改进的Hestenes SVD方法及其并行计算和在并联机器人中的应用

提出一种改进的Hestenes SVD处理方法,显著减少了矩阵奇异值分解计算的循环轮次数和正交化次数,也方便和加快了矩阵的求(伪)逆运算过程.研究了两种分别基于行划分和列划分策略的改进Hestenes SVD方法的并行计算方案,并对算法性能进行了分析.针对目前并联机器人计算需求不断扩大的特点,以6自由度并联机器人一、二阶影响系数矩阵为算例对改进Hestenes SVD方法及其并行算法进行了实验.结果表明该算法可大幅度提高矩阵奇异值分解的效率,益于基于大量影响系数矩阵运算的并联机器人运动学、动力学性能分析和实时控制.相关方法也适用于具有类似矩阵处理的其他诸多工程领域.     

六自由度并联机器人动力学方程

本文研究了6自由度并联机器人机构的显式动力学方程的建立。文中首先导出了构件6维惯性力矢关于主动副速度、加速度的显表达式,引入了仅与机构位形和质量分布有关的一、二阶惯性影响系数,进而应用达朗伯原理方便地建立起6自由度并联机器人的显式动力学方程。最后进行了实例计算。     

六自由度并联式机器人拉格朗日动力方程

本文对六自由度并联机器人的动力学问题进行了研究.文中根据一二阶影响系数矩阵,导出了仅依赖于系统的质量分布和几何特性的广义惯性张量和广义惯性功率模型矩阵,建立了多回路系统的拉格朗日动力方程和运动控制方程.最后给出了实例计算.     

基于神经网络的冗余度TT-VGT机器人的运动学求解

应用BP神经网络对冗余度TT-VGT机器人的位姿正解进行训练学习,进而求解机器人 的位姿反解问题．根据网络模型求得机器人的一、二阶影响系数,应用神经网络求解雅可比 矩阵的伪逆．并对七重四面体的变几何桁架机器人进行了仿真计算．     

一种新型6-PUS并联机构雕刻机

对一种新型6-PUS并联机构雕刻机进行了研究．在机构型式选定的基础上,以一、二阶影响系数矩阵为依据对机构性能进行了分析,由此可确定出运动学和动力学各项性能指标都较好的机构尺寸,突破了以往仅以一阶影响系数矩阵为依据进行性能分析的局限性,为设计性能优良的雕刻机机构尺寸提供了理论依据．     

机器人手部运动误差分析

本文首先引入三阶影响系数,进而系统地导出了串联机器人及并联机器人手部位姿误差、位姿速度误差、位姿加速度误差分析的显表达式,推导过程简明、形式简单,便于编程.最后给出了计算示例.     

一种混合驱动柔索并联仿生眼的轨迹规划

在与眼球运动相关的解剖学和运动学的基础上,设计了一种符合Listing定理的基于混合驱动柔索并联机构的3自由度机器人仿生眼.通过矢量封闭方法建立了逆运动学模型,求解出柔索并联机器人的雅可比矩阵和结构矩阵.利用达朗贝尔定理建立柔索并联机器人的力矩平衡方程组,采用广义逆矩阵的相关理论,以柔索张力矢量的2范数最小为目标进行张力优化.用蒙特卡洛方法计算出仿生眼球可达工作空间.最后,在Simulink环境下进行仿真,规划运动轨迹并得到柔索并联机器人运动特性的仿真结果,证明了本文设计的机构符合Listing定理.结果表明:基于混合驱动柔索并联机构的机器人仿生眼结构合理,数学模型正确.     

平行导路6-PSS并联机构运动学研究

文中提出了一种新型平行导路6-PSS结构并联机器人,介绍了这种机构的特点并对其运动学相关算法进行了深入研究,其中包括运动学反解、雅可比矩阵以及正解的求解方法,同时还与6-SPS结构并联机器人运动学相关的算法进行了比较.由于文中采用构造法计算雅可比矩阵,避免了以往对反解方程直接求导的计算方式,从而使雅可比矩阵的计算大为简化,而且也减少了正解的计算量、精度得到提高.实验结果证明,这些算法正确、实用.     

含被动高副的冗余驱动并联机器人优化设计

针对具有平移和旋转混合自由度的冗余驱动并联机器人,提出一种优化设计方法.首先,介绍了仿人类口颌设计的并联机器人,由6-PUS(prismatic-universal-spherical)并联机构模拟6条主要咀嚼肌,2个被动高副模拟下颌关节.针对机构含被动高副的特点,利用末端执行器上的3点描述位姿,建立其量纲一致的雅可比矩阵.基于机器人结构和尺寸对速度误差传递性能的影响的分析,给出了该冗余驱动并联机器人的优化方法.设置性能参数对该冗余驱动并联机器人进行了尺寸优化设计,与优化前机器人机构相比全局误差标准差下降了39.83％.结果表明所提出的优化设计方法提高了并联机构的速度传递性能,并可以扩展用于其他机器人的优化设计.     

Stanford机器人动力学性能分析与仿真

文中对 Stanford 机器人进行了动力学性能分析和实体及运动仿真.首先运用影响系数法建立机器人的影响系数矩阵,利用同时基于Jacobian 矩阵和 Hessian 矩阵的动力学性能指标进行分析,给出动力学性能指标图谱.在此基础上,运用MATLAB软件对Stanford机器人进行实体和速度、加速度仿真.根据性能分析和仿真结果,说明我们用同时基于Jacobian矩阵和Hessian矩阵的动力学性能指标进行分析Stanford机器人动力学性能的正确性,以及MATLAB的可视化技术在机器人领域中的应用和发展前景.     

Research on the inertia matching of the Stewart parallel manipulator

With the development of the parallel manipulator, inertia matching as an essential factor to realize good potentials of the parallel manipulator is taken serious gradually. However, neither definite inertia index nor inertia matching method has been proposed so far. In this paper, the above issues are discussed by taking the Stewart parallel manipulator as a study object. Firstly, adopting limb Jacobian matrices, the concise algebraic expression of the joint–space inertia matrix of the Stewart parallel manipulator is deduced, based on the dynamic modeling. Next, on the basis of the coupling analysis of the joint–space inertia matrix, the inertia index of the parallel manipulator, the Joint-Reflected Inertia, is proposed. Then, the practical inertia matching principles of the Stewart parallel manipulator are concluded on the basis of simulations, considering multiple factors, such as mechanical resonance frequency, acceleration torque and dynamic performance. Finally, the available range of the motor inertia is deduced, and the inertia matching of the Stewart parallel manipulator is finished as the case study. The inertia index and inertia matching method suggested in this paper can be further used in other parallel manipulators for dynamic analysis and motion system design.     

A scalability test for parallel code

Code scalability, crucial on any parallel system, determines how well parallel code avoids becoming a bottleneck as its host computer is made larger. The scalability of computer code can be estimated by statistically designed experiments that empirically approximate a multivariate Taylor expansion of the code's execution response function. Each suspected code bottleneck corresponds to a first-order term in the expansion, the coefficient for that term indicating how sensitive execution is to changes in the suspect location. However, it is the expansion coefficients for second-order interactions between code segments and the number of processors that are fundamental to discovering which program elements impede parallel speedup. A new, unified view of these second-order coefficients yields an informal relative scalability test of high utility in code development. Discussion proceeds through actual examples, including a straightforward illustration of the test applied to SLALOM, a complex, multiphase benchmark. A quick graphical shortcut makes the scalability test readily accessible.     

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.     

Kinematic Analysis of a Macro–Micro Redundantly Actuated Parallel Manipulator

In this paper the kinematic and Jacobian analysis of a macro–micro parallel manipulator is studied in detail. The manipulator architecture is a simplified planar version adopted from the structure of the Large Adaptive Reflector (LAR), the Canadian design of the next generation of giant radio telescopes. This structure is composed of two parallel and redundantly actuated manipulators at the macro and micro level, which both are cable-driven. Inverse and forward kinematic analysis of this structure is presented in this paper. Furthermore, the Jacobian matrices of the manipulator at the macro and micro level are derived, and a thorough singularity and sensitivity analysis of the system is presented. The kinematic and Jacobian analysis of the macro–micro structure is extremely important to optimally design the geometry and characteristics of the LAR structure. The optimal location of the base and moving platform attachment points in both macro and micro manipulators, singularity avoidance of the system in nominal and extreme maneuvers, and geometries that result in high dexterity measures in the design are among the few characteristics that can be further investigated from the results reported in this paper. Furthermore, the availability of the extra degrees of freedom in a macro–micro structure can result in higher dexterity provided that this redundancy is properly utilized. In this paper, this redundancy is used to generate an optimal trajectory for the macro–micro manipulator, in which the Jacobian matrices derived in this analysis are used in a quadratic programming approach to minimize performance indices like minimal micro manipulator motion or singularity avoidance criterion.     

A second-order scheme for integration of one-dimensional dynamic analysis

This paper proposes a second-order scheme of precision integration for dynamic analysis with respect to long-term integration. Rather than transforming into first-order equations, a recursive scheme is presented in detail for direct solution of the homogeneous part of second-order algebraic and differential equations. The sine and cosine matrices involved in the scheme are calculated using the so-called 2^N algorithm. Numerical tests show that both the efficiency and the accuracy of homogeneous equations can be improved considerably with the second-order scheme. The corresponding particular solution is also presented, incorporated with the second-order scheme where the excitation vector is approximated by the truncated Taylor series.     

Dynamics analysis of a 3-RRP spherical parallel manipulator using the natural orthogonal complement

In the present research, application of the Natural Orthogonal Complement (NOC) for the dynamic analysis of a spherical parallel manipulator, referred to as SST, is presented. Both inverse and direct dynamics are considered. The NOC and the SST fully parallel robot are explained. To drive the NOC for the SST manipulator, constraints between joint variables are written using the transformation matrices obtained from three different branches of the robot. The Newton–Euler formulation is used to model the dynamics of each individual body, including moving platform and legs of the manipulator. D’Alembert’s principle is applied and Newton–Euler dynamical equations free from non-working generalized constraint forces are obtained. Finally two examples, one for direct and one for inverse dynamics are presented. The correctness and accuracy of the obtained solution are verified by comparing with the solution of the virtual work method as well as commercial multi-body dynamics software.     

A Virtual Work Based Algorithm for Solving Direct Dynamics Problem of a 3-RRP Spherical Parallel Manipulator

In this paper, we use principle of virtual work to obtain the direct dynamics analysis of a 3-RRP spherical parallel manipulator, also called spherical star-triangle (SST) manipulator (Enferadi et al., Robotica 27, 2009). This manipulator has good accuracy and relatively a large workspace which is free of singularities (Enferadi et al., Robotica, 2009). The direct kinematics problem of this manipulator has eight solution (Enferadi et al., Robotica 27, 2009). Given a desired actuated joint trajectories, we first present an algorithm for selecting the admissible solution. Next, direct velocity and direct acceleration analysis are obtained in invariant form. The concept of direct link Jacobian matrices is introduced. The direct link Jacobian matrix relates motion of any link to vector velocity of actuated joints. Finally, dynamical equations of the manipulator are obtained using the principle of virtual work and the concept of direct link Jacobian matrices. This method allows elimination of constraint forces and moments at the passive joints from motion equations. Two examples are presented and trajectory of moving platform are obtained. Results are verified using a commercial dynamics modeling package as well as inverse dynamics analysis (Enferadi et al., Nonlinear Dyn 63, 2010).     

Dexterous Workspace Optimization of a Tricept Parallel Manipulator

The growing interest in the use of parallel manipulators in machining applications requires clear determination of the workspace and dexterity. In this paper, the workspace optimization of a Tricept parallel manipulator under joint constraints is performed. This parallel manipulator has complex degrees of freedom and, therefore, leads to dimensionally inhomogeneous Jacobian matrices. Here, we divide the Jacobian entries by units of length, thereby producing a new Jacobian that is dimensionally homogeneous. By multiplying the associated entries of the twist array to the same length, we made this array homogeneous as well. The workspace of the manipulator is parameterized using several design parameters and is optimized using a genetic algorithm. For the workspace of the manipulator, local conditioning indices and minimum singular values are calculated. For the optimal design, it is shown that by introducing the local conditioning indices and minimum singular values, the quality of the parallel manipulator is improved at the cost of workspace reduction.     

Position,Jacobian and workspace analysis of a 3-PSP spatial parallel manipulator

This paper investigates the problems of kinematics, Jacobian, singularity and workspace analysis of a spatial type of 3-PSP parallel manipulator. First, structure and motion variables of the robot are addressed. Two operational modes, non-pure translational and coupled mixed-type are considered. Two inverse kinematics solutions, an analytical and a numerical, for the two operational modes are presented. The direct kinematics of the robot is also solved utilizing a new geometrical approach. It is shown, unlike most parallel robots, the direct kinematics problem of this robot has a unique solution. Next, analytical expressions for the velocity and acceleration relations are derived in invariant form. Auxiliary vectors are introduced to eliminate passive velocity and acceleration vectors. The three types of conventional singularities are analyzed. The notion of non-pure rotational and non-pure translational Jacobian matrices is introduced. The non-pure rotational and non-pure translational Jacobian matrices are combined to form the Jacobian of constraint matrix which is then used to obtain the constraint singularity. Finally, two methods, a discretization method and one based on direct kinematics are presented and robot non-pure translation and coupled mixed-type reachable workspaces are obtained. The influence of tool length on workspace is also studied.