Relation between global velocity and local torque optimization of redundant manipulators

In this article, the relation between the global optimization of joint velocity and local optimization of joint torque is investigated. The local minimization of the weighted joint torques can be matched to the global optimization of the corresponding weighted joint velocities when the weighted matrices satisfy certain sufficient conditions. A straightforward matching is obtained using the local optimization of the inertia inverse weighted dynamic torque and the global minimization of the kinetic energy. Another easy solution can be found, as will be shown later, if the inertia matrix is a constant and gravity is neglected. Based on that, it can be seen why a Cartesian robot, which has a constant inertia matrix, is always stable. © 1994 John Wiley & Sons, Inc.     

Null space damping method for local joint torque optimization of redundant manipulators

In this article, a null space damping method is proposed that solves the stability problem commonly encountered in existing local joint torque optimization techniques applied to redundant manipulators. The damped joint motion is stable and globally outperforms undamped techniques in the sense of torque minimization capability. In addition, simulation results show that the resulting damped joint motion becomes conservative after an initial transient stage for cyclic end-effector trajectories, while undamped pseudoinverse solutions are reported to never lead to conservative motion. Three undamped and damped joint torque optimization algorithms are considered and discussed with comparison to the previous literature. The effectiveness of the proposed null space damping method is demonstrated by the results of two computer simulations. In addition, the minimization of electrical power consumption is addressed with respect to the results of this article.     

A unified quadratic-programming-based dynamical system approach to joint torque optimization of physically constrained redundant manipulators

In this paper, for joint torque optimization of redundant manipulators subject to physical constraints, we show that velocity-level and acceleration-level redundancy-resolution schemes both can be formulated as a quadratic programming (QP) problem subject to equality and inequality/bound constraints. To solve this QP problem online, a primal-dual dynamical system solver is further presented based on linear variational inequalities. Compared to previous researches, the presented QP-solver has simple piecewise-linear dynamics, does not entail real-time matrix inversion, and could also provide joint-acceleration information for manipulator torque control in the velocity-level redundancy-resolution schemes. The proposed QP-based dynamical system approach is simulated based on the PUMA560 robot arm with efficiency and effectiveness demonstrated.     

A dual neural network for constrained joint torque optimization of kinematically redundant manipulators

A dual neural network is presented for the real-time joint torque optimization of kinematically redundant manipulators, which corresponds to global kinetic energy minimization of robot mechanisms. Compared to other computational strategies on inverse kinematics, the dual network is developed at the acceleration level to resolve redundancy of limited-joint-range manipulators. The dual network has a simple architecture with only one layer of neurons and is proved to be globally exponentially convergent to optimal solutions. The dual neural network is simulated with the PUMA 560 robot arm to demonstrate effectiveness.     

A local solution with global characteristics for the joint torque optimization of a redundant manipulator

In this article, a stable local solution with global characteristics is developed for the joint torque optimization problem in redundant robotic manipulators. It is shown that the local optimization of the inertia inverse weighted dynamic torque corresponds to the global kinetic energy minimization problem. The proposed local-global alternative to the joint torque optimization problem is compared for stability and torque optimality with five different methods used for redundancy resolution of robotic manipulators at the acceleration level. The proposed local-global solution has been implemented and tested on a planar four-DOF kinematically redundant lab robot which was designed and built at Southwest Research Institute (SWRI). Several numerical simulations confirm the positive advantages of solutions which have a local as well as a global interpretation. In addition, a “dynamic manipulation index” is introduced to monitor the stability of an optimization problem in a kinematically redundant robot.     

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.     

A solution to the inverse kinematics of redundant manipulators

A solution to the inverse kinematics is a set of joint coordinates which correspond to a given set of task space coordinates (position and orientation of end effector). For the class of kinematically redundant robots, the solution is generically nonunique such that special methods are required for obtaining a solution. The method addressed in the paper, introduced earlier and termed “generalized inverse,” is based on a certain partitioning of the Jacobian functional corresponding to a nonlinear relationship of the inverse kinematics type. The article presents a new algorithm for solving the inverse kinematics using the method of generalized inverse based on a modified Newton-Raphson iterative technique. The new algorithm is efficient, converges rapidly, and completely generalizes the solution of the inverse kinematics problem for redundant robots. The method is illustrated by numerical examples.     

Improving local torque optimization techniques for redundant robotic mechanisms

Two techniques that improve existing local torque optimization methods for redundant robotic mechanisms are proposed. The first technique is based on a balancing scheme, which balances a joint torque norm against a norm of joint accelerations. Expressions have been derived utilizing the Lagrangian multipliers method. The other technique is based on a torque optimization method which minimizes torques through accelerations, obtained from the null-space of the Jacobian matrix. These accelerations are balanced against the minimum-norm acceleration component in order to improve the performance. Numerical simulations have been carried out which in most cases illustrate good performance capability from the viewpoint of torque optimization and global stability.     

Fuzzy logic-based optimization for redundant manipulators

Redundant manipulators have more degrees of freedom (DOF) than the DOF of the task space. This implies that the number of joint position variables is greater than the number of variables specifying the task. The problem of solving the kinematic equations for the joint variables is underspecified unless additional equations/constraints are introduced to obtain a well-posed problem. A dynamic level redundancy resolution is proposed. The joint space model is transformed to a reduced-order model in the pseudovelocity space. The elements of the foregoing transformation matrix indirectly determine the contribution of each joint to the total motion. These elements are selected using two fuzzy logic-based methods so as to minimize the instantaneous manipulator power: (1) in the velocity method, a space vector in the velocity relationship between the two spaces is determined by imposing a constraint on the continuity of the joint velocities at the time instant when the elements of the transformation matrix experience a discontinuity and (2) in the torque method, an alternative approach introduced to reduce the computational complexity, the changes in the transformation matrix are made continuous with respect to time by the appropriate choice of a space vector in the joint torque expression. Simulations are given.     

Error-back-propagation solution to the inverse kinematic problem of redundant manipulators

In this paper, the inverse kinematics problem of the generalized n-degrees-of-freedom robot is solved using the error-back-propagation algorithm. The efficiency of the proposed solution has been mewed for redundant manipulators using 5000 randomly chosen Cartesian coordinates within the robot's workspace. Comparison with two other methods, the well-known pseudoinverse method and a technique based on genetic algorithms, shows that the accuracy of the present method is substantially better.     

Torque optimization schemes for kinematically redundant manipulators

One of the important applications for the resolution of redundant manipulators is torque optimization, due to the fact that the actuators used for driving a manipulator have finite power ratings. Nevertheless, not many algorithms have been proposed to accomplish this objective. A survey of the existing local torque optimization control schemes is given in this article. It will be shown that all of them either encounter instability problems for long trajectories or fail in certain cases. For remedying these problems, the authors present the Minimum Velocity Norm (MVN) method, which is the most common approach for kinematic redundancy resolution and has never been adopted for torque optimization by other researchers. Simulation results show that the simple MVN method is moderate for short movements and is stable for long movements. Also, the MVN method can be applied to cases that may not be accomplished by some other approaches. Therefore, the MVN method is better than the other existing approaches for torque optimization. © 1994 John Wiley & Sons, Inc.     

A neuro-simulated annealing approach to the inverse kinematics solution of redundant robotic manipulators

The neural-network-based inverse kinematics solution is one of the recent topics in the robotics because of the fact that many traditional inverse kinematics problem solutions such as geometric, iterative and algebraic are inadequate for redundant robots. However, since the neural networks work with an acceptable error, the error at the end of inverse kinematics learning should be minimized. In this study, simulated annealing (SA) algorithm was used together with the neural-network-based inverse kinematics problem solution robots to minimize the error at the end effector. The solution method is applied to Stanford and Puma 560 six-joint robot models to show the efficiency. The proposed algorithm combines the characteristics of neural network and an optimization technique to obtain the best solution for the critical robotic applications. Three Elman neural networks were trained using separate training sets and different parameters, since one of them can give better results than the others can. The best result is selected within three neural network results by computing the end effector error via direct kinematics equation of the robotic manipulator. The decimal part of the neural network result was improved up to 10 digits using simulated annealing algorithm. The obtained best solution is given to the simulated annealing algorithm to find the best-fitting 10 digits for the decimal part of the solution. The end effector error was reduced significantly.     

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。     

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...     

Repeatability of redundant manipulators: mathematical solution ofthe problem

Consider a redundant manipulator whose hand is to trace a path in its workspace. A local control strategy that governs the manipulator is a law that assigns an infinitesimal change in the joint angles so that the hand will move infinitesimally in the direction designated by the path. Because of the redundancy, there can be many such control strategies. For some strategies it turns out that when the hand returns to its initial position, the joint angles do not always return to their initial values. To determine a priori whether a given local control strategy guarantees repeatability or not, it is necessary to deduce its global properties as well as its local properties. This is achieved by considering integral surfaces for a distribution in the joint space. This yields a necessary and sufficient condition, in terms of Lie brackets, for a control to be repeatable     

Analytic minimum-norm solution for rate coordination in redundant manipulators

In this article, we present a novel method that results in efficient minimum norm solution for the rate coordination problem in redundant manipulators. The theory is developed based upon a geometric interpretation that, for minimum norm criterion, vectors orthogonal to constraint space should pass through the origin of the solution space. It is shown that, for any spatial manipulator with 1, 2, or 3 degrees of redundancy, the minimum norm rate solution can be derived in analytic closed form. An example of the analytic formulation is given for a 3R planar case, substantiated with simulation results. The behavior of this algorithm in nonredundant and near singular situations is also discussed. The method offers an equivalent but much more efficient alternative to using the pseudoinverse in redundancy resolution and, in fact, is applicable to any underdetermined linear system. An alternative formulation of pseudoinverse arrived at in the course of the development is also presented. © 1992 John Wiley & Sons, Inc.     

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.     

冗余机械臂逆运动学求解方法研究进展

随着科学技术的发展,冗余机械臂凭借其多自由度的特性获得学者的广泛关注.其中包括执行指定任务时,需要将任务路径转换为关节空间轨迹,进行逆运动学求解,求取非线性函数的连续逆映射.该求解过程尤为重要且非常复杂,国内外学者对此开展了大量研究.这里将冗余机械臂逆运动学求解方法进行分类,归纳整理出各类求解方法,分别概述解析法、数值解法、智能算法以及对应子方法的基本原理、对比及研究现状.最后,指出逆运动学求解方法面临的核心问题以及发展趋势.     

Dynamic control of coordinated redundant robots with torque optimization

The problem of controlling a system of coordinated redundant robots with torque optimization based on joint redundancy is addressed. Local and global optimal control laws, both minimizing joint torque loading, are developed. A general method of load distribution among the coordinated robots is also proposed. The control problem is to regulate the motion of the object held by the coordinated robots and the internal force generated as a result of constraints on the object. The errors in the object motion and internal force converge asymptotically to zero under the proposed optimal control laws, when exact knowledge of the dynamic models is assumed. Furthermore, the robustness of the proposed method to model uncertainty is also analyzed. The motion and internal force errors are uniformly ultimately bounded under the proposed optimal controllers, when uncertainty in the dynamic models is assumed to exist.     

Dynamic control of redundant manipulators

Redundant manipulators provide increased flexibility for the execution of complex tasks. Redundancy is often required to maintain manipulability and avoid obstacles while completing the required task. Self-motion is the internal (joint) motion of the manipulator that does not contribute to the end effector motion. In this article we provide a dynamic feedback control law that guarantees the tracking of a desired end effector trajectory and provides redundancy resolution by making the self-motion of the manipulator flow along the projection of a given arbitrary vector field. By choosing this vector field to be the gradient of a cost function, for example, the manipulator can be made to seek an optimum configuration. The effectiveness of the control law is illustrated with simulation results.