Revolute manipulator workspace optimization: A comparative study

Robotic manipulators with three revolute families of positional configurations are very common in the industrial robots. The capability of a robot largely depends on the workspace of the manipulator apart from other parameters. In this work, an evolutionary optimization algorithm based on foraging behavior of Escherichia coli bacteria present in human intestine is utilized to optimize the workspace volume of a 3R manipulator. The proposed optimization method is subjected to some modifications for faster convergence than the original algorithm. Further, the method is also very useful in optimization problems in a highly constrained environment such as the robot workspace optimization. The test results are compared with standard results available using other optimization algorithms such as Differential Evolution, Genetic Algorithm and Particle Swarm Optimization. In addition, this work extends the application of the proposed algorithm to two different industrial robots. An important implication of this paper is that the present algorithm is found to be superior to other methods in terms of computational efficiency.     

基于蒙特卡罗方法的除冰机器人作业空间边界提取

设计了一种输电线路除冰机器人的机械结构, 分析了该机构的作业空间问题. 在计算过程中, 引入Monte Carlo方法得到了机器人操作臂的工作空间. 采用该方法可避免对机器人运动方程的求逆解计算, 极大地简化了计算过程. 分析并指出传统的机器人工作空间边界提取方法精度有限, 且存在理论上的缺陷; 提出了一种新的基于局部点象限分布的边界点提取方法, 文中给出的算例表明, 该方法不仅精度高, 并且非常适合于处理机器人工作空间边界问题.     

机器人操作臂工作空间的混合计算方法

机器人操作臂工作空间的形状和体积的精确计算对于其优化问题是非常重要的。为此首先根据从关节空间到工作空间的运动映射关系,使用蒙特卡洛方法产生由点组成的三维机器人工作空间。然后,通过把这些点分解成一系列的切片,获得机器人工作空间每层的二维边界曲线;基于切片曲线,由三维重构的方法产生边界曲面。最后,用数值积分的方法计算了机器人工作空间的体积。     

Singularity analysis and detection of 6-UCU parallel manipulator

6-UCU kind Gough–Stewart platform (GSP) has been used extensively in practice. The singularity of GSP has been studied by many scholars, but their works mainly focused on finding the methods to divide the cases of singularity or searching the solutions with Jacobian matrices. On the other hand, this paper studies the singularities of 6-UCU parallel manipulator caused by not only the active joints but also passive universal joints. Two types of singularity are derived based on a degree of freedom method by using screw theory. Singularity detection is essential to certify the absence of singularity within a prescribed workspace or a reachable workspace for a practical use of the 6-UCU parallel manipulator. Algorithms are proposed by using evolutionary strategy to detect the singularity in the desired or reachable workspace of the 6-UCU parallel manipulator. Case studies are presented to demonstrate the effectiveness of the proposed singularity detection methods.     

On the workspace boundary determination of serial manipulators with non-unilateral constraints

Broadly applicable analytical algorithms for workspace of serial manipulators with non-unilateral constraints are developed and illustrated. The Jacobian row-rank deficiency method is employed to determine the singularities of these manipulators. There are four types of singularity sets: Type I: position Jacobian singularities; Type II: instantaneous singularities that are due to a generalized joint that is reaching its apex; Type III: domain boundary singularities, which are associated with the initial and final values of the time interval; Type IV: coupled singularities, which are associated with a relative singular Jacobian, where the null space is reduced in one sub-matrix due to either of two occurrences: a Type II or a Type III singularity. All of the singular surfaces are hypersurfaces that extend internally and externally the workspace envelope. Intersecting singular surfaces identifies singular curves that partition singular surfaces into subsurfaces, and a perturbation method is used to identify regions (curve segments/surface patches) of the hypersurfaces that are on the boundary. The formulation is illustrated by implementing it to a spatial 3-degree of freedom (DOF) and a spatial 4-DOF manipulator.     

Probability-Based Weighting of Performance Criteria for Redundant Manipulators

A method to simultaneously optimize multiple performance criteria for a redundant manipulator is presented. Preferred formulation requirements for the criteria are discussed, and previously proposed normalization methods are examined. A statistically based variable weighting technique is developed and evaluated. A seven-degree-of-freedom Robotics Research Corporation manipulator is used as a test bed for the multiple criteria optimization scheme.     

A multi-level optimization methodology for determining the dextrous workspaces of planar parallel manipulators

A numerical multi-level optimization methodology is proposed for determining dextrous workspaces of 3-degree-of-freedom (3-dof) planar parallel manipulators, in which it is required that at any point within the workspace, the manipulator is able to assume any orientation in a specified range. The method starts by finding a single initial point on the boundary of the dextrous workspace. This first stage requires the successive solution of three separate optimization sub-problems, where the evaluation of the objective function for the second problem and the constraint functions in the third problem are determined by the solution of appropriate optimization problems at a lower level. Once the boundary point is identified, further successive points along the dextrous workspace boundary are traced by the application of the so-called chord method. In the latter procedure, the determination of each successive boundary point is also obtained via a constrained optimization problem, where the constraint functions are again evaluated via the solution of an optimization problem at a lower level. The proposed method is illustrated by its successful application to three different manipulator design geometries, and for various ranges of dexterity. An abbreviated version of this paper was presented at the 5th ASMO UK/ISSMO conference on Engineering Design Optimization, Stratford upon Avon, UK, July 12–13, 2004.     

Interior and exterior boundaries to the workspace of mechanical manipulators

Analytical methods for identifying the boundary to the workspace of serial mechanical manipulators and the boundary to voids in the workspace are presented. The determination of parametric equations of surface patches that envelop the workspace of serial manipulators was presented elsewhere and is extended in this paper to an analytical method for void identification. Because of the ability to identify closed-form surface patches that exist internal and external to the workspace, a mathematical formulation based on the concept of a normal acceleration function is introduced. Admissible motion in the normal direction to a point on a singular surface is delineated and characterized by definiteness properties of a quadratic form. An enclosure bound by surface patches that do not admit normal motion is identified as a void. Several examples are treated using this formulation to illustrate the method.     

The design of a new remote manipulator for space operation using a 4-cable-driven thrusters-embedded configuration

A new remote manipulator based on cable-driven parallel mechanism (CDPM) is designed for space long-distance operations (e.g. space capture/docking and other long-distance space activities) in this paper. By controlling the cables and thrusters which are equipped on the manipulator simultaneously, the new remote manipulator can achieve expected position, linear velocity, and angular velocity. The new manipulator has a larger controllable workspace compared with usual CDPMs. The structure and characteristics of this manipulator are discussed in this paper. The volume and characteristics of the workspace are also discussed. The influence of the distance on the static equilibrium is studied. The simulation results show that the workspace of this new manipulator is larger than usual CDPM’s. The results also indicate that the cable forces and thruster vectors can completely constrain the manipulator and meet the requirements of space activities. The results of the simulation also show that the controllable workspace of the manipulator is not continuous at some regions. Hence, trajectory planning is necessary.     

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.     

Workspace Determination of General 6-d.o.f. Cable Manipulators

This paper addresses workspace determination of general 6-d.o.f. cable-driven parallel manipulators with more than seven cables. The workspace under study is called force-closure workspace, which is defined as the set of end-effector poses satisfying the force-closure condition. Having force-closure in a specific end-effector pose means that any external wrench applied to the end-effector can be balanced through a set of non-negative cable forces under any motion condition of the end-effector. In other words, the inverse dynamics problem of the manipulator always has a feasible solution at any pose in the force-closure workspace. The workspace can be determined by the Jacobian matrix and, thus, it is consistent with the usual definition of workspace in the robotics literature. A systematic method of determining whether or not a given end-effector pose is in the workspace is proposed. Based on this method, the shape, boundary, dimensions and volume of the workspace of a 6-d.o.f., eight-cable manipulator are discussed.     

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.     

机器人工作空间的界限面及其位置奇异曲面的代数求解方法

本文提出了一个求解运动副转角或移动有限制的任意机械手的工作空间界限面及其位置奇异曲面的代数方法。得出了手部参考点在固定坐标系中的一系列位置奇异曲面方程。并以5R,6R和5R-P机器人为例,使用计算机绘制出其工作空间上述各种曲面的子午截面曲线图。结果与其它方法相比,具有精度高,运算快的特点,不仅具有理论意义,而且还有实用价值。     

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．     

Robotic Workspaces after a Free-Swinging Failure

A robotic manipulator can fail in many different ways, and its capabilities after a failure are a major concern, especially for manipulators used in hazardous and remote environments, where the cost of repair or replacement is high. This article presents a study of the workspaces of robotic arms after a free-swinging failure, defined as a hardware or software failure that prevents the application of actuator torque on a joint. Two analytical methods are discussed. The first is for planar arms only and is based on a positional inverse-kinematic algorithm that uses polynomial roots, guaranteeing that all solutions, and therefore the postfailure workspace, can be found. The second method has no such guarantee, but is applicable to general spatial manipulators. It is based on a differential technique for tracing the postfailure workspace boundary.     

机器人灵活工作空间的边界分析

机器人灵活工作空间的分析是机器人运动学至今没有解决的一个问题.由于机器人在灵活工作空间中工作不会受到本身机构对它的限制.所以,机器人灵活工作空间的大小对于提高机器人的操作性能就显得格外重要.本文旨在解决机器人灵活工作空间边界的计算问题.首先.它分析了灵活工作空间边界的性质;其次,用一种新的方法——网络跟踪法确定了灵活工作空间在横截面内的边界;最后.提出了灵活工作空间端边界的求解方法.     

Workspace analysis for haptic feedback manipulator in virtual cockpit system

To obtain natural space experience of haptic interaction for users in virtual cockpit systems (VCS), a haptic feedback system and a workspace analysis framework for haptic feedback manipulator (HFM) are presented in this paper. Firstly, improving the classical three-dimensional workspace obtained by the Monte Carlo method, a novel workspace representation method, oriented workspace, is presented, which can indicate both the position and the orientation of the end-effector. Then, aimed at the characters of HFMs, the oriented workspace is divided into the effective workspace and the prohibited area by extracting the control panel area. At last, the effective workspace volume and the control panel area are calculated by the double-directed extremum method, with the accuracy improved by repeatedly adding and extracting boundary points. By simulation, the area in which interactions between the manipulator and users hand performed is determined and accordingly the effective workspace along with its boundary and volume are obtained in a relative high precision, which lay a basis for haptic interaction in VCS.     

A New Approach to the Architecture Optimization of a General 3-PUU Translational Parallel Manipulator

This paper presents a new approach to the architecture optimization of a general 3-PUU translational parallel manipulator (TPM) based on the performance of a weighted sum of global dexterity index and a new performance index-space utility ratio (SUR). Both the inverse kinematics and forward kinematics solutions are derived in closed form, and the Jacobian matrix is derived analytically. The manipulator workspace is generated by a numerical searching method with the physical constraints taken into consideration. Simulation results illustrate clearly the necessity to introduce a mixed performance index using space utility ratio for architectural optimization of the manipulator, and the optimization procedure is carried out with the goal of reaching a compromise between the two indices. The analytical results are helpful in designing a general 3-PUU TPM, and the proposed design methodology can also be applied to architectural optimization for other types of parallel manipulators.     

Design Strategy of Serial Manipulators With Certified Constraint Satisfaction

This paper presents the design strategy of serial manipulators with constraint satisfaction. The algorithm provides certified solutions to the range of values of the manipulator design parameters that satisfy the given constraints for all points inside a desired workspace. Alternatively, it can also be used to obtain the achievable workspace of a particular manipulator topology within which a set of given constraints are satisfied. This strategy can therefore be applied to the general case of a serial manipulator design problem, robots of adjustable parameters, or even reconfigurable robot strategy to obtain a suitable topology. The interval-based algorithm was implemented on an example serial anthropomorphic manipulator with joint displacement constraints and obtains the possible variations to the manipulator topology that allow the required workspace to be achievable under the given joint displacement constraints. Results are presented and discussed.      

基于AutoCAD平台的六自由度并联机器人

本文研究基于AutoCAD平台的六自由度并联机器人在姿态给定情况下工作空间(即位置工作空 间)的几何确定方法,该方法以机器人的运动学反解为基础,得出Stewart并联机器人和6-R TS并联机器人位置工作空间的边界方程,从而得出Stewart并联机器人的位置工作空 间是6个球体的交集,6-RTS并联机器人在姿态给定时其工作空间是6个相同的规则曲面体 的交集．基于AutoCAD平台,其交集以及交集的容积可以很容易的得出,该方法是确定六自 由度并联机器人工作空间的一种简单、有效方法．