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.     

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.     

Task-based configuration control of redundant manipulators

This article establishes new goals for redundancy resolution based on manipulator dynamics and end-effector characteristics. These goals can be accomplished by employing the recently developed configuration control approach. Redundancy resolution is achieved by controlling the joint inertia matrix or the end-effector mass matrix that affect the inertial torques or by reducing the joint torques due to gravity loading and payload. The manipulator mechanical advantage and velocity ratio are also used as performance measures to be improved by proper utilization of redundancy. Furthermore, end-effector compliance, sensitivity, and impulsive force at impact are introduced as redundancy-resolution criteria. The new goals for redundancy resolution presented in this article allow a more efficient utilization of the redundant joints based on the desired task requirements. Simple case studies using computer simulations are described for illustration.     

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.     

Data-Driven Human-Robot Interaction Without Velocity Measurement Using Off-Policy Reinforcement Learning

In this paper, we present a novel data-driven design method for the human-robot interaction (HRI) system, where a given task is achieved by cooperation between the human and the robot. The presented HRI controller design is a two-level control design approach consisting of a task-oriented performance optimization design and a plant-oriented impedance controller design. The task-oriented design minimizes the human effort and guarantees the perfect task tracking in the outer-loop, while the plant-oriented achieves the desired impedance from the human to the robot manipulator end-effector in the inner-loop. Data-driven reinforcement learning techniques are used for performance optimization in the outer-loop to assign the optimal impedance parameters. In the inner-loop, a velocity-free filter is designed to avoid the requirement of end-effector velocity measurement. On this basis, an adaptive controller is designed to achieve the desired impedance of the robot manipulator in the task space. The simulation and experiment of a robot manipulator are conducted to verify the efficacy of the presented HRI design framework.      

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.     

冗余机器人系统的自运动控制

研究冗余机器人系统的自运动控制问题，给出一种非连续切换控制算法。该算法可以在保持机器人手端任务向量不变的情况下，使关节构形收敛到期望位置。与以往的算法相比，所提出的算法可以跳出局部最小点，并使关节收敛到期望构形。对三杆平面机器人系统进行的计算机仿真证实了算法的有效性。     

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.     

Calculation of repeatable control strategies for kinematically redundant manipulators

A kinematically redundant manipulator is a robotic system that has more than the minimum number of degrees of freedom that are required for a specified task. Due to this additional freedom, control strategies may yield solutions which are not repeatable in the sense that the manipulator may not return to its initial joint configuration for closed end-effector paths. This paper compares two methods for choosing repeatable control strategies which minimize their distance from a nonrepeatable inverse with desirable properties. The first method minimizes the integral norm of the difference of the desired inverse and a repeatable inverse while the second method minimizes the distance of the null vectors associated with the desired and the repeatable inverses. It is then shown how the two techniques can be combined in order to obtain the advantages of both methods. As an illustrative example the pseudoinverse is approximated in a region of the joint space for a seven-degree-of-freedom manipulator.     

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     

Canonical parameterization of excess motor degrees of freedom withself-organizing maps

The problem of sensorimotor control is underdetermined due to excess (or "redundant") degrees of freedom when there are more joint variables than the minimum needed for positioning an end-effector. A method is presented for solving the nonlinear inverse kinematics problem for a redundant manipulator by learning a natural parameterization of the inverse solution manifolds with self-organizing maps. The parameterization approximates the topological structure of the joint space, which is that of a fiber bundle. The fibers represent the "self-motion manifolds" along which the manipulator can change configuration while keeping the end-effector at a fixed location. The method is demonstrated for the case of the redundant planar manipulator. Data samples along the self-motion manifolds are selected from a large set of measured input-output data. This is done by taking points in the joint space corresponding to end-effector locations near "query points", which define small neighborhoods in the end-effector work space. Self-organizing maps are used to construct an approximate parameterization of each manifold which is consistent for all of the query points. The resulting parameterization is used to augment the overall kinematics map so that it is locally invertible. Joint-angle and end-effector position data, along with the learned parameterizations, are used to train neural networks to approximate direct inverse functions.     

Predictive end-point trajectory control of elastic manipulators

This article presents an approach to end-point trajectory control of elastic manipulators based on the nonlinear predictive control theory. Although this approach is applicable to manipulators of general configuration, only planar flexible multi-link manipulators are considered. A predictive control law is derived by minimizing a quadratic function of the trajectory error of the end-points of each link, elastic modes, and control torques. This approach avoids the instability of the zero dynamics encountered in the controller design using feedback linearization and variable structure control techniques for end-point control. Furthermore, the derived predictive controller is robust to uncertainty in the system parameters. Simulation results are presented for a one-link flexible manipulator to show that in the closed-loop system accurate end-point trajectory control and vibration damping can be accomplished. © 1996 John Wiley & Sons, Inc.     

欠驱动冗余度空间机器人优化控制

欠驱动控制是空间技术中容错技术的重要方面.本文研究了被动关节中有制动器的欠驱动冗余度空间机器人系统的运动优化控制问题.从系统动力学方程出发,分析了欠驱动冗余度空间机器人的优化能力和控制方法;给出了主、被动关节间的耦合度指标;提出了欠驱动冗余度空间机器人系统的“虚拟模型引导控制”方法,在这种方法中采用与欠驱动机器人机构等价的全驱动机器人作为模型来规划机器人的运动,使欠驱动系统在关节空间中逼近给出的规划轨迹,实现了机器人末端运动的连续轨迹运动优化控制;通过末关节为被动关节的平面三连杆机器人进行了仿真,仿真的结果证明了提出算法的有效性.     

空间机器人最优能耗捕获目标的自适应跟踪控制

提出了一种能够引导末端执行器以期望速度跟踪目标的轨迹规划方法。该方法可以实现避障并满足关节限制要求。基于轨迹规划方法,设计了一种利用自由飘浮空间机器人跟踪与捕获章动自旋卫星的自适应控制策略。此外,该控制策略还考虑了最优能耗、测量误差和优化误差。首先,为了使执行器的跟踪误差和机械臂的能耗最小,将空间机器人的控制策略描述为一个关于关节速度、力矩和避障距离的不等式约束优化问题。然后,推导出一个系数为下三角矩阵的显式状态方程,并对目标函数进行解耦和线性化。设计了一种关节速度和力矩分段优化方法去代替传统的凸二次规划方法求解最优问题,这种方法具有较高的计算效率。最后,利用李雅普诺夫稳定性理论验证了所提控制方法的收敛性。     

Torque Optimizing Control with Singularity-Robustness for Kinematically Redundant Robots

A new control method for kinematically redundant manipulators having the properties of torque-optimality and singularity-robustness is developed. A dynamic control equation, an equation of joint torques that should be satisfied to get the desired dynamic behavior of the end-effector, is formulated using the feedback linearization theory. The optimal control law is determined by locally optimizing an appropriate norm of joint torques using the weighted generalized inverses of the manipulator Jacobian-inertia product. In addition, the optimal control law is augmented with fictitious joint damping forces to stabilize the uncontrolled dynamics acting in the null-space of the Jacobian-inertia product. This paper also presents a new method for the robust handling of robot kinematic singularities in the context of joint torque optimization. Control of the end-effector motions in the neighborhood of a singular configuration is based on the use of the damped least-squares inverse of the Jacobian-inertia product. A damping factor as a function of the generalized dynamic manipulability measure is introduced to reduce the end-effector acceleration error caused by the damping. The proposed control method is applied to the numerical model of SNU-ERC 3-DOF planar direct-drive manipulator.     

Two recurrent neural networks for local joint torque optimizationof kinematically redundant manipulators

This paper presents two neural network approaches to real-time joint torque optimization for kinematically redundant manipulators. Two recurrent neural networks are proposed for determining the minimum driving joint torques of redundant manipulators for the eases without and with taking the joint torque limits into consideration, respectively. The first neural network is called the Lagrangian network and the second one is called the primal-dual network. In both neural-network-based computation schemes, while the desired accelerations of the end-effector for a specific task are given to the neural networks as their inputs, the signals of the minimum driving joint torques are generated as their outputs to drive the manipulator arm. Both proposed recurrent neural networks are shown to be capable of generating minimum stable driving joint torques. In addition, the driving joint torques computed by the primal-dual network are shown never exceeding the joint torque limits.     

基于末端圆周运动的可变形臂旋量参数快速标定算法

针对家庭服务机器人工作的非结构化环境,设计了一种可以根据任务需求相应地调整连杆形状的可变形操作臂．该操作臂工作空间易于拓展、灵活度较高且成本低廉．但臂形的改变也给操作臂的建模和控制带来了困难．首先,可变形臂的运动学参数发生了巨大且无规律的变化,使得固结在连杆上的坐标系脱离连杆本体,变得不可测量．其次,为适应不同任务需求,可变形臂的连杆形状需要经常改变,而传统标定方法往往追求更高的标定精度而非标定效率,因而需要开发一种耗时较短的标定方法．最后,可变形臂的标定方法必须简便而易于在家庭环境中实施．针对上述问题,本文提出了一种基于末端圆周运动的可变形臂旋量参数快速标定算法．对于任意一个旋转关节,单独转动该关节时,操作臂末端的轨迹形成了一个圆弧,且该关节轴垂直于圆弧所在平面（旋转平面）并经过圆弧的圆心．基于该性质,利用随机抽样一致性（RANSAC）算法和最小二乘算法来拟合操作臂末端轨迹,从而获取操作臂的旋量参数初值．在获取到初值的基础上,提出了一种扩展卡尔曼滤波（EKF）算法进一步优化旋量参数,提高标定精度．仿真和实验结果验证了本文方法的有效性．     

Inverse kinematics of planar redundant manipulators via virtual links with configuration index

This article presents a new method for generating inverse kinematic solutions for planar manipulators with large redundancy (hyper-redundant manipulators). The proposed method starts by decomposing a planar redundant manipulator into a series of local planar arms that are either 2-link or 3-link manipulator modules, and connecting the conjunction points between them with virtual links. The manipulator then can be handled by a simple virtual link system, which may be conveniently divided into non-singular and singular cases depending on its configuration. When the virtual link system is no longer effective due to a singular configuration, the displacement of the end-effector is then allocated to virtual links according to a displacement distribution criterion. A dexterity index called the “configuration index” distinguishes the non-singular and singular cases. The concept of virtual link is shown by computer simulations to be simple and effective for the inverse kinematics of a planar hyper-redundant manipulator with a discrete model. In particular, it can be applied to solving the inverse kinematics of a SCARA-type spatial redundant manipulator whose redundancy is included in its planar mechanism. © 1994 John Wiley & Sons, Inc.     

Visual Motor Control of a 7 DOF Robot Manipulator Using Function Decomposition and Sub-Clustering in Configuration Space

This paper deals with real-time implementation of visual-motor control of a 7 degree of freedom (DOF) robot manipulator using self-organized map (SOM) based learning approach. The robot manipulator considered here is a 7 DOF PowerCube manipulator from Amtec Robotics. The primary objective is to reach a target point in the task space using only a single step movement from any arbitrary initial configuration of the robot manipulator. A new clustering algorithm using Kohonen SOM lattice has been proposed that maintains the fidelity of training data. Two different approaches have been proposed to find an inverse kinematic solution without using any orientation feedback. In the first approach, the inverse Jacobian matrices are learnt from the training data using function decomposition. It is shown that function decomposition leads to significant improvement in accuracy of inverse kinematic solution. In the second approach, a concept called sub-clustering in configuration space is suggested to provide multiple solutions for the inverse kinematic problem. Redundancy is resolved at position level using several criteria. A redundant manipulator is dexterous owing to the availability of multiple configurations for a given end-effector position. However, existing visual motor coordination schemes provide only one inverse kinematic solution for every target position even when the manipulator is kinematically redundant. Thus, the second approach provides a learning architecture that can capture redundancy from the training data. The training data are generated using explicit kinematic model of the combined robot manipulator and camera configuration. The training is carried out off-line and the trained network is used on-line to compute the joint angle vector to reach a target position in a single step only. The accuracy attained is better than the current state of art.     

Nonlinear control with end-point acceleration feedback for a two-link flexible manipulator: Experimental results

Experimental results for end-point positioning of multi-link flexible manipulators through end-point acceleration feedback are presented in this article. The advocated controllers are implemented on a two-link flexible arm developed at the Control/Robotics Research Laboratory at Polytechnic University. The advocated approach in this article is based on a two-stage control design. The first stage is a nonlinear (1) feedback linearizing controller corresponding to the rigid body motion of the manipulator. Because this scheme does not utilize any feedback from the end-point motion, significant vibrations are induced at the end effector. To this effect, and to enhance the robustness of the closed-loop dynamics to parameter variations, the inner loop is augmented with an outer loop based on a linear output LQR design that utilizes an end-point acceleration feedback. The forearm of the manipulator is significantly more flexible as compared with the upper arm. Experimental and simulation results validate the fact that the end-effector performance is significantly better with the proposed (1) feedback linearizing control as compared with the linear independent joint PD control. In addition, the nonlinear control offers other advantages in terms of smaller and smoother actuator torques and reducing the effects of nonlinearities. Close conformation between simulation and experimental results validates the accuracy of the model.