Parallel manipulator kinematics learning using holographic neural network models

The forward kinematic problem of parallel manipulators is resolved using a holographic neural paradigm. In a holographic neural model, stimulus–response (input–output) associations are transformed from the domain of real numbers to the domain of complex vectors. An element of information within the holographic neural paradigm has a semantic content represented by phase information and a confidence level assigned in the magnitude of the complex scalar. Networks are trained on a database generated from the closed-form inverse kinematic solutions. After the learning phase, the networks are tested on trajectories which were not part of the training data. The simulation results, given for a planar three-degree-of-freedom parallel manipulator with revolute joints and for a spherical three-degree-of-freedom parallel manipulator, show that holographic neural network models are feasible to solve the forward kinematic problem of parallel manipulators.     

Singularity loci of planar parallel manipulators with revolute actuators

The determination of the singularity loci of planar parallel manipulators is addressed in this paper. The inverse kinematics of two kinds of planar parallel manipulators (a two-degree-of-freedom manipulator and a three-degree-of-freedom manipulator) are first computed and their velocity equations are then derived. At the same time, the branches of the manipulators are distinguished by the introduction of a branch index K_i. Using the velocity equations, the singularity analysis of the manipulators is completed and expressions which represent the singularity of the manipulators are obtained. A polynomial form of the singularity loci is also derived. For the first type of singularity of parallel manipulators, the singularity locus is obtained by finding the workspace limits of the manipulators. For the second type of singularity, the loci are obtained through the solution of nonlinear algebraic equations obtained from the velocity analysis. Finally, the graphical representation of the complete singularity loci of the manipulators is illustrated with examples. The algorithm introduced in this paper allows the determination of the singularity loci of planar parallel manipulators with revolute actuators, which has been elusive to previous approaches.     

Design philosophy of an isotropic six-axis serial manipulator

Presented in this paper is the design philosophy employed for the constructtion of DIESTRO, an isotropic, six-axis, serial manipulator. The kinematic criteria applied so far in manipulator design have been based largely on kinematic solvability, in the sense of allowing for closed-form inverse kinematic solutions. As opposed to this rather limiting criterion, DIESTRO was designed kinematically so as to having a set of configurations in which its Jacobian matrix allows its inversion without roundoff error amplification. Although the basic kinematic chain is of the serial type, this design criterion led to an architecture not admitting closed-form inverse kinematic solutions. The central task was to produce an accurate robot under the prescribed specifications. It is believed that, under similar workspace and load specifications, the particularly challenging design of many other serial manipulators with complex architectures can benefit from the design guidelines given here.     

Redundancy modelling and resolution for robotic mobile manipulators: a general approach

In this work the topic of kinematic redundancy modelling and resolution for robotic mobile manipulators is considered. A set of redundancy parameters is introduced to define a general inverse kinematic procedure for mobile manipulators. Then, redundancy is treated as a non-linear optimization problem with the purpose of finding robot configurations that maximize the designed metric measures. Some strategies to design the optimization objective function are introduced in order to achieve desirable redundant behaviours, such as obstacles avoidance, mobile base motions reductions and dexterity optimization. Moreover, the robot controller has been developed following an object-oriented software architecture principle that allows to keep it general and robot independent. As a prove of reliability and generality of our approach, the same controller has been used to control several different mobile manipulators in a simulation environment, as well as a real KUKA youBot robot.     

Kinematics and dynamics analyses of a parallel manipulator with three active legs and one passive leg by a virtual serial mechanism

A novel CAD variation geometry approach and a virtual serial mechanism approach are proposed for analyzing the kinematics and dynamics of a parallel manipulator with three SPS-type active legs and one PU-type constrained passive leg. First, a simulation mechanism of this parallel manipulator is created, and some kinematic characteristics are analyzed. Second, the inverse formulae for solving pose and Jocabian matrix are derived, and workspace and singularity are determined. Third, a virtual serial mechanism is created, and the analytic formulae for solving active forces and constrained wrench of these parallel manipulators are derived. The analytic results are verified by using its simulation mechanism.     

Kinematic analysis and singularity representation of spatial five-degree-of-freedom parallel mechanisms

This article addresses the kinematic modeling and the determination of the singularity loci of spatial five-degree-of-freedom parallel mechanisms with prismatic or revolute actuators. The architecture of the spatial five-degree-of-freedom parallel mechanisms is first introduced. Then, algorithms are derived for the solution of the inverse kinematic problem for the two types of mechanisms considered here. Two different methods are presented for the derivation of the velocity equations and the corresponding Jacobian matrices are derived. The numerical determination of the workspace boundaries is then briefly discussed. Finally, the determination of the singularity loci is performed, using the velocity equations, and examples are given to illustrate the results. It is shown that the vector formulation of the velocity equations leads to more efficient algorithms for the determination of the singularity loci. Spatial five-degree-of-freedom parallel mechanisms can be used in several robotic applications as well as in flight simulators. The kinematic analysis and the determination of the singularity loci are very important design issues. © 1997 John Wiley & Sons, 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.     

Equivolumetric partition of solid spheres with applications to orientation workspace analysis of robot manipulators

Orientation workspace analysis is a critical issue in the design of robot manipulators, especially the spherical manipulators. However, there is a lack of effective methods for such analysis, because the orientation workspace of a robot manipulator is normally a subset of SO(3) (the special orthogonal group) with a complex boundary. Numerical approaches appear more practical in actual implementations. For numerical analysis, a finite partition of the orientation workspace in its parametric domain is necessary. It has been realized that the exponential coordinates parameterization is more appropriate for finite partition. With such a parameterization, the rigid body rotation group, i.e., SO(3), can be mapped to a solid sphere D/sup 3/ of radius /spl pi/ with antipodal points identified. A novel partition scheme is proposed to geometrically divide the parametric domain, i.e., the solid sphere D/sup 3/ of radius /spl pi/, into finite elements with equal volume. Subsequently, the volume of SO(3) can be numerically computed as a weighted volume sum of the equivolumetric elements, in which the weightages are the element-associated integration measures. In this way, we can simplify the partition scheme and also reduce the computation efforts, as the elements in the same partition layer (along the radial direction) have the same integration measure. The effectiveness of the partition scheme is demonstrated through analysis of the orientation workspace of a three-degree-of-freedom spherical parallel manipulator. Numerical convergence on various orientation workspace measures, such as the workspace volume and the global condition index, are obtained based on this partition scheme.     

A comparison between the Denavit–Hartenberg and the screw-based methods used in kinematic modeling of robot manipulators

This paper aims to integrate didactically some engineering concepts to understand and teach the screw-based methods applied to the kinematic modeling of robot manipulators, including a comparative analysis between these and the Denavit–Hartenberg-based methods. In robot analysis, kinematics is a fundamental concept to understand, since most robotic mechanisms are essentially designed for motion. The kinematic modeling of a robot manipulator describes the relationship between the links and joints that compose its kinematic chain. To do so, the most popular methods use the Denavit–Hartenberg convention or its variations, presented by several author and robot publications. This uses a minimal parameter representation of the kinematic chain, but has some limitations. The successive screw displacements method is an alternative representation to this classic approach. Although it uses a non-minimal parameter representation, this screw-based method has some advantages over Denavit–Hartenberg. Both methods are here presented and compared, concerning direct/inverse kinematics of manipulators. The differential kinematics is also discussed. Examples of kinematic modeling using both methods are presented in order to ease their comparison.     

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.     

6-PSS并联机器人操作机平动工作空间解析

提出一种求解6-PSS并联机器人操作机平动工作空 间 边界的解析方法．该方法将平动工作空间问题归结为三类子空间边界求交问题,即分别由六 张球面片交集构成的上、下边界与由六张椭圆柱面交集构成的侧面边界的求交问题．文中还 提出主工作空间的概念和相应的解析表达及工作空间评价指标,并探讨了设计参数对评价指 标的影响规律．     

Robotica: a Mathematica package for robot analysis

Robotica is a computer aided design package for robotic manipulators developed in the Coordinated Science Laboratory at the University of Illinois at Urbana-Champaign. It encapsulates over 30 functions into a Mathematica package allowing efficient symbolic and numeric calculation of kinematic and dynamic equations for multi-degree-of-freedom manipulators. An X-Windows front end that utilizes the interprocess communication features of Mathematica 2.1 has also been created for ease of use. This paper describes the most important features of the package and how they are used     

Performance investigations on optimum mechanical design aspects of planar parallel manipulators

This paper presents a comparative analysis of three degrees of freedom planar parallel robotic manipulators (x, y and θ_z motion platforms) namely 2PRP-PPR, 2PRR-PPR, 3PPR (Hybrid), 3PRP (Hephaist) and 3PPR U-base in terms of optimal kinematic design performance, static structural stiffness and dynamic performance (energy and power consumption). Kinematic and dynamic performance analyses of these platforms have been done using multibody dynamics software (namely ADAMS/View). Static stiffness of the above-mentioned manipulators have been analysed, compared using the conventional joint space Jacobian stiffness matrix method, and this method has been verified through a standard finite-element software (namely NASTRAN) as well. The size of the fixed base or aspect ratio (width/height) can be varied for various working conditions to understand its design parameters and optimal design aspects which are depending on the fixed base structure. Different aspect ratios (fixed base size) are considered for the comparative analyses of isotropy, manipulability and stiffness for the above-mentioned planar parallel manipulators. From the numerical simulation results, it is observed that the 2PRP-PPR manipulator is associated with a few favourable optimum design aspects such as singularity-free workspace, better manipulability, isotropy, higher stiffness and better dynamic performance in terms of power and energy requirement as compared to other planar parallel manipulators.     

A unified algorithm to determine the reachable and dexterous workspace of parallel manipulators

This paper presents a novel idea for determining the reachable and dexterous workspace of parallel manipulators. Both the reachable workspace and dexterous workspace are utmost important for optimal design and performance comparison of manipulators, because each configuration or point in this region has specified kinematic dexterity by the designer. We propose a uniform algorithm, called stratified workspace boundary determining algorithm (SWBDA), which considers various physical and contrived constraints. The problems of determining the reachable and dexterous workspace boundaries are defined and the unified method is applied to solve all the problems of this kind. The validity and efficiency of the proposed method are verified with two kinds of representative parallel manipulator, since their relational results were studied in literatures. Finally, the advantages of the proposed method are summarized by comparing with other methods.     

Review of the Robotica software package for robotic manipulators

Robotica is a computer-aided design package for robotic nmanipulators developed at the Coordinated Science Laboratory at the University of Illinois at Urbana- Champaign. The package is a collection of function definitions for the Mathematica symbolic mathematics program. Robotica can be used either with an X- Windows graphical user interface (GUI) on a Sun Workstation or as an included function definition file within Mathematica. The primary feature of Robotica is the ability to compute, symbolically or numerically, the kinematic and dynamic equations of arbitrary robot systems utilizing the standard Denevit-Hartenburg (DH) kinematic convention. Robotica also provides the ability to visualize these arbitrary manipulators using the X- Windows graphical interface to the Mathematica graphics routines. The paper looks at the usage of Robotica at the Air Force Institute of Technology, comments on the features of Robotica, and needs for improvement and suggestions for future development     

Kinematic analysis of a 3-PRS parallel manipulator

Although the current 3-PRS parallel manipulators have different methods on the arrangement of actuators, they may be considered as the same kind of mechanism since they can be treated with the same kinematic algorithm. A 3-PRS parallel manipulator with adjustable layout angle of actuators has been proposed in this paper. The key issues of how the kinematic characteristics in terms of workspace and dexterity vary with differences in the arrangement of actuators are investigated in detail. The mobility of the manipulator is analyzed by resorting to reciprocal screw theory. Then the inverse, forward, and velocity kinematics problems are solved, which can be applied to a 3-PRS parallel manipulator regardless of the arrangement of actuators. The reachable workspace features and dexterity characteristics including kinematic manipulability and global dexterity index are derived by the changing of layout angle of actuators. Simulation results illustrate that different tasks should be taken into consideration when the layout angles of actuators of a 3-PRS parallel manipulator are designed.     

A new reconfigurable parallel mechanism using novel lockable joints for large scale manufacturing

A new lockable spherical joint is proposed in this paper, and it can be used as a revolute joint, a universal joint or a spherical joint. Three locking methods are introduced to construct the lockable spherical joint. Based on the proposed lockable spherical joint, a new reconfigurable parallel mechanism (RPM) with large positioning workspace is presented. The RPM has a tripod architecture with a lockable joint in each limb, which enables it three types of parallel mechanisms in six motion cases. Mobility analysis of the six motion cases is conducted. The new RPM can realize both translation and rotation by changing operative modes, which can be employed as machine tools, fixtures or manipulators. Based on the new RPM, two modular reconfigurable manufacturing systems are designed for aircraft assembly production, and a reconfiguration strategy is presented.     

Extreme reaches and reachable workspace analysis of general parallel robotic manipulators

This article presents a systematic numerical method for analyzing the extreme reaches and the reachable workspace of general parallel robotic manipulators. In this method, finding the extreme reach is formulated as an optimization problem. The closed loops of the robot are virtually disconnected into open kinematic chains. Violations of the loop closure constraints and the position error of the end-effector are included in the objective function as penalty terms. This formulation not only is conceptually straightforward, but also can effectively reduce the problem size. The problem is solved by using a two-stage sequential unconstrained minimization algorithm. A procedure for determining the boundary surfaces of the reachable workspace is also presented. © 1998 John Wiley & Sons, Inc. 15: 145–159, 1998     

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.