responsive and accurate.

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.     

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.     

Design parameter evaluation based on human operation for tip mechanism of forceps manipulator using surgical robot simulation

We proposed a design method for pediatric surgical robots that evaluates the workspace and view information in computer simulator before the actual robot is developed. In this study, we investigated a suturing task in a virtual environment using forceps manipulators with different mechanical parameters. We reproduced the surgical workspace for congenital esophageal atresia and measured the working volume and invisible area to obtain suitable parameters for the suturing task. We also calculated the suitable mechanical parameters using Pareto optimal solution method and verified the mechanical parameters in Pareto optimal solution. We verified from the experimental results that there is a trade-off between the working volume and invisible area during the suturing task. Moreover, we determined from the calculation results that the mechanical design of the forceps manipulator is influenced by the invisible area during the suturing task. Finally, we confirmed that it is possible to obtain suitable parameters for surgical robots using the proposed method.     

State and Impedance Reflection Based Control Interface for Bilateral Telerobotic System with Asymmetric Delay

In this paper, we investigate state and imped-ance reflection based robust control strategy for bilateral shared telerobotic system under unsymmetrical time varying delay. Shared input for both master and slave robot is designed by combining delayed position and position-velocity signals with impedance reflection properties of the interaction between slave and environment and between human and master robot manipulator. Adaptive control algorithm is proposed to estimate the interaction properties between human and master manipulator and between slave and remote environment. Then, the delayed estimated interaction properties are reflected back to the master and slave robot manipulator to match with the estimated impedance properties of the interaction between human and remote environment. We combine robust term with adaptive control term to deal with the uncertainty associated with gravity loading vector, unmodeled dynamic and external disturbance. The stability conditions with time varying delays are derived by using Lyapunov-Krasovskii functional. Experimental results are given to demonstrate the validity of the proposed design for real-time applications.     

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.