Model reference adaptive impedance control in Cartesian coordinates for physical human–robot interaction

In this paper, a nonlinear model reference adaptive impedance controller is proposed and tested. The controller provides asymptotic tracking of a reference impedance model for the robot end-effector in Cartesian coordinates applicable to rehabilitation robotics or any other human–robot interactions such as haptic systems. The controller uses the parameters of a desired stable reference model which is the target impedance for the robot’s end-effector. It also considers uncertainties in the model parameters of the robot. The asymptotic tracking is proven using Lyapunov stability theorem. Moreover, the adaptation law is proposed in joint space for reducing the complexity of its calculations; however, the controller and the stability proof are all presented in Cartesian coordinates. Using simulations and experiments on a two DOFs robot, the effectiveness of the proposed controller is investigated.     

On the Passivity-Based Impedance Control of Flexible Joint Robots

In this paper, a novel type of impedance controllers for flexible joint robots is proposed. As a target impedance, a desired stiffness and damping are considered without inertia shaping. For this problem, two controllers of different complexity are proposed. Both have a cascaded structure with an inner torque feedback loop and an outer impedance controller. For the torque feedback, a physical interpretation as a scaling of the motor inertia is given, which allows to incorporate the torque feedback into a passivity-based analysis. The outer impedance control law is then designed differently for the two controllers. In the first approach, the stiffness and damping terms and the gravity compensation term are designed separately. This outer control loop uses only the motor position and velocity, but no noncollocated feedback of the joint torques or link side positions. In combination with the physical interpretation of torque feedback, this allows us to give a proof of the asymptotic stability of the closed-loop system based on the passivity properties of the system. The second control law is a refinement of this approach, in which the gravity compensation and the stiffness implementation are designed in a combined way. Thereby, a desired static stiffness relationship is obtained exactly. Additionally, some extensions of the controller to viscoelastic joints and to Cartesian impedance control are given. Finally, some experiments with the German Aerospace Center (DLR) lightweight robots verify the developed controllers and show the efficiency of the proposed control approach.     

A novel contour error compensator for 3‐PRPS platform

Using a mathematical model to represent the nonlinear characteristics in dynamics of robot manipulators is rather difficult. To reduce the Cartesian space contour error, this study presents a novel contour error compensator influenced by the parameter and unstructured uncertainties in robot manipulators. The proposed compensator is based on the strategy of a Cartesian space cross‐coupled control and the transform relations between Cartesian space and joint space. In addition, the joint space compensated control effort derives reducing the Cartesian space contour error. Consequently, the contour error can be reduced via the theoretical analysis. Moreover, a PC based, 3‐PRPS platform control system is constructed to closely examine the effects of the controller. Experiment results indicate that the controller can reduce the contour error as expected. Furthermore, the forward and the inverse kinematics are derived, along with the forward kinematics solved using the numerical method. The work space of the platform is also described in a three‐dimensional Cartesian space. © 2000 John Wiley & Sons, Inc.     

地面装调的空间机械臂在空间应用时的自适应鲁棒控制

针对空间机械臂在轨操控过程中,重力加速度不同于地面装调阶段的重力加速度,会随着空间位置的改变而变化的问题.本文提出了一种自适应鲁棒控制策略,用于空间机械臂的末端控制,从而使在地面重力条件下装调好的空间机械臂能够在空间微重力条件下实现在轨操控任务.通过分析重力项对空间机械臂轨迹跟踪控制的影响,设计自适应律在线估计重力加速度,从而得到重力项的估计,系统的不确定性通过鲁棒控制器来补偿.基于李雅普诺夫理论证明了闭环系统的稳定性.仿真结果表明,在地面装调阶段的重力环境下和空间应用阶段的微重力环境下,该控制器对空间机械臂的末端控制均能达到较高的轨迹跟踪精度,具有重要的工程应用价值.     

考虑重力影响的空间机械臂轨迹跟踪滑模控制

针对空间机械臂由地面装调到空间应用过程中重力环境发生变化的问题,使用滑模控制器对空间机械臂进行控制,通过将配置特殊的非线性结构-fal函数引入趋近律的设计中,提出一种新的基于趋近律的滑模控制方法,并基于李亚普诺夫理论证明了闭环系统的渐近稳定性。仿真结果表明该方法能够很好地完成不同重力环境下机械臂的轨迹跟踪控制任务,并具有较强的鲁棒性。     

不确定性自由漂浮空间机器人神经自适应控制

针对具有模型不确定性以及外部干扰下的自由漂浮空间机器人,采用一种整体逼近的神经网络自适应控制方法。该方法采用RBF神经网络对不同重力环境下系统模型的不确定项进行整体逼近,对系统的不确定项进行在线自适应学习。神经网络的逼近误差以及外界干扰由鲁棒项进行消除。该方法不依赖于系统模型,简化了控制系统的结构,在考虑重力等不确定项的情况下不用改变控制器也能进行控制,并且根据李亚普诺夫理论证明了所设计控制器使系统渐进稳定。在不同重力环境下进行了仿真,验证了控制方案的有效性。     

A Neural Network Adaptive Controller for End-effector Tracking of Redundant Robot Manipulators

In this paper we propose a neural network adaptive controller to achieve end-effector tracking of redundant robot manipulators. The controller is designed in Cartesian space to overcome the problem of motion planning which is closely related to the inverse kinematics problem. The unknown model of the system is approximated by a decomposed structure neural network. Each neural network approximates a separate element of the dynamical model. These approximations are used to derive an adaptive stable control law. The parameter adaptation algorithm is derived from the stability study of the closed loop system using Lyapunov approach with intrinsic properties of robot manipulators. Two control strategies are considered. First, the aim of the controller is to achieve good tracking of the end-effector regardless the robot configurations. Second, the controller is improved using augmented space strategy to ensure minimum displacements of the joint positions of the robot. Simulation examples are also presented to verify the effectiveness of the proposed approach.     

An Adaptive Regulator of Robotic Manipulators in the Task Space

This note addresses the problem of position control of robotic manipulators both nonredundant and redundant in the task space. A computationally simple class of task space regulators consisting of a transpose adaptive Jacobian controller plus an adaptive term estimating generalized gravity forces is proposed. The Lyapunov stability theory is used to derive the control scheme. The conditions on controller gains ensuring asymptotic stability are obtained herein in a form of simple inequalities including some information extracted from both robot kinematic and dynamic equations. The performance of the proposed control strategy is illustrated through computer simulations for a direct-drive arm of a SCARA type redundant manipulator with the three revolute kinematic pairs operating in a two-dimensional task space.     

Asynchronous control of rotation and translation for a robot vehicle

Robot arms require an ‘arm controller’ to command joint motors to achieve a coordinated motion in an external Cartesian coordinate space. In the same sense, robot vehicles require a ‘vehicle controller’ to command the motors to achieve a coordinated motion specified in terms of an external Cartesian coordinate space. This paper presents the design of a general purpose vehicle controller.

The vehicle controller is designed as a three-layer structure. The top layer is an interpreter which assures a control protocol based on asynhcronous commands and independent control of orientation and forward displacement. The middle layer is a control loop which maintins an estimate of the vehicle's position and orientation, as well as their uncertainties. The control loop generates estimates and commands translation and rotation in terms of a ‘virtual vehicle’. The bottom layer is a translator between the ‘virtual vehicle’ and whatever physical vehicle on which the controller is implemented.     

Feedback control for robotic manipulator with an uncertain Jacobian matrix

In most applications of robots, a desired path for the end‐effector is usually specified in task space such as Cartesian space. One way to move the robot along this path is to solve the inverse kinematics problem to generate the desired angles in joint space. However, it is a very time consuming task to solve the inverse kinematics problem. Furthermore, in the presence of uncertainty in kinematics, it is impossible to derive the desired joint angle from the desired end‐effector path and the Jacobian matrix of the mapping from joint space to task space. In this article, a feedback control law using an uncertain Jacobian matrix is proposed for setpoint control of robots. Sufficient conditions for the bound of the estimated Jacobian matrix and stability conditions for the feedback gains are presented to guarantee the stability and passivity of the robots. A gravity regressor with an uncertain Jacobian matrix is also proposed for gravitational force compensation when the gravitational force is uncertain. Simulation results are presented to illustrate the performance of the proposed controllers. ©1999 John Wiley & Sons, Inc.     

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.     

Operating robot manipulators through kinematic singularities using a continuously sliding mode control

Planning the motion of end-effectors of robot manipulators can be carried out more directly in the Cartesian space compared to the joint space. Yet, Cartesian paths may include singular configurations where conventional control schemes suffer from excessive joint velocities and loss of tracking accuracy. The difficulties arise because the Jacobian matrix that is used to establish a linear relation between the velocities in the task and joint spaces loses rank at singularities. The problem can be resolved by using a local second-order approximation of robot kinematics for the joint velocities, which is called Resolved Motion Quadratic Rate Control. In this article, we present a control strategy based on this approach and a recently developed variable structure control scheme. The controller receives Cartesian inputs whenever the manipulator is outside the singular domain. Otherwise, it uses resolved motion quadratic rate control to compute the required joint inputs. Numerical simulation is performed to show that the proposed control scheme provides accurate tracking of the desired motion without inducing excessive control activity when operating robot manipulators through singular configurations. © 1994 John Wiley & Sons, Inc.     

Adaptive variable structure controller of redundant robots with mobile/fixed obstacles avoidance

In this paper, a variable structure adaptive controller is proposed for redundant robot manipulators constrained by moving obstacles. The main objective of the controller is to force the model states of the robot to track those of a chosen reference model. In addition, the controller is designed directly in Cartesian space and no knowledge on the dynamic model is needed, except its structure. The parameters of the controller are adapted using adaptive laws obtained via Lyapunov stability analysis of the closed loop. The performances of the proposed controller are evaluated using a 3 DOF robot manipulator evolving in a vertical plane constrained by a mobile obstacle. The obtained results show its effectiveness compared to other tested variable structure controllers.     

Fuzzy PID control of space manipulator for both ground alignment and space applications

Considering gravity change from ground alignment to space applications, a fuzzy proportional-integral-differential (PID) control strategy is proposed to make the space manipulator track the desired trajectories in different gravity environments. The fuzzy PID controller is developed by combining the fuzzy approach with the PID control method, and the parameters of the PID controller can be adjusted on line based on the ability of the fuzzy controller. Simulations using the dynamic model of the space manipulator have shown the effectiveness of the algorithm in the trajectory tracking problem. Compared with the results of conventional PID control, the control performance of the fuzzy PID is more effective for manipulator trajectory control.     

PD manipulator controller with fuzzy adaptive gravity compensation

This paper presents a PD manipulator controller with fuzzy adaptive gravity compensation. The main idea is to use a fuzzy adaptive controller to compensate for the gravity term of the robotic manipulator. This controller is designed by using Lyapunov's stability theorem, which guarantees system stability. Simulation is implemented on a two‐link manipulator by using MATALAB and SIMULINK. The results show that this fuzzy adaptive controller makes the manipulator trajectory converge to a desired position. Compared with other proposed fuzzy adaptive manipulator controllers, the PD manipulator controller with fuzzy adaptive gravity compensation is conceptually and structurally simpler and guarantees zero position error. ©2000 John Wiley & Sons, Inc.     

基于结构光的机器人弧焊混合视觉伺服控制

A novel hybrid visual servoing control method based on structured light vision is proposed for robotic arc welding with a general six degrees of freedom robot. It consists of a position control inner-loop in Cartesian space and two outer-loops. One is position-based visual control in Cartesian space for moving in the direction of weld seam, i.e., weld seam tracking, another is image-based visual control in image space for adjustment to eliminate the errors in the process of tracking. A new Jacobian matrix from image space of the feature point on structured light stripe to Cartesian space is provided for differential movement of the end-effector. The control system model is simplified and its stability is discussed. An experiment of arc welding protected by gas CO_2 for verifying is well conducted.     

Real-time implementation of a robust adaptive controller for arobotic manipulator based on digital signal processors

Presents an approach to the design and real-time implementation of an adaptive controller for a robotic manipulator based on digital signal processors. The Texas Instruments DSP (TMS320C31) chips are used in implementing real-time adaptive control algorithms to provide enhanced motion control performance for robotic manipulators. In the proposed scheme, adaptation laws are derived from the direct model reference adaptive control principle based on the improved Lyapunov second method. The proposed adaptive controller consists of an adaptive feedforward and feedback controller and PI-type time-varying auxiliary control elements. The proposed control scheme is simple in structure, fast in computation, and suitable for real-time control. Moreover, this scheme does not require any accurate dynamic modeling nor values of manipulator parameters and payload. Performance of the proposed adaptive controller is illustrated by simulation and experimental results for an industrial robot with four joints in the joint space and Cartesian space     

模糊CMAC神经网络用于MIMO非线性系统的反馈线性化

针对一类多输入多输出（ＭＩＭＯ）连续时间非线性系统,应用模糊ＣＭＡＣ神经网络,给出一种状态反馈控制器,用于使状态反馈可线笥化的未知的非线性动态系统儿得要求的患 很弱的假设条件下,应用李雅普诺夫稳定性理论严格地证明了闭环系统内的所有信号为一致最终有界（ＵＵＢ）。     

Pose Control of a Lake Surface Cleaning Robot Using Backstepping and Polar Coordinates

In this paper, the stabilization control problem of a lake surface cleaning robot (LSCR) that is driven by a driving and steering mechanism is addressed. Since the LSCR has more degrees of freedom than the number of control inputs, its motion is subject to non-holonomic constraints. Generally, this kind of system cannot be asymptotically stabilized using a time-invariant smooth feedback controller in the Cartesian coordinates. A novel controller using the vector backstepping technique for controlling the position and orientation of the LSCR is presented. We first represent the pose of the LSCR by a polar coordinate system centered at the desired pose and transform the dynamics equation of the LSCR from the Cartesian coordinates to the polar coordinates. Then a feedback control law is derived to yield global asymptotic convergence of the position and orientation of the system to the desired values using the vectorial backstepping design scheme. We prove the asymptotic stability of the system under the control of the proposed method using the Lyapunov theory. Simulations have been carried out to demonstrate the performance of the proposed controller.     

Global PID Control of Robot Manipulators Equipped with PMSMs

This paper is concerned with PID position regulation of robot manipulators actuated by permanent magnet synchronous motors (PMSMs). We present a global asymptotic stability proof when the electric dynamics of these actuators is taken into account. Our controller is so simple that it differs from standard field oriented control (SFOC) of PMSMs in only three simple nonlinear terms that have to be added and a nonlinear PID controller which is used instead of a classical PID controller. Thus, our proposal represents the closest result to SFOC of PMSMs provided with a formal global asymptotic stability proof. We present an advancement, if modest, towards presenting a global stability proof for SFOC when used in robotics.