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.     

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.     

基于模糊神经网络的机器人逆运动学问题

针对机器人逆运动学问题，本文指出了基于模糊神经网络（FNN，Fuzzy Neural Network）的解决方案，阐述了基本设计思想和具体算法过程，给出了二自由度刚性机器人的仿真结果，以表明该方案的有效性和可行性。     

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.     

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 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.     

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.     

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.     

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.     

A computer-aided geometric approach to inverse kinematics

This paper presents a geometric approach to solving the inverse kinematics for three-joint placeable robotic manipulators. The distinct feature of this approach is that it uses geometric variables such as length, area ratio, and Pythagoras difference to find the closed form solutions. It is proved here that for any three-joint placeable manipulator there exists a geometric variable that keeps constant during the evolution of the manipulator. With this invariant, a characteristic equation of the manipulator can be derived and can be transformed into a polynomial equation with degree up to four. Therefore the closed form solution of the three-joint placeable manipulator can be obtained. A characteristic equation of the three-revolute-joint manipulator produced by this approach with the assistance of Maple is listed in the Appendix. The possible application of this geometric approach to a six-joint manipulator is also discussed in the paper. © 1998 John Wiley & Sons, Inc. 15: 131–143, 1998     

Reliability-based approach to the inverse kinematics solution of robots using Elman's networks

The solution of inverse kinematics problem of redundant manipulators is a fundamental problem in robot control. The inverse kinematics problem in robotics is the determination of joint angles for a desired cartesian position of the end effector. For the solution of this problem, many traditional solutions such as geometric, iterative and algebraic are inadequate if the joint structure of the manipulator is more complex. Furthermore, many neural network approaches have been done to this problem. But the neural network-based solutions are not much reliable due to the error at the end of learning. Therefore, a reliability-based neural network inverse kinematics solution approach has been presented, and applied to a six-degrees of freedom (dof) robot manipulator in this paper. The structure of the proposed method is based on using three networks designed parallel to minimize the error of the whole system. Elman network, which has a profound impact on the learning capability and performance of the network, is chosen and designed according to the proposed solution method. At the end of parallel implementation, the results of each network are evaluated using direct kinematics equations to obtain the network with best result.     

A design approach to adaptive model-following control of robotic manipulators

In this paper, the robot dynamics are represented by a nonlinear state-space model containing a disturbance term due to gravitational loading. Using a suitable linear time-invariant reference model, an adaptive model-following control problem is formulated which satisfies the matching conditions. The control input is designed to have two components: a nonadaptive linear component to do the task of model-following and a nonlinear unit-vector component based on hyperstability theory to do the adaptive task. An additional integral feedback term is further superimposed and then the overall asymptotic hyperstability is established. The simulation results on the first three joints of PUMA 560 robot manipulator indicate the potential of our design approach.Based on research supported by Kuwait University Research Administration under Grant No. EE 049.     

A dynamic programming approach to trajectory planning of robotic manipulators

This paper presents a solution to the problem of minimizing the cost of moving a robotic manipulator along a specified geometric path subject to input torque/force constraints, taking the coupled, nonlinear dynamics of the manipulator into account. The proposed method uses dynamic programming (DP) to find the positions, velocities, accelerations, and torques that minimize cost. Since the use of parametric functions reduces the dimension of the state space from2nfor ann- jointed manipulator, to two, the DP method does not suffer from the "curse of dimensionality." While maintaining the elegance of our previous trajectory planning method, we have developed the DP method for the general case where 1) the actuator torque limits are dependent on one another, 2) the cost functions can have an arbitrary form, and 3) there are constraints on the jerk, or derivative of the acceleration. Also, we have shown that the DP solution converges as the grid size decreases. As numerical examples, the trajectory planning method is simulated for the first three joints of the PACS arm, which is a cylindrical arm manufactured by the Bendix Corporation.     

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.     

Endogenous configuration space approach to mobile manipulators: A derivation and performance assessment of Jacobian inverse kinematics algorithms

By a mobile manipulator we mean a robotic system composed of a non-holonomic mobile platform and a holonomic manipulator fixed to the platform. A taskspace of the mobile manipulator includes positions and orientations of its end effector relative to an inertial coordinate frame. The kinematics of a mobile manipulator are represented by a driftless control system with outputs. Admissible control functions of the platform along with joint positions of the manipulator constitute the endogenous configuration space. Endogenous configurations have a meaning of controls. A map from the endogenous configuration space into the taskspace is referred to as the instantaneous kinematics of the mobile manipulator. Within this framework, the inverse kinematic problem for a mobile manipulator amounts to defining an endogenous configuration that drives the end effector to a desirable position and orientation in the taskspace. Exploiting the analogy between stationary and mobile manipulators we present in the paper a collection of regular and singular Jacobian inverse kinematics algorithms. Their performance is evaluated on the basis of intense computer simulations.     

A hybrid strategy to solve the forward kinematics problem in parallel manipulators

A parallel manipulator is a closed kinematic structure with the necessary rigidity to provide a high payload to self-weight ratio suitable for many applications in manufacturing, flight simulation systems, and medical robotics. Because of its closed structure, the kinematic control of such a mechanism is difficult. The inverse kinematics problem for such manipulators has a mathematical solution; however, the forward kinematics problem (FKP) is mathematically intractable. This work addresses the FKP and proposes a neural-network-based hybrid strategy that solves the problem to a desired level of accuracy, and can achieve the solution in real time. Two neural-network (NN) concepts using a modified form of multilayered perceptrons with backpropagation learning were implemented. The better performing concept was then combined with a standard Newton-Raphson numerical technique to yield a hybrid solution strategy. Simulation studies were carried out on a flight simulation syystem to check the validity o the approach. Accuracy of close to 0.01 mm and 0.01/spl deg/ in the position and orientation parameters was achieved in less than two iterations and 0.02 s of execution time for the proposed strategy.     

Exact solution to the inverse kinematics problem of a standard 6-axis robot manipulator

Presented are four sets of exact solutions for the vector of the joint angles {θ_i} pertaining to the inverse kinematics problem of a standard 6-axis robot manipulator with two different kinds of gripper configurations. Here a standard 6-axis robot is meant to be a general computer-controlled revolute robot with base, shoulder, elbow, wrist pitch, wrist yaw, wrist roll, and gripping action. Explicit solutions are obtained using Denavit-Hartenberg homogeneous transformations. Furthermore, the inverse solutions are examined by means of a direct kinematic computer program.     

An approach to adaptive control of robotic manipulators

The control synthesis for the robotic systems in which parameters are partially unknown is considered. We propose synthesis of robust, non-adaptive, decentralized control which has to stabilize robots for all allowable variations of the parameters. If the robust non-adaptive control cannot withstand all expected variations of parameters, we propose synthesis of indirect adaptive control, i.e. the estimation of the robot parameters is performed first and then used for adjusting the decentralized control gains. The non-adaptive and adaptive control syntheses are illustrated by simulation of an industrial robot with unknown payload mass.     

A neuro-genetic-simulated annealing approach to the inverse kinematics solution of robots: a simulation based study

In this study, a hybrid intelligent solution system including neural networks, genetic algorithms and simulated annealing has been proposed for the inverse kinematics solution of robotic manipulators. The main purpose of the proposed system is to decrease the end effector error of a neural network based inverse kinematics solution. In the designed hybrid intelligent system, simulated annealing algorithm has been used as a genetic operator to decrease the process time of the genetic algorithm to find the optimum solution. Obtained best solution from the neural network has been included in the initial solution of genetic algorithm with randomly produced solutions. The end effector error has been reduced micrometer levels after the implementation of the hybrid intelligent solution system.