Recurrent neural networks for minimum infinity-norm kinematiccontrol of redundant manipulators

This paper presents two neural network approaches to minimum infinity-norm solution of the velocity inverse kinematics problem for redundant robots. Three recurrent neural networks are applied for determining a joint velocity vector with its maximum absolute value component being minimal among all possible joint velocity vectors corresponding to the desired end-effector velocity. In each proposed neural network approach, two cooperating recurrent neural networks are used. The first approach employs two Tank-Hopfield networks for linear programming. The second approach employs two two-layer recurrent neural networks for quadratic programming and linear programming, respectively. Both the minimal 2-norm and infinity-norm of joint velocity vector can be obtained from the output of the recurrent neural networks. Simulation results demonstrate that the proposed approaches are effective with the second approach being better in terms of accuracy and optimality     

冗余机械臂优化控制新方法

针对五自由度冗余机械臂,提出了一种新的基于伪逆的优化控制方法：利用一个可调权值因子,将最小速度范数方法（加速度层）和最小加速度范数方法进行加权组合,来实现对冗余机械臂的运动控制。该优化方法可以实现关节速度范数和关节加速度范数的同时最小化,而且使得机械臂的关节速度在运动末态时接近零。计算机仿真结果进一步验证了所给出的优化控制方法的可行性和优越性。     

An inverse kinematic solution for kinematically redundant robot manipulators

An inverse kinematic analysis addresses the problem of computing the sequence of joint motion from the Cartesian motion of an interested member, most often the end effector. Although the rates and accelerations are related linearly through the Jacobian, the positions go through a highly nonlinear transformation from one space to another. Hence, the closed-form solution has been obtained only for rather simple manipulator configurations where joints intersect or where consecutive axes are parallel or perpendicular. For the case of redundant manipulators, the number of joint variables generally exceeds that of the constraints, so that in this case the problem is further complicated due to an infinite number of solutions. Previous approaches have been directed to minimize a criterion function, taking into account additional constraints, which often implies a time-consuming optimization process. In this article, a different approach is taken to these problems. A Newton-Raphson numerical procedure has been developed based on a composite Jacobian which now includes rows for all members under constraint. This procedure may be applied to solve the inverse kinematic problem for a manipulator of any mechanical configuration without having to derive beforehand a closed-form solution. The technique is applicable to redundant manipulators since additional constraints on other members as well as on the end effector may be imposed. Finally, this approach has been applied to a seven degree-of-freedom manipulator, and its ability to avoid obstacles is demonstrated.     

冗余机械臂角偏差消去方案之原理分析

本文利用优化方法及递归神经网络实时求解器消除冗余机器手臂在运动过程中出现的角偏差问题.鉴于机器手臂都存在着关节物理约束,我们的优化方案也因此考虑关节极限和关节速度极限的躲避.更重要的是,本文详细分析了该成功解决关节角偏差问题的二次型性能指标的设计原理.仿真结果证实了该方法的可行性与有效性.     

Kinematic control of redundant robot manipulators: A tutorial

In this paper, we present a tentatively comprehensive tutorial report of the most recent literature on kinematic control of redundant robot manipulators. Our goal is to lend some perspective to the most widely adopted on-line instantaneous control solutions, namely those based on the simple manipulator's Jacobian, those based on the local optimization of objective functions in the null space of the Jacobian, those based on the task space augmentation by additional constraint tasks (with task priority), and those based on the construction of inverse kinematic functions.     

A global approach for the optimal path generation of redundant robot manipulators

In this article the optimal path generation of redundant robot manipulators is considered as an optimization problem, with given kinematics and subject to the robot requirements and a singularities avoidance constraint. This problem is formulated as a constrained continuous optimal control problem, which allows to consider joints and velocities constraints and/or manipulator dynamics. This approach is exemplified for a planar redundant manipulator and the resultant state constrained problem is solved by an efficient iterative numerical technique.     

Remedy scheme and theoretical analysis of joint-angle drift phenomenon for redundant robot manipulators

A quadratic programming (QP)-based method, as a remedy for joint angle drifts, is employed for redundant robot manipulators with physical constraints (e.g., joint-angle limits and joint-velocity limits) considered. By using the QP-based redundancy-resolution scheme, real-time repetitive motion planning (RMP) can be achieved in a drift-free manner. Theoretical analyses based on gradient-descent and neural-dynamic methods are also conducted. Based on analyses, the efficacy of the presented QP-based RMP scheme for redundant manipulators is successfully explained. To demonstrate the effectiveness of the RMP scheme, different kinds of redundant robot manipulators, such as PA10, PUMA560, and a six-link planar robot arm, are tested in order to perform circular and straight line end-effector trajectories by using computer simulations. Both theoretical analysis and computer simulation results have demonstrated the efficacy of the QP-based RMP scheme.     

A recurrent neural network for minimum infinity-norm kinematiccontrol of redundant manipulators with an improved problem formulationand reduced architecture complexity

This paper presents an improved neural computation where scheme for kinematic control of redundant manipulators based on infinity-norm joint velocity minimization. Compared with a previous neural network approach to minimum infinity-non kinematic control, the present approach is less complex in terms of cost of architecture. The recurrent neural network explicitly minimizes the maximum component of the joint velocity vector while tracking a desired end-effector trajectory. The end-effector velocity vector for a given task is fed into the neural network from its input and the minimum infinity-norm joint velocity vector is generated at its output instantaneously. Analytical results are given to substantiate the asymptotic stability of the recurrent neural network. The simulation results of a four-degree-of-freedom planar robot arm and a seven-degree-of-freedom industrial robot are presented to show the proposed neural network can effectively compute the minimum infinity-norm solution to redundant manipulators.     

A new torque minimization method for heavy-duty redundant manipulators used in nuclear decommissioning tasks

Intelligent Service Robotics - This paper presents an approach to optimize the control torque of heavy-duty redundant manipulators used for dismantling nuclear power plants. Such manipulators must...     

Task-directed inverse kinematics for redundant manipulators

This paper presents kinematic algorithms for resolved-rate based inverse kinematics of redundant manipulators. Efficient and robust Jacobian and weighted damped least squares algorithms are given which provide a method that allows full utilization of the redundancy to best achieve task requirements. A nominal set of task space variables is suggested and procedures for modifying this specification or their relative priorities due to changing task requirements or events are discussed. Examples are shown using a simulation of the seven degree-of-freeom Robotics Research manipulator. These simulations demonstrate the singularity robustness of the algorithms and the ability to smoothly transition between task parameterizations and relative priorities.     

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     

面向冗余度机械臂QP问题求解的E47和94LVI数值算法

冗余度机械臂的二次规划(QP)问题同时受制于等式约束、不等式约束和双端约束,且面向冗余度机械臂实时控制的该类QP问题的求解对运算实时性有较高要求。考虑同时受制于上述三种约束的二次规划问题的求解,给出并研究两种数值算法(E47和94LVI算法)。这类带约束的二次规划问题被等价转换为分段线性投影方程。应用E47和94LVI算法求解上述分段线性投影方程,从而得到二次规划问题的最优数值解。同时,通过大量的数值实验,研究两种算法面向冗余度机械臂的QP问题求解性能,并给出E47、94LVI算法与经典有效集算法的对比实验结果。最终证实了E47和94LVI两种算法在求解二次规划问题上的高效性和优越性。     

Force polytope and force ellipsoid for redundant manipulators

Evaluation of force/motion capabilities for a manipulator is useful both in the design phase and in the operational phase. Manipulability ellipsoids and polytopes are well-known tools used to represent these capabilities graphically. This article focuses on the evaluation of force capabilities for redundant manipulators, for which additional constraints must be imposed on the available joint torques to satisfy the static assumption. An algorithm to correctly evaluate the task space force polytope is given and a new definition of the force ellipsoid is proposed. The obtained results can be applied also to nonredundant manipulators in singular configurations. Numerical results are provided in the case of a planar redundant arm. ©1997 John Wiley & Sons, Inc.     

Flexible control for robot manipulators

We designed, implemented, and tested a real-time flexible controller for manipulating different types of robots and control algorithms. The robot-independent, IBM PC-based multiprocessor system contains a DSP56001 master controller, six independent HCTL-1100 joint processors for accurate robotic joint control, and an interface computer board for processor communication. The joint processors operate in four user-defined modes and can be connected directly to an incremental optical encoder, which accommodates specialized applications and eliminates extra hardware     

Finite-time control for robot manipulators

Finite-time control of the robot system is studied through both state feedback and dynamic output feedback control. The effectiveness of the proposed approach is illustrated by both theoretical analysis and computer simulation. In addition to offering an alternative approach for improving the design of the robot regulator, this research also extends the study of the finite-time control problem from second-order systems to a large class of higher order nonlinear systems.     

Fault identification for robot manipulators

Several factors must be considered for robotic task execution in the presence of a fault, including: detection, identification, and accommodation for the fault. In this paper, a nonlinear observer is used to identify a class of actuator faults once the fault has been detected by some other method. Advantages of the proposed fault-identification method are that it is based on the nonlinear dynamic model of a robot manipulator (and hence, can be extended to a number of general Euler Lagrange systems), it does not require acceleration measurements, and it is independent from the controller. A Lyapunov-based analysis is provided to prove that the developed fault observer converges to the actual fault. Experimental results are provided to illustrate the performance of the identification method.     

An adaptive impedance/force controller for robot manipulators

A solution to the adaptive control of constrained robots in the presence of uncertainty in the robot model parameters is presented. The controller design is based on a singular systems model representation and fixed controller design. The adaptive control law consists of the computed torque controller plus the introduction of the parameter estimates and an additional compensation through an extra signal. Some properties of the reduced form robot model are presented and exploited to prove the asymptotic tracking properties of the adaptive controller. Also, the inclusion of the impedance control objective allows the accommodation of tangential forces that may appear in the constrained task     

Stable neurovisual servoing for robot manipulators

In this paper, we propose a stable neurovisual servoing algorithm for set-point control of planar robot manipulators in a fixed-camera configuration an show that all the closed-loop signals are uniformly ultimately bounded (UUB) and converge exponentially to a small compact set. We assume that the gravity term and Jacobian matrix are unknown. Radial basis function neural networks (RBFNNs) with online real-time learning are proposed for compensating both gravitational forces and errors in the robot Jacobian matrix. The learning rule for updating the neural network weights, similar to a back propagation algorithm, is obtained from a Lyapunov stability analysis. Experimental results on a two degrees of freedom manipulator are presented to evaluate the proposed controller.     

Hybrid adaptive control for robot manipulators

A hybrid adaptive control scheme is proposed for robot manipulators. Unmodelled dynamics have been considered in the robot model. The standard RLS algorithm has been modified to take into account these unmodelled dynamics. Global stability of the system is ensured.     

Robust adaptive control for robot manipulators

A composite adaptive control law for robot manipulators in task space, which uses both the tracking error and the prediction error to drive parameter estimation, is developed in this paper. It is shown that global stability and convergence can be achieved for the adaptive control algorithm in the ideal case, and furthermore that the algorithm can be easily modified by using parameter projection to achieve robustness with respect to a class of unmodelled dynamics. In addition, the algorithm has the advantage that no requirement is needed for the inverse of the jacobian matrix or for the bounded inverse of the estimated inertia matrix. A simulation example is provided for performance demonstration.