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.     

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.     

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.     

面向冗余机器人实时控制的逆运动学求解有效方法

针对7自由度冗余机器人实时运动控制,对机器人逆运动学提出了一种新的求解方法.采用位姿分解方式,使7自由度冗余机器人逆运动学简化为4自由度位置逆运动学求解.在梯度投影法得到位置优化解的基础上,利用机器人封闭解公式求得一组优化解.通过对7自由度机器人仿真分析,表明了该方法的有效性.     

A neural-network committee machine approach to the inverse kinematics problem solution of robotic manipulators

In robotics, inverse kinematics problem solution is a fundamental problem in robotics. Many traditional inverse kinematics problem solutions, such as the geometric, iterative, and algebraic approaches, are inadequate for redundant robots. Recently, much attention has been focused on a neural-network-based inverse kinematics problem solution in robotics. However, the result obtained from the neural network requires to be improved for some sensitive tasks. In this paper, a neural-network committee machine (NNCM) was designed to solve the inverse kinematics of a 6-DOF redundant robotic manipulator to improve the precision of the solution. Ten neural networks (NN) were designed to obtain a committee machine to solve the inverse kinematics problem using separately prepared data set since a neural network can give better result than other ones. The data sets for the neural-network training were prepared using prepared simulation software including robot kinematics model. The solution of each neural network was evaluated using direct kinematics equation of the robot to select the best one. As a result, the committee machine implementation increased the performance of the learning.     

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.     

A strictly convergent real-time solution for inverse kinematics of robot manipulators

Inverse Kinematics has been recognized as an important problem in robotics applications. A robot independent solution can only be obtained through numerical methods, but most solutions which use this approach have problems with convergence especially near singularity points. This article develops a strictly convergent algorithm and a special-purpose Inverse Kinematics Processor (IKP) to obtain the solution in real time. While the algorithm is based on open-loop integration of rates, the absolute position deviation is used as a criterion to control the iteration, and a feedback mechanism has been especially designed to eliminate problems with long-term drift or with initial errors in the solution. The architecture of the IKP is based on a high-speed floating-point arithmetic processor and is designed to perform the common matrix-vector operations efficiently with a minimum processor cycle time. The algorithm has been simulated on the proposed architecture, and the results show its robustness and real-time capability. For a six degree-of-freedom robot manipulator (for which no closed-form solution exist), the Inverse Kinematics solution may be obtained at an approximate 2 khz rate with an error which is within standard repeatability limits.     

An improved approach to the solution of inverse kinematics problems for robot manipulators

A structured artificial neural-network (ANN) approach has been proposed here to control the motion of a robot manipulator. Many neural-network models use threshold units with sigmoid transfer functions and gradient descent-type learning rules. The learning equations used are those of the backpropagation algorithm. In this work, the solution of the kinematics of a six-degrees-of-freedom robot manipulator is implemented by using ANN. Work has been undertaken to find the best ANN configurations for this problem. Both the placement and orientation angles of a robot manipulator are used to fin the inverse kinematics solutions.     

A biomimetic approach to inverse kinematics for a redundant robot arm

Redundant robots have received increased attention during the last decades, since they provide solutions to problems investigated for years in the robotic community, e.g. task-space tracking, obstacle avoidance etc. However, robot redundancy may arise problems of kinematic control, since robot joint motion is not uniquely determined. In this paper, a biomimetic approach is proposed for solving the problem of redundancy resolution. First, the kinematics of the human upper limb while performing random arm motion are investigated and modeled. The dependencies among the human joint angles are described using a Bayesian network. Then, an objective function, built using this model, is used in a closed-loop inverse kinematic algorithm for a redundant robot arm. Using this algorithm, the robot arm end-effector can be positioned in the three dimensional (3D) space using human-like joint configurations. Through real experiments using an anthropomorphic robot arm, it is proved that the proposed algorithm is computationally fast, while it results to human-like configurations compared to previously proposed inverse kinematics algorithms. The latter makes the proposed algorithm a strong candidate for applications where anthropomorphism is required, e.g. in humanoids or generally in cases where robotic arms interact with humans.     

General-purpose inverse kinematics transformations for robotic manipulators

Real-time robot control requires efficient inverse kinematics transformations to compute the temporal evolution of the joint coordinates from the motion of the end-effector. The development of a coherent, general-purpose framework, incorporating position, velocity and acceleration transformations, is the theme of this paper. In this framework, the computational requirements of a new inverse kinematic algorithm are delineated. The algorithm is applicable to serial (open-chain) manipulators with arbitrary axes of motion. Comparative evaluations of the computational cost of the algorithm demonstrate its efficacy and feasibility for real-time applications.     

Repeatability of inverse kinematics algorithms for mobile manipulators

We introduce and examine the property of repeatability of inverse kinematics algorithms for mobile manipulators. Similarly to stationary manipulators, repeatability of mobile manipulators is defined by requiring that a closed path in the task space should be transformed by the inverse kinematics algorithm into a closed path in the configuration space. In a simply connected, singularity-free region of the task space, a necessary and sufficient condition for repeatability is derived as the integrability condition of a distribution associated with the inverse kinematics algorithm.     

A balancing technique to stabilize local torque optimization solution of redundant manipulators

A technique that stabilizes the existing local torque optimization solutions for redundant manipulators is proposed in this article. The technique is based on a balancing scheme, which balances a solution of joint torque-minimization against a solution of joint velocity-minimization. Introducing the solution of joint velocity-minimization in the approach prevents occurrence of high joint velocities, and thus results in stable optimal arm motions and guarantees the joint velocities at end of motion to be near zero. Computer simulations were executed on a three-link planar rotary manipulator to verify the performance of the proposed local torque optimization technique and to compare its performance with existing ones for various straight line trajectories. © 1996 John Wiley & Sons, Inc.     

Extended Jacobian inverse kinematics algorithms for mobile manipulators

We consider the inverse kinematic problem for mobile manipulators consisting of a nonholonomic mobile platform and a holonomic manipulator on board the platform. The kinematics of a mobile manipulator are represented by a driftless control system with outputs together with the associated variational control system. The output reachability map of the driftless control system determines the instantaneous kinematics, while the output reachability map of the variational system plays the role of the analytic Jacobian of the mobile manipulator. Relying on a formal analogy between the kinematics of stationary and mobile manipulators we exploit the extended Jacobian construction in order to design a collection of extended Jacobian inverse kinematics algorithms for mobile manipulators. It has been proved mathematically and confirmed in computer simulations that these algorithms are capable of efficiently solving the inverse kinematic problem. Moreover, a choice of the Jacobian extension may lay down some guidelines for the platform‐manipulator motion coordination. © 2002 Wiley Periodicals, Inc.     

A new inverse kinematics algorithm for binary manipulators with many actuators

In this paper we present a new, and extremely fast, algorithm for the inverse kinematics of discretely actuated manipulator arms with many degrees of freedom. Our only assumption is that the arm is macroscopically serial in structure, meaning that the overall structure is a serial cascade of units with each unit having either a serial or parallel kinematic structure. Our algorithm builds on previous works in which the authors and coworkers have used the workspace density function in a breadthfirst search for solving the inverse kinematics problem. The novelty of the method presented here is that only the 'mean' of this workspace density function is used. Hence the requirement of storing a sampled version of the workspace density function (which is a function on a six-dimensional space in the case of a spatial manipulator) is circumvented. We illustrate the technique with both planar revolute and variable-geometry-truss manipulators, and briefly describe a new manipulator design for which this algorithm is applicable.     

A more general closed-form solution to the inverse kinematics of mechanical arms

This paper presents solutions to a number of different classes of robot manipulators obtained by locking the redundant joints in a redundant arm. This effort is part of the study of the flexibility offered by the introduction of additional degrees of freedom in mechanical arms. When the extra joints are randomly locked at arbitrary angles, the resultant will be non-redundant arms of various structure for each class of which kinematic solutions are required. The solutions thus cover a whole range of existing and future arm kinematics.     

A geometric method for determining joint rotations in the inverse kinematics of robotic manipulators

An inverse‐kinematics algorithm has been developed to evaluate the joint rotations of a robotic manipulator given the orientation of its hand link. The method mimics the way a person would determine the joint rotations by assembling the links comprising the robot mechanism and making adjustments in the joint displacements until the hand link is in the desired situation. An example is given where it is shown that the method is reasonably robust, can be applied to any design of robot, and is competitive with alternative highly‐mathematical, specific‐robot specialized, computational‐intensive schemes. ©2000 John Wiley & Sons, Inc.     

Classification and characterization of inverse kinematics solutions for anthropomorphic manipulators

Topological properties of the kinematics map are exploited to develop a novel method for redundancy parameterization and extremely fast inverse kinematics solutions for 7-DOF anthropomorphic manipulators and animation characters. The method consists of generating joint angles vectors (configurations) and determining their associated hand position/orientation (pose) via the known forward kinematics. The generated data are classified into various inverse kinematics solutions manifolds. These manifolds are subsequently segmented so that the redundancy can be parameterized and the solutions can be represented by simple equations whose parameters are stored for rapid online computation. During the online phase, given the desired hand pose, the appropriate stored parameters are retrieved and various inverse kinematics solutions are computed. The online time to provide various solutions is of the order of several microseconds, which allow real-time inverse kinematics evaluations for fast moving animation characters or manipulators.     

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     

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.