Learning from hint for the conservative motion of the constrained industrial redundant manipulators

A neural network (NN)-based kinematic inversion of industrial redundant arms is developed in this paper to conserve the joint configuration in cyclic trajectories. In the developed approach, the Widrow–Hoff NN with an online adaptive learning algorithm derived by applying Lyapunov approach is introduced. Since this kinematic inversion has an infinite number of joint angle vectors, a fuzzy neural network system is designed to provide an approximate value for that vector. Feeding this vector as an additional hint input vector to the NN limits and guides the output of the NN within the self-motion of the manipulator. The derivation of the candidate Lyapunov function, which is designed to achieve the joint configurations conservation in addition to the joint limits avoidance, leads to a computationally efficient online learning algorithm of the NN. Simulations are conducted for the PA-10 redundant manipulator to bear out the efficacy of the developed approach for tracking closed trajectories.     

Kinematic control of a redundant manipulator using an inverse-forward adaptive scheme with a KSOM based hint generator

This paper proposes an online inverse-forward adaptive scheme with a KSOM based hint generator for solving the inverse kinematic problem of a redundant manipulator. In this approach, a feed-forward network such as a radial basis function (RBF) network is used to learn the forward kinematic map of the redundant manipulator. This network is inverted using an inverse-forward adaptive scheme until the network inversion solution guides the manipulator end-effector to reach a given target position with a specified accuracy. The positioning accuracy, attainable by a conventional network inversion scheme, depends on the approximation error present in the forward model. But, an accurate forward map would require a very large size of training data as well as network architecture. The proposed inverse-forward adaptive scheme effectively approximates the forward map around the joint angle vector provided by a hint generator. Thus the inverse kinematic solution obtained using the network inversion approach can take the end-effector to the target position within any arbitrary accuracy.In order to satisfy the joint angle constraints, it is necessary to provide the network inversion algorithm with an initial hint for the joint angle vector. Since a redundant manipulator can reach a given target end-effector position through several joint angle vectors, it is desirable that the hint generator is capable of providing multiple hints. This problem has been addressed by using a Kohonen self organizing map based sub-clustering (KSOM-SC) network architecture. The redundancy resolution process involves selecting a suitable joint angle configuration based on different task related criteria.The simulations and experiments are carried out on a 7 DOF PowerCube? manipulator. It is shown that one can obtain a positioning accuracy of 1 mm without violating joint angle constraints even when the forward approximation error is as large as 4 cm. An obstacle avoidance problem has also been solved to demonstrate the redundancy resolution process with the proposed scheme.     

Neural network-based adaptive controller design of roboticmanipulators with an observer

A neural network (NN)-based adaptive controller with an observer is proposed for the trajectory tracking of robotic manipulators with unknown dynamics nonlinearities. It is assumed that the robotic manipulator has only joint angle position measurements. A linear observer is used to estimate the robot joint angle velocity, while NNs are employed to further improve the control performance of the controlled system through approximating the modified robot dynamics function. The adaptive controller for robots with an observer can guarantee the uniform ultimate bounds of the tracking errors and the observer errors as well as the bounds of the NN weights. For performance comparisons, the conventional adaptive algorithm with an observer using linearity in parameters of the robot dynamics is also developed in the same control framework as the NN approach for online approximating unknown nonlinearities of the robot dynamics. Main theoretical results for designing such an observer-based adaptive controller with the NN approach using multilayer NNs with sigmoidal activation functions, as well as with the conventional adaptive approach using linearity in parameters of the robot dynamics are given. The performance comparisons between the NN approach and the conventional adaptation approach with an observer is carried out to show the advantages of the proposed control approaches through simulation studies     

Reaching with multi-referential dynamical systems

We study a reaching movement controller for a redundant serial arm manipulator, based on two principles believed to be central to biological motion control: multi-referential control and dynamical system control. The resulting controller is based on two concurrent dynamical systems acting on different, yet redundant variables. The first dynamical system acts on the end-effector location variables and the second one acts on the joint angle variables. Coherence constraints are enforced between those two redundant representations of the movement and can be used to modulate the relative influence of each dynamical system. We illustrate the advantages of such a redundant representation of the movement regarding singularities and joint angle avoidance.     

Repetitive motion of redundant robots planned by three kinds of recurrent neural networks and illustrated with a four-link planar manipulator’s straight-line example

In this paper, a dual neural network, LVI (linear variational inequalities)-based primal-dual neural network and simplified LVI-based primal-dual neural network are presented for online repetitive motion planning (RMP) of redundant robot manipulators (with a four-link planar manipulator as an example). To do this, a drift-free criterion is exploited in the form of a quadratic performance index. In addition, the repetitive-motion-planning scheme could incorporate the joint physical limits such as joint limits and joint velocity limits simultaneously. Such a scheme is finally reformulated as a quadratic program (QP). As QP real-time solvers, the aforementioned three kinds of neural networks all have piecewise-linear dynamics and could globally exponentially converge to the optimal solution of strictly-convex quadratic-programs. Furthermore, the neural-network based RMP scheme is simulated based on a four-link planar robot manipulator. Computer-simulation results substantiate the theoretical analysis and also show the effective remedy of the joint angle drift problem of robot manipulators.     

Fault-tolerant motion planning and control of redundant manipulator

One important issue in the motion planning of a kinematic redundant manipulator is fault tolerance. In general, if the motion planner is fault tolerant, the manipulator can achieve the required path of the end-effector even when its joint fails. In this situation, the contribution of the faulty joint to the end-effector is required to be compensated by the healthy joints to maintain the prescribed end-effector trajectory. To achieve this, this paper proposes a fault-tolerant motion planning scheme by adding a simple fault-tolerant equality constraint for the faulty joint. Such a scheme is then unified into a quadratic program (QP), which incorporates joint-physical constraints such as joint limits and joint-velocity limits. In addition, a numerical computing solver based on linear variational inequalities (LVI) is presented for the real-time QP solving. Simulative studies and experimental results based on a six degrees-of-freedom (DOF) redundant robot manipulator with variable joint-velocity limits substantiate the effectiveness of the proposed fault-tolerant scheme and its solution.     

Bi-criteria Velocity Minimization of Robot Manipulators Using a Linear Variational Inequalities-Based Primal-Dual Neural Network and PUMA560 Example

In this paper, to diminish discontinuity points arising in the infinity-norm velocity minimization scheme, a bi-criteria velocity minimization scheme is presented based on a new neural network solver (i.e., a primal-dual neural network based on linear variational inequalities (LVI)). Such a kinematic control scheme of redundant manipulators can incorporate joint physical limits such as joint limits and joint velocity limits simultaneously. Moreover, the presented kinematic control scheme can be formulated as a quadratic programming (QP) problem. As a real-time QP solver, the LVI-based primal-dual neural network is established with a simple piecewise linear structure and higher computational efficiency. Computer simulations performed based on a PUMA560 manipulator are presented to illustrate the validity and advantages of such a bi-criteria neural control scheme for redundant robots.     

Position control of two-arm manipulators for coordinated point-to-point motion

A trajectory planning and motion control algorithm is; presented for the point-to-point (PTP) motion of two-arm manipulators cooperating on a task. The proposed method considers the multi-arm manipulator as a system when formulating its kinematic model and obtains a global solution to the system, as opposed to individual arm solutions. For PTP motion control between two arm configurations, a simple trajectory is first assumed by defining joint velocity profiles and maximum allowable task space errors between the two end effectors of the manipulator. The task space errors during the motion are then continuously monitored to take corrective action when necessary to prevent those errors from exceeding the given tolerance limits. The main objective of this method is to reduce the number of inverse kinematics solutions during the real-time control of the two-arm system. The algorithm is illustrated by a numerical example for an eight degree-of-freedom kinematically redundant planar two-arm system.     

Static modeling and control of redundant manipulators

This paper develops unified static models for control of a redundant manipulator. We introduce the Premultiplier Diagram to describe the static behavior of a redundant manipulator. This diagram provides insight into the algebra and physics related to redundant manipulators. We derive redundancy expressions for the joint displacement, joint torque and joint stiffness matrix. These redundancy expressions are composed of a particular (net) part and a homogeneous (null) part. Based on the orthogonality property between the net and the null components, we propose an extension of the stiffness control scheme for redundant manipulators. We also show how the decomposed and decoupled static behavior of redundant manipulators can be used to derive an optimal control strategy.     

一种基于矢量分析的视觉伺服冗余机器人运动规划方法

本文提出了一种适用于视觉伺服冗余机器人的运动规划方法．针对大多数具有三轴 相交手腕的操作臂，文章把操作臂的运动规划分解为两个方面．一方面，采用腕部速度矢量 在操作臂关节空间极小最小二乘分解的方法规划操作臂关节速度．另一方面，用欧拉角矢量 递推的方法规划操作臂手爪的姿态．该方法的特点是物理意义明确，算法简单．同时具有一 定的运动学鲁棒性．文中还采用该方法对8R操作臂进行了仿真研究．     

弧焊机器人焊缝跟踪神经网络控制器

介绍了一种能提高高弧焊机器人焊缝跟踪精度的神经网络控制器,通过神经网络的补偿作用,弥补了由于无法知道机器人精确模型所造成的控制上的误差,不同于机器人控制中传统的网络控制器,本文提出并应用了基于笛卡尔空间轨迹控制的机器人焊缝跟踪神经网络,大大简化了控制算法,计算机模拟及实验表明,该控制器非常适用于只的实际焊接,对于现有机器人,无须改变其控制器内部结构,即可应用该技术,与常用的机器人关节力矩控制法相比     

Visual motor control of a 7 DOF robot manipulator using a fuzzy SOM network

A fuzzy self-organizing map (SOM) network is proposed in this paper for visual motor control of a 7 degrees of freedom (DOF) robot manipulator. The inverse kinematic map from the image plane to joint angle space of a redundant manipulator is highly nonlinear and ill-posed in the sense that a typical end-effector position is associated with several joint angle vectors. In the proposed approach, the robot workspace in image plane is discretized into a number of fuzzy regions whose center locations and fuzzy membership values are determined using a Fuzzy C-Mean (FCM) clustering algorithm. SOM network then learns the inverse kinematics by on-line by associating a local linear map for each cluster. A novel learning algorithm has been proposed to make the robot manipulator to reach a target position. Any arbitrary level of accuracy can be achieved with a number of fine movements of the manipulator tip. These fine movements depend on the error between the target position and the current manipulator position. In particular, the fuzzy model is found to be better as compared to Kohonen self-organizing map (KSOM) based learning scheme proposed for visual motor control. Like existing KSOM learning schemes, the proposed scheme leads to a unique inverse kinematic solution even for a redundant manipulator. The proposed algorithms have been successfully implemented in real-time on a 7 DOF PowerCube robot manipulator, and results are found to concur with the theoretical findings.     

Robust motion control with the consideration algorithm of joint torque saturation for a redundant manipulator

As each joint actuator of a robot manipulator has a limit value of torque, the motion control system should consider the torque saturation. In order to consider the torque saturation in a transient state, this paper proposes a new redundant motion control system using the autonomous consideration algorithm on torque saturation. A Jacobian matrix of a redundant robot manipulator can select the optimal one considering its motion energy in the steady state. When the motion control system carries out fast motion and quick disturbance suppression, a high joint torque is required in a transient state. In the experimental results, under the condition of having a large payload torque and a fast motion reference, the proposed redundant manipulator control realizes the quick robot motion robustly and smoothly.     

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.     

Trajectory Tracking Control of an Underactuated Underwater Vehicle Redundant Manipulator System

The purpose of this study is to control the position of an underactuated underwater vehicle manipulator system (U‐UVMS). It is possible to control the end‐effector using a regular 6‐DOF manipulator despite the undesired displacements of the underactuated vehicle within a certain range. However, in this study an 8‐DOF redundant manipulator is used in order to increase the positioning accuracy of the end‐effector. The redundancy is resolved according to the criterion of minimal vehicle and joint motions. The underactuated underwater vehicle redundant manipulator system is modeled including the hydrodynamic forces for the manipulator in addition to those for the autonomous underwater vehicle (AUV). The shadowing effects of the bodies on each other are also taken into account when computing the hydrodynamic forces. The Newton‐Euler formulation is used to derive the system equations of motion including the thruster dynamics. In order to establish the end‐effector trajectory tracking control of the system, an inverse dynamics control law is formulated. The effectiveness of the control law even in the presence of parameter uncertainties and disturbing ocean currents is illustrated by simulations.     

Adaptive neural control for an uncertain robotic manipulator with joint space constraints

In this paper, adaptive neural tracking control is proposed for a robotic manipulator with uncertainties in both manipulator dynamics and joint actuator dynamics. The manipulator joints are subject to inequality constraints, i.e., the joint angles are required to remain in some compact sets. Integral barrier Lyapunov functionals (iBLFs) are employed to address the joint space constraints directly without performing an additional mapping to the error space. Neural networks (NNs) are utilised to compensate for the unknown robot dynamics and external force. Adapting parameters are developed to estimate the unknown bounds on NN approximations. By the Lyapunov synthesis, the proposed control can guarantee the semi-global uniform ultimate boundedness of the closed-loop system, and the practical tracking of joint reference trajectory is achieved without the violation of predefined joint space constraints. Simulation results are given to validate the effectiveness of the proposed control scheme.     

Kinematic aspects of a robot-positioner system in an arc welding application

This paper focuses on the kinematic control of a redundant robotic system taking into account particularities of the arc welding technology. The considered system consists of a 6-axis industrial robot (welding tool manipulator) and a 2-axis welding positioner (workpiece manipulator) that is intended to optimise a weld joint orientation during the technological process. The particular contribution of the paper lies in the area of the positioner inverse kinematics, which is a key issue of such system off-line programming and control. It has been proposed a novel formulation and a closed-form solution of the inverse kinematic problem that deals with the explicit definition of the weld joint orientation relative to the gravity. Similar results have also been obtained for the known problem statement that is based on a unit vector transformation. For both the cases, a detailed investigation of the singularities and uniqueness-existence topics have been carried out. The presented results are implemented in a commercial software package and verified for real-life applications in the automotive industry.     

A dual neural network for redundancy resolution of kinematically redundant manipulators subject to joint limits and joint velocity limits

In this paper, a recurrent neural network called the dual neural network is proposed for online redundancy resolution of kinematically redundant manipulators. Physical constraints such as joint limits and joint velocity limits, together with the drift-free criterion as a secondary task, are incorporated into the problem formulation of redundancy resolution. Compared to other recurrent neural networks, the dual neural network is piecewise linear and has much simpler architecture with only one layer of neurons. The dual neural network is shown to be globally (exponentially) convergent to optimal solutions. The dual neural network is simulated to control the PA10 robot manipulator with effectiveness demonstrated.     

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.     

A study of guaranteed cost control of a manipulator with a passive revolute joint

In this article, we consider the robust control problem of a two-link RR manipulator with uncertainty in the joint angle which is caused by several factors. The first purpose is to derive an uncertain linear time-invariant (LTI) system for a two-link RR manipulator which includes uncertainty in the rotational angle of each joint. The uncertainty is expressed in a system structure matrix in an explicit form. For this uncertain system, we apply guaranteed cost control. Finally, we show the effectiveness of our method by a numerical example.