A kinematic analysis of the space station remote manipulator system (SSRMS)

An efficient reverse analysis of three 6-degree-of-freedom (dof) subchains of the 7-dof SSRMS is presented. The first subchain is formed by locking the seventh joint. The second subchain is formed by locking the second joint, while the third subchain is formed by locking the first joint (the grounded joint is counted as the first joint in the chain). There are a maximum of eight different arm configurations in each of the three subchains, and these were determined by employing a computer-efficient algorithm, which required the rooting of only at most quadratic polynomials. The algorithms were implemented, and the SSRMS was employed in an animated environment to perform and practice a number of useful tasks for space station servicing. The locking of the second joint has the advantage in that an operator could, at the outset, choose the orientation of the plane that contains the two longest links (the upper arm and forearm) so as to avoid collisions with obstacles. However, it has the disadvantage that when the second joint angle equals 0° or 180°, the manipulator is in a singularity configuration (a singularity analysis of the SSRMS is presented in a second article). It is interesting to note that this plane can also be oriented by specifying the first joint angle. This has the distinct advantage that the plane can be oriented arbitrarily and, in this way, the singularity is avoided.     

Inverse dynamics of a parallel manipulator

Presented is an analysis of the kinematics and the inverse dynamics of a proposed three degree of freedom (dof) parallel manipulator resembling the Stewart platform in a general form. In the kinematic analysis, the inverse kinematics, velocity, and acceleration analyses are performed, respectively, using vector analysis and general homogeneous transformations. An algorithm to solve the inverse dynamics of the proposed parallel manipulator is then presented using a Lagrangian technique. In this case, it is found that one should introduce and subsequently eliminate Lagrange multipliers to arrive at the governing equations. Numerical examples are finally carried out to examine the validity of the approach and the accuracy of the numerical technique employed. The trajectory of motion of the manipulator is also performed using a cubic spline. © 1994 John Wiley & Sons, Inc.     

Parallel computation of manipulator inverse dynamics

In this article, parallel computation of manipulator inverse dynamics is investigated. A hierarchical graph-based mapping approach is devised to analyze the inherent parallelism in the Newton-Euler formulation at several computational levels, and to derive the features of an abstract architecture for exploitation of parallelism. At each level, a parallel algorithm represents the application of a parallel model of computation that transforms the computation into a graph whose structure defines the features of an abstract architecture, i.e., number of processors, communication structure, etc. Data flow analysis is employed to derive the time lower bound in the computation as well as the sequencing of the abstract architecture. The features of the target architecture are defined by optimization of the abstract architecture to exploit maximum parallelism while minimizing various overheads and architectural complexity. An algorithmically specialized, highly parallel, MIMD-SIMD architecture is designed and implemented that is capable of efficient exploitation of parallelism at several computational levels. The computation time of the Newton-Euler formulation for a 6-degree-of-freedom (dof) general manipulator is measured as 187 μs. The increase in computation time for each additional dof is 23 μs, which leads to a computation time of less than 500 μs, even for a 12-dof redundant arm.     

Development of the Omni Directional Intelligent Navigator

The Autonomous Systems Laboratory is in the midst of developing an advanced underwater robotic technology test platform. The platform consists of the Omni-Directional Intelligent Navigator (ODIN) and the Integrated Graphic Workstation (IGW). ODIN is a six degree-of-freedom (dof) underwater vehicle with dual operational modes (autonomous and tethered) and a single dof mechanical manipulator. IGW is a real-time, 3-dimensional graphic monitoring, testing, and evaluation workstation. This paper presents ODIN's mechanical and electrical specifications; its vehicle dynamics and depth control system; its recent simulation and experimental results; and IGW's specifications     

Motion pattern analysis of parallel kinematic machines: A case study

This paper looks at the “five-axis machines” for machining operations. These machines have five (or six at maximum) degrees of freedom (dof). The output motion must have at least three translational and two rotational dof. This output motion pattern can be obtained with different structural topologies: serial, parallel, hybrid and with serial and/or parallel manipulators working in co-operation. The latter allows higher motion ranges in rotational and translational dof. Moreover, it provides a good stiffness, a highly valued requisite in applications like machining. Manipulators of this type are characterized by their kinematics to be integrated in the CNC, which requires the study of the relative motion between their modules. This motion is usually complex, and in certain cases presents kinematic relations not evident. This work presents a methodology to solve the motion pattern out of the direct and inverse kinematics of the relative motion between the modules of which the manipulator is composed. On the one hand, the spindle is mounted on a parallel module. On the other hand, the working table is mounted on a serial module. This methodology was applied to the Hermes parallel manipulator in combination with rotary and linear tables. As a result, a series of considerations regarding other possible combinations between modules was made and a new machine is proposed.     

Model-free robot joint position regulation and tracking with prescribed performance guarantees

The problem of robot joint position control with prescribed performance guarantees is considered; the control objective is the error evolution within prescribed performance bounds in both problems of regulation and tracking. The proposed controllers do not utilize either the robot dynamic model or any approximation structures and are composed by simple PID or PD controllers enhanced by a proportional term of a transformed error through a transformation related gain. Under a sufficient condition for the damping gain, the proposed controllers are able to guarantee (i) predefined minimum speed of convergence, maximum steady state error and overshoot concerning the position error and (ii) uniformly ultimate boundedness (UUB) of the velocity error. The use of the integral term reduces residual errors allowing the proof of asymptotic convergence of both velocity and position errors to zero for the regulation problem under constant disturbances. Performance is a priori guaranteed irrespective of the selection of the control gain values. Simulation results of a three dof spatial robotic manipulator and experimental results of one dof manipulator are given to confirm the theoretical findings.     

Computer generation of symbolic kinematics for robot manipulators

Computer generation of symbolic solutions for the direct and inverse robot kinematics is a desired capability not previously available to robotics engineers. In this article, we present a methodology for the design of a software system capable of solving the direct and inverse kinematics for n degree of freedom (dof) manipulators in symbolic form. The inputs to the system are the Denavit-Hartenberg parameters of the manipulator. The outputs of the system are the direct and inverse kinematics solutions in symbolic form. The system consists of a symbolic processor to perform matrix and algebraic manipulations and an expert system to solve the class of nonlinear equations involved in the solution of the inverse kinematics problem. The system can be used to study robot kinematics configurations whose inverse kinematics solutions are not known to exist a priori. Two examples are included to illustrate its capabilities. The first example provides explicit analytical solutions, previously believed nonexistent, for a 3 dof manipulator. A second example is included for a robot whose inverse kinematics solution requires intensive algebraic manipulations.     

Effect of tension parameters and intervals on splines-under-tension based robot trajectory planning

The new trajectory planner using cubic spline functions under tension in joint coordinates is developed and implemented in the 6 dof articulated robot with a parallel drive arm mechanism to improve the smoothness of the joint trajectories and positioning accuracy of the manipulator. Also, the optimal selection of the tension parameter and time interval selection schemes are investigated in this study. © 1994 John Wiley & Sons, Inc.     

On the dynamics and control of flexible joint space manipulators

Space manipulator systems are designed to have lightweight structure and long arms in order to achieve reduction of fuel consumption and large reachable workspaces, respectively. Such systems are subject to link flexibilities. Moreover, space manipulator actuators are usually driven by harmonic gear mechanisms which lead to joint flexibility. These types of flexibility may cause vibrations both in the manipulator and the spacecraft making the positioning of the end-effector very difficult. Here, both types of flexibilities are lumped at the joints and the dynamic equations of a general flexible joint space manipulator are derived. Their internal structure is highlighted and similarities and differences with fixed-base robots are discussed. It is shown that one can exploit the derived dynamic structure in order to design a static feedback linearization control law and obtain an exact linearization and decoupling result. The application of such controllers is desired in space applications due to their small computational effort. In case of fixed-base manipulators, the effective use of a static feedback controller is feasible only if a simplified model is considered. Then, the proposed static feedback linearization control law is applied to achieve end-effector precise trajectory tracking in Cartesian space maintaining a desirable non-oscillatory motion of the spacecraft. The application of the proposed controller is illustrated by a planar seven degrees of freedom (dof) system.     

Synthesis and analysis of a new class of six-degree-of-freedom parallel minimanipulators

A new class of 6-degree-of-freedom (dof) parallel minimanipulators is introduced. The minimanipulators are designed to provide high resolution and high stiffness for fine position and force control in a hybrid serial-parallel manipulator system. Two-dof planar linkages and inextensible limbs are used to improve positional resolution and stiffness of the minimanipulators. The 2-dof linkages serve as drivers for the minimanipulators. The minimanipulators require only three inextensible limbs and, unlike most of the six-limbed parallel manipulators, their direct kinematics can be reduced to solving a polynomial in a single variable. In addition, by using three limbs instead of six other benefits such as lower possibility of mechanical interference between limbs can be realized. All of the minimanipulator actuators are base-mounted. As a result, higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. In addition to the design discussion, kinematic analysis of the minimanipulators is also presented. © 1993 John Wiley & Sons, Inc.     

Design of reconfigurable coupled-serial-chain-based manipulation assistive aids

Our goal is to design a reconfigurable single degree-of-freedom (dof) articulated manipulation assistive aid, whose end-effector is required to closely approximate a series of constrained planar paths. To this end, we investigate the viability of the coupled-serial-chain configuration manipulator design created by constraining the relative rotations of a revolute-jointed serial-chain manipulator with linear cable–pulley couplings. The forward kinematics equations take the form of a finite trigonometric series in terms of the input crank rotations. Our proposed Fourier-based synthesis method exploits this special structure to facilitate the design synthesis of such manipulators. We then examine design enhancements, to permit this manipulator to be reconfigured for multiple sets of constrained end-effector tasks, by controlled variation of the principal structural parameters. Particular attention is paid to the creation of a physical prototype, which facilitates such reconfiguration.     

A Geometric Theory for Analysis and Synthesis of Sub-6 DoF Parallel Manipulators

Mechanism synthesis is mostly dependent on the designer's experience and intuition and is difficult to automate. This paper aims to develop a rigorous and precise geometric theory for analysis and synthesis of sub-6 DoF (or lower mobility) parallel manipulators. Using Lie subgroups and submanifolds of the special Euclidean group SE(3), we first develop a unified framework for modelling commonly used primitive joints and task spaces. We provide a mathematically rigorous definition of the notion of motion type using conjugacy classes. Then, we introduce a new structure for subchains of parallel manipulators using the product of two subgroups of SE(3) and discuss its realization in terms of the primitive joints. We propose the notion of quotient manipulators that substantially enriches the topologies of serial manipulators. Finally, we present a general procedure for specifying the subchain structures given the desired motion type of a parallel manipulator. The parallel mechanism synthesis problem is thus solved using the realization techniques developed for serial manipulators. Generality of the theory is demonstrated by systematically generating a large class of feasible topologies for (parallel or serial) mechanisms with a desired motion type of either a Lie subgroup or a submanifold.     

Pose optimization in robotic machining using static and dynamic stiffness models

Industrial robots are typically not used for milling of hard materials due to their low stiffness compared to traditional machine tools. Due to milling being a five degree of freedom (dof) operation, a typical six dof serial manipulator introduces a redundant degree of freedom in the robot pose. This redundancy can be exploited to optimize the pose of the robot during milling to minimize force-induced deflections at the end-effector. Stiffness modeling and optimization techniques for industrial robots utilizing both static (no mass and damping terms) and dynamic (mass and damping terms included) models exist. This paper presents a comparative study of robot pose optimization using static and dynamic stiffness models for different cutting scenarios. Milling experiments show that while a dynamic model-based robot pose optimization yields significant improvement over a static model-based optimization for cutting conditions where the time varying cutting forces approach the robot's natural frequencies, a static model-based optimization is sufficient when the frequency content of the cutting forces are not close to the robot's natural frequencies.     

Forward kinematics of a class of parallel (Stewart) platforms with closed-form solutions

This article studies the geometrical condition for closed-form solutions of forward kinematics of parallel platforms. It is shown that closed-form solutions are available if 1 rotational degree of freedom (dof) of the moving platform is decoupled from the other 5 dof. Geometrically, this condition is satisfied when five end-points at the moving platform (or at the base) are colinear. A general case that these five points do not coincide with each other is studied first and is shown to have 16 possible closed-form solutions. The variations of parallel platforms that satisfy the above-mentioned geometrical condition are then discussed. Some of them have the additional feature that the three rotational dof are fully decoupled from the 3 translational dof and their closed-form solutions are further simplified. One particular case has extremely simple forward kinematics and could be used as an alternative to the Stewart platform.     

空间缩放式六自由度并联平台机构及位置分析

本文提出了一种以缩放机构为分支的新型六自由度空间并联机器人机构模型．文中讨论了它的机构学特点，给出了位置反解的方法，推导出了位置正解的８次封闭解法，并进行了数值验证．     

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 Family of Symmetrical Lower‐Mobility Parallel Mechanisms with Spherical and Parallel Subchains

This paper presents a new family of symmetrical lower‐mobility parallel mechanisms (PMs) with spherical and parallel subchains, which consists of two 5‐DOF (degrees of freedom) PMs, one 4‐DOF PM and five 3‐DOF PMs. The basic feature of this family is that each limb consists of five revolute pairs and can be constructed with two subchains, a 2R pointing subchain and a 3R parallel subchain, or a 3R spherical subchain and a 2R parallel subchain. Different geometrical arrangements of the limbs lead to different degrees of freedom. All the PMs of this family can be modularized easily due to the simple structure of the subchains. © 2003 Wiley Periodicals, Inc.     

基于多体力学的车辆动力学控制系统仿真及优化

利用多体分析软件ADAMS建立了多自由度汽车整车多体动力学仿真模型,并进一步简化为15自由度非线性模型,结合2自由度线性模型建立PID控制策略,进行了冰面单周正弦工况下的汽车操纵稳定性仿真试验研究,采用自适应模拟退火算法与非线性序列二次规划法相结合的组合优化方法对控制系统的控制参数进行了分析和优化.结果表明,该控制方法能够大幅度提高车辆的操纵稳定性和安全性,能够适应复杂的路面和行驶工况,取得了良好的效果.     

求解并联机床工作空间的算法分析和研究

本文针对三自由度并联机床的机构进行了分析,并求出了其位置逆解。在此基础上对求解其工作空间所采用的算法进行了研究和分析,重点给出了边界搜索法的设计方法,并进行了相关算法的分析。结果表明,在机构没有空洞的情况下,边界搜索法是一种理想的求解工作空间的算法     

A 6-DOF adaptive parallel manipulator with large tilting capacity

In this paper, a novel 6 degrees of freedom (DOFs) adaptive parallel manipulator with large tilting capacity is presented. The manipulator consists of four identical peripheral limbs and one center limb connecting the base and the moving platform. Due to the special architecture, the doubly actuated center limb of the manipulator could have infinite inverse solutions. In every configuration of the end-effector, the manipulator can adapt its center limb to the position and orientation with best dexterity. An optimization equation for obtaining the optimized dexterity of the manipulator is introduced to solve this nonholonomic problem, which also makes the manipulator capable of large tilting capacity. Targeting for the application of five-face machining, the detailed kinematic analysis of the manipulator is developed, which includes the closed-form solutions of inverse position problems, the singularity, dexterity, workspace and tilting capability. The analysis developed in this paper shows that the proposed manipulator has large tilting capacity and thus a suitable candidate for five-face machining.