Solving the forward kinematics of parallel manipulators with a genetic algorithm

A floating point genetic algorithm is proposed to solve the forward kinematic problem for parallel manipulators. This method, adapted from studies in the biological sciences, allows the use of inverse kinematic solutions to solve forward kinematics as an optimization problem. The method is applied to two 3-degree-of-freedom planar parallel manipulators and to a 3-degree-of-freedom spherical manipulator. The method converges to a solution within a broader search domain compared to a Newton-Raphson scheme. © 1996 John Wiley & Sons, Inc.     

Parametric motor control: A new approach to the control of point-to-point manipulator movements

We propose a control scheme for point-to-point movements of robotic manipulators, which is based on an established concept about human movement control. In this approach, actuator drive signals have an invariant shape and are parametrically modified to fit the requirements of different tasks. The appropriate parameter values are provided by an Artificial Neural Network before movement onset. Explicit solutions of the inverse kinematic and inverse dynamic equations, or multiple feedback loops, are not required for this approach. We found that Parametric Motor Control yields satisfactory performance, allowing the manipulator to discriminate between targets in a 5×3 grid and to generalize to new target locations. The new control scheme has potential benefits for scenarios where complex manipulators must be controlled in real time. © 1997 John Wiley & Sons, Inc.     

Infinity-norm acceleration minimization of robotic redundant manipulators using the LVI-based primal–dual neural network

Kinematically redundant manipulators admit an infinite number of inverse kinematic solutions and hence the optimization of different performance measures corresponding to various task requirements must be considered. Joint accelerations of these mechanisms are usually computed by optimizing various criteria defined using the two-norm of acceleration vectors in the joint space. However, in formulating the optimization measures for computing the inverse kinematics of redundant arms, this paper investigates the use of the infinity norm of joint acceleration (INAM) (also known as the minimum-effort solution). The infinity norm of a vector is its maximum absolute value component and hence its minimization implies the determination of a minimum-effort solution as opposed to the minimum-energy criterion associated with the two-norm. Moreover, the new scheme reformulates the task as the online solution to a quadratic programming problem and incorporates three levels of joint physical limits, thus keeping the acceleration within a given range and avoiding the torque-instability problem. In addition, since the new scheme adopts the LVI-based primal–dual neural network, it does not entail any matrix inversion or matrix–matrix multiplication, which was embodied in other's researches with expensive O(n³)$O(n^3)$ operations. This new proposed QP-based dynamic system scheme is simulated based on the PUMA560 robot arm.     

An offset error compensation method for improving ANN accuracy when used for position control of precision machinery

Artificial Neural Networks (ANNs) have recently become the focus of considerable attention in many disciplines, including robot control, where they can be used as a general class of nonlinear models to solve highly nonlinear control problems. Feedforward neural networks have been widely applied for modelling and control purposes. One of the ANN applications in robot control is for the solution of the inverse kinematic problem, which is important in path planning of robot manipulators. This paper proposes an iterative approach and an offset error compensation method to improve the accuracy of the inverse kinematic solutions by using an ANN and a forward kinematic model of a robot. The offset error compensation method offers potential to generate accurately the inverse solution for a class of problems which have an easily obtained forward model and a complicated solution.Now Lecturing in Taiwan.     

An algorithmic approach to coordinate transformation for robotic manipulators

Coordinate transformation is one of the most important issues in robotic manipulator control. Robot tasks are naturally specified in work space coordinates, usually a Cartesian frame, while control actions are developed on joint coordinates. Effective inverse kinematic solutions are analytical in nature; they exist only for special manipulator geometries and geometric intuition is usually required. Computational inverse kinematic algorithms have recently been proposed; they are based on general closed-loop schemes which perform the mapping of the desired Cartesian trajectory into the corresponding joint trajectory. The aim of this paper is to propose an effective computational scheme to the inverse kinematic problem for manipulators with spherical wrists. First an insight into the formulation of kinematics is given in order to detail the general scheme for this specific class of manipulators. Algorithm convergence is then ensured by means of the Lyapunov direct method. The resulting algorithm is based on the hand position and orientation vectors usually adopted to describe motion in the task space. The analysis of the computational burden is performed by taking the Stanford arm as a reference. Finally a case study is developed via numerical simulations.     

Selection Based on the Pareto Nondomination Criterion for Controlling Code Growth in Genetic Programming

The rapid growth of program code is an important problem in genetic programming systems. In the present paper we investigate a selection scheme based on multiobjective optimization. Since we want to obtain accurate and small solutions, we reformulate this problem as multiobjective optimization. We show that selection based on the Pareto nondomination criterion reduces code growth and processing time without significant loss of solution accuracy.     

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.     

Optimal Trajectory Planning for Wheeled Mobile Robots Based on Kinematics Singularity

This research introduces a new optimality criterion for motion planning of wheeled mobile robots based on a cost index that assesses the nearness to singularity of forward and inverse kinematic models. Slip motions, infinite estimation error and impossible control actions are avoided escaping from singularities. In addition, high amplification of wheel velocity errors and high wheel velocity values are also avoided by moving far from the singularity. The proposed cost index can be used directly to complement path-planning and motion-planning techniques (e.g. tree graphs, roadmaps, etc.) in order to select the optimal collision-free path or trajectory among several possible solutions. To illustrate the applications of the proposed approach, an industrial forklift, equivalent to a tricycle-like mobile robot, is considered in a simulated environment. In particular, several results are validated for the proposed optimality criterion, which are extensively compared to those obtained with other classical optimality criteria, such as shortest-path, time-optimal and minimum-energy.     

Visual servoing of redundant manipulator with Jacobian matrix estimation using self-organizing map

Vision based redundant manipulator control with a neural network based learning strategy is discussed in this paper. The manipulator is visually controlled with stereo vision in an eye-to-hand configuration. A novel Kohonen’s self-organizing map (KSOM) based visual servoing scheme has been proposed for a redundant manipulator with 7 degrees of freedom (DOF). The inverse kinematic relationship of the manipulator is learned using a Kohonen’s self-organizing map. This learned map is shown to be an approximate estimate of the inverse Jacobian, which can then be used in conjunction with the proportional controller to achieve closed loop servoing in real-time. It is shown through Lyapunov stability analysis that the proposed learning based servoing scheme ensures global stability. A generalized weight update law is proposed for KSOM based inverse kinematic control, to resolve the redundancy during the learning phase. Unlike the existing visual servoing schemes, the proposed KSOM based scheme eliminates the computation of the pseudo-inverse of the Jacobian matrix in real-time. This makes the proposed algorithm computationally more efficient. The proposed scheme has been implemented on a 7 DOF PowerCube? robot manipulator with visual feedback from two cameras.     

A Lattice BGK Scheme with General Propagation

The standard Lattice BGK (LBGK) scheme often encounters numerical instability in simulation of fluid flow with small kinematic viscosity or as the nondimensional relaxation time is close to 0.5. In this paper, based on a time-splitting scheme for the Boltzmann equation with discrete velocities, a new LBGK scheme with general propagation step is proposed to address this problem. In this model, two free parameters are introduced into the propagation step, which can be adjusted to obtain a small kinematic viscosity and improved numerical stability as well. Numerical simulations of the two-dimensional Taylor vortex and the unsteady Womersley flow are carried out to test the kinematic viscosity, numerical diffusion, and numerical stability of the proposed scheme.     

A comparative study of nonlinear optimization and Taguchi methods applied to the intelligent control of manufacturing processes

current investigation focused on neural-network-based control of manufacturing processes utilizing an optimization scheme. In an earlier study, Demirci and Coulter introduced the utilization of neural networks for the intelligent control of molding processes. In that study, a forward model neural network, employed with a search strategy based on the factorial design of experiments method, was shown to successfully control the flow progression during injection molding processes. Recently, Demirciet al. showed that the search mechanism based on the factorial design of experiments method can be intolerable in time during on-line control of manufacturing processes, and suggested an inverse model neural network. This inverse model neural network was shown to be beneficial as it totally eliminated time-consuming parameter searches, but it required a harder mapping than the forward model neural network and thus its performance was inferior. In the present study, the authors investigated two different optimization methods that were utilized in making the search method of the forward control scheme more efficient. The first method was Taguchi's method of parameter design, and the second method was a nonlinear optimization method known as Nelder and Mead's downhill simplex method. These two methods were separately utilized in creating an efficient search method to be used with the forward model neural network. The performance of the resulting two control methods was compared with each other as well as with that of the forward control scheme utilizing a search strategy based on the factorial design of experiments method. Although the applications in this study were on molding processes, the method can be applied to any manufacturing process for which a process model and anin-situ sensing scheme exists.     

Kinematics and control of a fully parallel force-reflecting hand controller for manipulator teleoperation

Force feedback can enhance the efficiency of a teleoperation system by providing the operator with a sense of feel of the forces and torques arising from the interaction of the slave manipulator with the remote environment. This article addresses the kinematic analysis and control of a Parallel FOrce-Reflecting Hand Controller (PFORHC) whose design and implementation are based on a fully parallel mechanism. Kinematic analysis on the PFORHC is performed and results in a closed-form solution for the inverse kinematics. The forward kinematics is solved by Newton-Raphson's method. A fixed-gain PD control scheme is developed for force feedback control. Experiments are conducted to study the performance of the force-reflecting capability of the PFORHC. Experimental results show that the force control scheme utilizing a handgrip force sensor provides smaller steady-state errors as compared to the case utilizing no handgrip force sensor.     

A parallel approach of the inverse kinematics solutions for robots using a transputer network

This article presents a parallel method for computing inverse kinematics solutions for robots with closed-form solutions moving along a straight line trajectory specified in Cartesian space. Zhang and Paul's approach¹ is improved for accuracy and speed. Instead of using previous joint positions as proposed by Zhang and Paul, a first order prediction strategy is used to decouple the dependency between joint positions, and a zero order approximation solution is computed. A compensation scheme using Taylor series expansion is applied to obtain the trajectory gradient in joint space to replace the correction scheme proposed by Zhang and Paul. The configuration of a Mitsubishi RV-M1 robot is used for the simulation of a closed-form inverse kinematics solutions. An Alta SuperLink/XL with four transputer nodes is used for parallel implementation. The simulation results show a significant improvement in displacement tracking errors and joint configuration errors along the straight line trajectory. The computational latency is reduced as well. The modified approach proposed in this work is more accurate and faster than Zhang and Paul's approach for robots with closed-form inverse kinematics solutions. © 1996 John Wiley & Sons, Inc.     

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.     

Blind Image Deblurring via Adaptive Optimization with Flexible Sparse Structure Control

Blind image deblurring is a long-standing ill-posed inverse problem which aims to recover a latent sharp image given only a blurry observation. So far, existing studies have designed many effective priors w.r.t. the latent image within the maximum a posteriori (MAP) framework in order to narrow down the solution space. These non-convex priors are always integrated into the final deblurring model, which makes the optimization challenging. However, due to unknown image distribution, complex kernel structure and non-uniform noises in real-world scenarios, it is indeed challenging to explicitly design a fixed prior for all cases. Thus we adopt the idea of adaptive optimization and propose the sparse structure control (SSC) for the latent image during the optimization process. In this paper, we only formulate the necessary optimization constraints in a lightweight MAP model with no priors. Then we develop an inexact projected gradient scheme to incorporate flexible SSC in MAP inference. Besides l_p-norm based SSC in our previous work, we also train a group of denoising convolutional neural networks (CNNs) to learn the sparse image structure automatically from the training data under different noise levels, and we show that CNNs-based SSC can achieve similar results compared with l_p-norm but are more robust to noise. Extensive experiments demonstrate that the proposed adaptive optimization scheme with two types of SSC achieves the state-of-the-art results on both synthetic data and real-world images.

     

Analytical Inverse Kinematic Computation for 7-DOF Redundant Manipulators With Joint Limits and Its Application to Redundancy Resolution

This paper proposes an analytical methodology of inverse kinematic computation for 7 DOF redundant manipulators with joint limits. Specifically, the paper focuses on how to obtain all feasible inverse kinematic solutions in the global configuration space where joint movable ranges are limited. First, a closed-form inverse kinematic solution is derived based on a parameterization method. Second, how the joint limits affect the feasibility of the inverse solution is investigated to develop an analytical method for computing feasible solutions under the joint limits. Third, how to apply the method to the redundancy resolution problem is discussed and analytical methods to avoid joint limits are developed in the position domain. Lastly, the validity of the methods is verified by kinematic simulations.      

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.     

Closed-form inverse kinematic solution for fluoroscopic C-arms

This paper presents a closed-form solution to the inverse kinematic problem for general fluoroscopic C-arms. The resulting algorithm determines the necessary joint parameters for imaging a given point of interest p→ from a given direction z→. The existence and uniqueness of the solution is proven for all p→ and z→. The inverse kinematics lays the basis for a completely robotized C-arm. The paper describes some applications for such an automatized device and presents the first results.     

Evaluation of Neural and Genetic Algorithms for Synthesizing Parallel Storage Schemes

Exploiting compile time knowledge to improve memory bandwidth can produce noticeable improvements at runtime.^{(1, 2)} Allocating the data structure⁽¹⁾ to separate memories whenever the data may be accessed in parallel allows improvements in memory access time of 13 to 40%. We are concerned with synthesizing compiler storage schemes for minimizing array access conflicts in parallel memories for a set of compiler predicted data access patterns. The access patterns can be easily found for many synchronous dataflow computations like multimedia compression/decompression algorithms, DSP, vision, robotics, etc. A storage scheme is a mapping from array addresses into storages. Finding a conflict-free storage scheme for a set of data patterns is NP-complete. This problem is reduceable to weighted graph coloring. Optimizing the storage scheme is investigated by using constructive heuristics, neural methods, and genetic algorithms. The details of implementation of these different approaches are presented. Using realistic data patterns, simulation shows that memory utilization of 80% or higher can be achieved in the case of 20 data patterns over up to 256 parallel memories, i.e., a scalable parallel memory. The neural approach was relatively very fast in producing reasonably good solutions even in the case of large problem sizes. Convergence of proposed neural algorithm seems to be only slightly dependent on problem size. Genetic algorithms are recommended for advanced compiler optimization especially for large problem sizes; and applications which are compiled once and run many times over different data sets. The solutions presented are also useful for other optimization problems.     

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.