Stiffness and dexterous performances optimization of large workspace cable-driven parallel manipulators

Cable-driven parallel manipulators (CDPMs) provide an easy way to achieve large workspace since flexible cables can be readily stored on reels. Generally, cables are treated as massless and inextensible that can only be tensioned. But for large workspace applications, cable curve due to their self-weight must be considered. In this paper, a curved cable is modeled as the series of an inextensible parabolic cable and a flat elastic cable to accurately account for its curve effect. The stiffness and Jacobian matrices of CDPMs are derived, which provide quantitative representations of stiffness and dexterity of manipulators. An optimization model is presented to simultaneously improve the stiffness and dexterity by selecting proper sectional area of cables and other structural parameters. Numerical examples demonstrate the curve effect on the stiffness of manipulators and a remarkable improvement of the performances can be obtained by properly determining structural parameters.     

A geometrical workspace calculation method for cable-driven parallel manipulators on minimum tension condition

In this paper, a geometrical expression to delineate the sum of tensions (i.e. minimum 1-norm tensions) of 2-DoF planar cable-driven parallel manipulators (CDPMs) is proposed and proofed, which can be used to reduce calculation time of workspace determination. Furthermore, this paper also presents a systematic analysis on the relation between cable tension and workspace by means of convex analysis. In order to obtain wrench-feasible workspace, a unified and feasible algorithm is adopted in simulation examples of spatial CDPMs with different configurations, which demonstrate that the proposed method is valid and straightforward to calculate workspace.     

Optimization of Actuator Forces in Cable-Based Parallel Manipulators Using Convex Analysis

In cable-driven parallel manipulators (CPMs), cables can perform only under tension, and therefore, redundant actuation, which can be provided by redundant limbs, is needed to maintain the cable tensions. By optimizing the distribution of the forces in the cables and the redundant limbs, the average size of actuators can be reduced resulting in lower cost. Optimizing the force distribution in CPMs requires consideration for the inequality constraints imposed on the cable forces as a result of the unilateral driving property of the cables. In this study, a projection method is presented to calculate optimum solutions for the actuators force distribution in CPMs. Two solutions are presented: 1) a minimum-norm solution that minimizes the 2-norm of all forces in the cables and redundant limbs and 2) a solution that minimizes the 2-norm of the forces in the cables only. The optimization problem is formulated as a projection on an intersection of convex sets and the Dykstra's projection method is used to obtain the solutions. This method is successfully applied to a 3-DOF CPM.     

Inverse Kinematics and Workspace Analysis of a 3 DOF Flexible Parallel Humanoid Neck Robot

To mimic the human neck’s three degree-of-freedom (DOF) rotation motion, we present a novel bio-inspired cable driven parallel robot with a flexible spine. Although there exists many parallel robotic platform that can mimic the human neck motion, most of them have only two DOF, with the yaw motion being actuated separately. The presented flexible parallel humanoid neck robot employs a column compression spring as the main body of cervical vertebra and four cables as neck muscles to connect the base and moving platform. The pitch and roll movements of moving platform are realized by the two dimensional lateral bending motion of the flexible spring, and a bearing located at the top of the compression spring and embedded in the moving platform is used to achieve the yaw motion of the moving platform. By combing the force and torque balance equations with the lateral bending statics of the spring, inverse kinematics and optimizing the cable placements to minimize the actuating cable force are investigated. Moreover, the translational workspace corresponding to pitch and roll movements and rotational workspace corresponding to yaw movement are analyzed with positive cable tension constraint. Extensive simulations were performed and demonstrated the feasibility and effectiveness of the proposed inverse kinematics and workspace analysis of the novel 3 DOF flexible parallel humanoid neck robot.     

Determination and Management of Cable Interferences Between Two 6-DOF Foot Platforms in a Cable-Driven Locomotion Interface

The intrinsic interaction of a robotic system that includes two 6-degree-of-freedom cable-driven platforms sharing a common workspace might result in cable interferences for random trajectories. This paper presents and analyzes computational methods for geometrically determining and managing these interferences for any trajectory constrained with variable loads. The algorithms considered determine which cable can be released from an active actuation state while allowing control in a minimal tension state, thereby ensuring that both platforms stay in a controllable workspace. The process of managing cable interferences constitutes a challenge as one must take into account the inherent limitations of the workspace, which not only include the possibility of interference itself, but also the geometry of the cable-driven locomotion interface (CDLI), its dynamics, the nonideal behavior of real cables, and the requirement that both platforms must be completely constrained at any time. As releasing a cable from an active actuation state might generate tension discontinuities in the other cables, this paper also proposes collision prediction schemes that are only applied to redundant actuators in order to reduce or completely eliminate such discontinuities. Finally, a simulation of a CDLI embedded as a peripheral in a virtual environment, in which the load applied on each platform comes from the wrench measured under the foot for a natural gait walking, is thoroughly analyzed.     

Design of a large-scale cable-driven robot with translational motion

The design of a new cable-driven robot for large-scale manipulation is presented with focus on the tension condition in the cables. In this robot, the arrangement of the cables is such that the moving platform has three translational motions. The robot has potentials for large-scale robotic manipulations, machining of large parts and material handling. The design analysis presented here is towards the synthesis of the robot as well as the sizing of the actuators and cables. The synthesis of this robot is dependent on the results of the tensionable workspace analysis previously published by the Alikhani et al. [6]. The analysis of the cable forces is presented in detail, which is then used to size the actuators. For this purpose, a geometrical approach is used to represent the capability of the end-effector for applying forces and moments as convex polyhedra. The design problem is then reduced to the sizing of these polyhedra according to the design requirements and manufacturing limitations. A prototype is also designed and fabricated, which is presented at the end to further elaborate on the proposed approach.     

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.     

Design of cable-driven parallel manipulators for a specific workspace using interval analysis

In this paper, we present a method, based on interval analysis, to solve the problem of designing cable-driven parallel manipulators (CDPMs) for a desired workspace. The constraint of having positive cable tensions ensuring the equilibrium of the platform has to be satisfied within the given workspace. The proposed algorithm is based on interval analysis, which covers the entire workspace and hence guarantees a singularity-free workspace. Furthermore, the algorithm is capable of finding all possible solutions for this problem and an optimal one is selected according to the user-defined criterion. Two examples are selected to show the efficiency of the developed algorithm in solving this complex problem. The first one deals with the design of a planar CDPM and the second one considers a spatial CDPM. In both cases, the algorithm succeeded to find all possible designs from which the designer can select a solution that fits best his application.     

Analysis of the wrench-closure workspace of planar parallel cable-driven mechanisms

The mobile platform of a parallel cable-driven mechanism is connected in parallel to a base by lightweight links, such as cables. Since the cables can only work in tension, the set of poses of the mobile platform for which the cables can balance any external wrench, i.e., for which the platform of the mechanism is fully constrained, is often limited or even nonexistent. Thus, the study and determination of this set of poses, called the wrench-closure workspace (WCW), is an important issue for parallel cable-driven mechanisms. In this paper, the case of planar parallel cable-driven mechanisms is addressed. Theorems that characterize the poses of the WCW are proposed. Then, these theorems are used to disclose the parts of the reachable workspace which belong to the WCW. Finally, an efficient algorithm that determines the constant-orientation cross-sections of these parts is introduced.     

基于性能驱动的船载稳定平台尺度参数优化设计

为提升船载稳定平台的运动学性能,针对■并联机构的尺度参数优化问题,以机构的工作空间体积和全域力传递率为综合评价指标,采用小生境遗传算法优化得到稳定平台的最佳几何构形。具体地,采用数值法与解析法相结合的方式判断支链长度、关节转角、奇异位形等约束条件的生效情况,求解出并联稳定平台的工作空间;基于力雅可比矩阵逆矩阵的最小奇异值定义机构的局部力传递性能,以工作空间内局部力传递率的平均值作为全域力传递性能评价指标;以工作空间体积和全域力传递率的加权和为优化目标,采用小生境自适应遗传算法完成优化求解,获得最优尺度参数。与初始构形的性能对比分析表明,优化构形在力传递性能方面有35%的提升,具有更好的综合运动学性能。制作试验样机并完成相关实验,验证了所提尺度参数优化方法的有效性。最后探讨了多目标优化过程中不同的权重系数取值对优化结果的作用规律,发现选用均衡的权重可获得更佳的综合性能。     

五轴并联机床的尺度综合

基于逆向思维提出了一种满足工作空间要求的五轴并联机床的尺度综合方法．首先用极坐标来描述并联机床的姿态空间；然后基于工作空间的要求得到运动平台上铰链点与固定平台上铰链点的距离极值表达式；最后考虑到杆件的力传递性能，得到一组性能较优的参数．该方法对类似的并联机构的尺度综合具有较高的参考价值．     

Optimal design of a 3-PUPU parallel robot with compliant hinges for micromanipulation in a cubic workspace

In recent years, nanotechnology has been developing rapidly due to its potential applications in various fields that new materials and products are produced. In this paper, a novel macro/micro 3-DOF parallel platform is proposed for micro positioning applications. The kinematics model of the dual parallel mechanism system is established by the stiffness model with individual wide-range flexure hinge and the vector-loop equation. The inverse solutions and parasitic rotations of the moving platform are obtained and analyzed, which are based on a parallel mechanism with real parameters. The reachable and usable workspace of the macro motion and micro motion of the mechanism are plotted and analyzed. Finally, based on the analysis of parasitic rotations and usable workspace of micro motion, an optimization for the parallel manipulator is presented. The investigations of this paper will provide suggestions to improve the structure and control algorithm optimization for the dual parallel mechanism in order to achieve the features of both larger workspace and higher motion precision.     

Combined Inverse Kinematic and Static Analysis and Optimal Design of a Cable-Driven Mechanism with a Spring Spine

Abstract

A special humanoid neck with low motion noise requirements yields a cable-driven parallel mechanism to imitate the rotational motion of a human neck. The fixed base and moving platform of the mechanism are connected by four cables and a column compression spring. The four cables are actuated separately, while the spring can support weight on the moving platform. Although similar mechanisms exist in the literature, the analysis of them is scarce because a flexible spring instead of a rigid kinematic chain is used as the spine. With the spring’s lateral buckling motion, a new approach must be adopted to solve the kinematics. In this paper, we propose a method that combines the kinematics with the statics to solve them simultaneously. The configuration of the moving platform is parameterized with four parameters, one of which is considered as parasitic motion. Using the spring’s lateral buckling equation, we can obtain the parasitic motion and solve the inverse position problem. The optimal design for cable placements is then performed to minimize the actuation force. The method in this paper provides a novel way to analyze parallel mechanisms with a spring spine and it can be applied to other mechanisms with flexible spines.     

Dimensional synthesis of a robotized cell of support fixture

In this paper, an optimal designed 8-SPU parallel mechanism, acting as a cell of the self-configurable fixture which is used to support and clamp the thin-walled, large-scale plate and shell workpiece in automotive, aircraft and ship manufacturing industries, is proposed. In order to locate the maximum workspace with the global dexterity and conformity dexterity, single and multiple objective optimizations are performed under conditions of geometric constraints and kinematic performance indices by particle swarm optimization. The structural comprehensive parameters of parallel mechanism, such as the layout of joint points on the upper platform, the angle between two limbs of leg, and the ratio of radii of fixed to moving platforms, are optimized to obtain the optimal design dimensions. Furthermore, the effect of the optimized variables on kinematic performance indices is also intensively investigated. The compared results of the two optimization approaches indicate the feasibility of the proposed procedures.     

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.     

Dimensional optimization of 6-DOF 3-CCC type asymmetric parallel manipulator

In this paper, dimensional optimization of a six-degrees-of-freedom (DOF) 3-CCC (C: cylindrical joint) type asymmetric parallel manipulator (APM) is performed by using particle swarm optimization (PSO). The 3-CCC APM constructed by defining three angle and three distance constraints between base and moving platforms is a member of 3D3A generalized Stewart–Gough platform (GSP) type parallel manipulators. The dimensional optimization purposes to find the optimum limb lengths, lengths of line segments on the base and moving platforms, attachment points of the line segments on the base platform, the orientation angles of the moving platform, and position of the end-effector in the reachable workspace in order to maximize the translational and orientational dexterous workspaces of the 3-CCC APM, separately. The dexterous workspaces are obtained by applying condition number and minimum singular values of the Jacobian matrix. The optimization results are compared with the traditional GSP manipulator for illustrating the kinematic performance of 3-CCC APM. Optimizations show that 3-CCC APM have superior dexterous workspace characteristics than the traditional GSP manipulator.     

Wrench-feasible workspace generation for cable-driven robots

This paper presents a method for analytically generating the boundaries of the wrench-feasible workspace (WFW) for cable robots. This method uses the available net wrench set, which is the set of all wrenches that a cable robot can apply to its surroundings without violating tension limits in the cables. The geometric properties of this set permit calculation of the boundaries of the WFW for planar, spatial, and point-mass cable robots. Complete analytical expressions for the WFW boundaries are detailed for a planar cable robot and a spatial point-mass cable robot. The analytically determined boundaries are verified by comparison with numerical results. Based on this, several workspace properties are shown for point-mass cable robots. Finally, it is shown how this workspace-generation approach can be used to analytically formulate other workspaces.     

Randomized Optimal Design of Parallel Manipulators

This work intends to deal with the optimal kinematic synthesis problem of parallel manipulators under a unified framework. Observing that regular (e.g., hyper-rectangular) workspaces are desirable for most machines, we propose the concept of effective regular workspace, which reflects simultaneously requirements on the workspace shape and quality. The effectiveness of a workspace is characterized by the dexterity of the mechanism over every point in the workspace. Other performance indices, such as manipulability and stiffness, provide alternatives of dexterity characterization of workspace effectiveness. An optimal design problem, including constraints on actuated/passive joint limits and link interference, is then formulated to find the manipulator geometry that maximizes the effective regular workspace. This problem is a constrained nonlinear optimization problem without explicitly analytical expression. Traditional gradient based approaches may have difficulty in searching the global optimum. The controlled random search technique, as reported robust and reliable, is used to obtain an numerical solution. The design procedure is demonstrated through examples of a Delta robot and a Gough-Stewart platform.     

Workspace and dynamic performance evaluation of the parallel manipulators in a spray-painting equipment

The paper deals with the workspace and dynamic performance evaluation of the PRR–PRR parallel manipulator in spray-painting equipment. Functional workspace of planar fully parallel robots is often limited because of interference among their mechanical components. The proposed 3-DOF planar parallel manipulator with two kinematic chains connecting the moving platform to the base can reduce interference while still maintaining 3 DOFs. Based on the kinematics, four working modes are analyzed and singularity is studied. The workspace is investigated and the inverse dynamics is formulated using the virtual work principle. The dynamic performance evaluation indices are designed on the basis of maximum and minimum magnitude of acceleration vector of the moving platform produced by a unit actuated force. The index not only can evaluate the accelerating performance of a manipulator, but also can reflect the isotropy of accelerating performance. Workspace and dynamic performances of the four working modes are compared and the optimal working mode for the painting of a large object with conical surface is determined.     

单目视觉系统自运动的滚动时域估计算法

单目视觉系统的自运动估计是计算机视觉领域中的一个关键问题。针对包含有建筑、树木等一般景物特征的应用环境,提出一种单目摄像机位姿估计的滚动时域位姿估计算法。首先分析极线约束方程的不同形式,建立多帧图像闭环之间的时空相关位姿约束,归纳全局最优模型。然后,采用滚动时域方法实现时域窗口内多时刻摄像机位姿的优化估计,实现算法复杂程度和精度的折衷。另外,在室外复杂应用环境下,对常规极约束、冗余极约束和滚动时域冗余极约束这3种位姿估计优化算法进行实验对比,验证该方法的有效性。