6-DOF并联机器人位置正解的实用解法

对6-DOF并联机器人的位置正解进行了研究和分析,通过位置反解的求解思路来解位置正解的问题。将上下平台统一在一个坐标系下。按照空间两点间距离计算公式,以6个杆的伸长值为已知量,位姿参数为未知量,建立关于6个杆的参数方程。通过迭代法求得位姿参数。特点之一是未知量个数少,计算精度高;另一特点是从实现的角度来阐述,实用性强。通过实验验证该思路满足即时控制的要求。     

Analytical kinematics models and special geometries of a class of 4-DOF parallel mechanisms

The paper discusses forward and inverse kinematics of a class of four-degree-of-freedom (DOF), four-legged parallel mechanisms providing three rotational and one translational DOFs. A fully parametric analytical form solution to the inverse-position problem is provided. All working modes of the mechanism are shown and discussed. The equations of the forward-position problem are obtained under different leg arrangements, and a numerical example is provided. New special geometries in the class are proposed, including one suitable for keyhole surgery.     

Analytic singularity analysis of a 4-DOF parallel robot based on Jacobian deficiencies

In this paper, analytic singularity analysis of a 4-DOF parallel robot H4 is addressed. Since a parallel manipulator consisting of several serial chains has complex singularities in the workspace, the determination of singular configurations is very important in design, trajectory planning, and control. The classical method to determine singular configurations is to find the determinant of the Jacobian matrix. However, the Jacobian matrix of a parallel manipulator is complex in general and thus it is not easy to find the determinant of the Jacobian matrix. Therefore, we focus on the analytic singularity analysis of a 4-DOF parallel robot H4 using Jacobian deficiencies. A subset of the whole singularities and the intuitively predictable ones are only derived using Jacobian matrix deficiency. Three type singularities, i.e., overmobility, undermobility and combined singularities, have been presented.     

Closed-form solutions of the parallel plate problem

Closed-form solutions to the parallel plate problem have been derived for design of electrostatic devices that employ the parallel plate. With dimensionless height and force introduced to simplify the nonlinear parallel plate problem, a simple cubic equation implying behavior of the height of the movable plate corresponding an applied voltage has been derived and theoretically solved to provide closed-form solutions of the movable plate height, effective stiffness, resonant frequency, capacitance and their sensitivities to voltage. The theoretical height agreed well with experimental data obtained from a surface-micromachined parallel plate. When the applied voltage approaches the pull-in voltage, the height of the movable plate reaches 2/3 of the initial height, the effective stiffness and resonant frequency go to zero and the capacitance becomes 3/2 times the initial capacitance. These closed-form solutions can be used to analyze and design micro- and nano-devices employing electrostatic parallel plates.     

Tolerance design of a 2-DOF overconstrained translational parallel robot

This paper deals with the tolerance design of a two-degree-of-freedom translational parallel robot module for high-speed pick-and-place operations. The module is an overconstrained parallel mechanism using two sets of parallelograms in each limb. A probabilistic model of the uncompensatable pose error is formulated, together with a compatibility condition to ensure the mobility of the robot. Based upon this model, optimization of the tolerances of the geometric source errors and joint clearances is conducted, subject to a set of appropriate constraints. Simulation and experimental results are given to demonstrate the effectiveness of this approach.     

6-DOF并联机器人并行控制算法与优化

为了实现对6-DOF并联机器人实时在线控制,并能取得良好的控制效果,对其运动控制算法的结构进行了深入剖析与研究,尤其对上平台中心的运动速度和角速度的计算及液压缸各杆的伸长速度计算矩阵进行了细致的研究,提出了并行算法及CPU的优化分配策略,大大提高了并联机器人的实时控制质量.     

Structural design and kinematics of a new parallel reconfigurable robot

Reconfigurable robots can be defined as a group of robots that can have different geometries, thus obtaining different structures derived from the basic one, having different degrees of freedom and workspaces. Thanks to the optimum dexterity they offer, the user can accomplish a large variety of industrial tasks, using a structurally optimized robot leading towards better energy control and efficiency especially in case of batch size production lines where the task (for the robot) may vary periodically. Reconfigurable systems are a challenge for numerous scientists, due to the advantage of dealing with changes and uncertainties on the ever-changing manufacturing market. One of the main problems of reconfigurable robots is the proper structural geometry determination, so that the resulting structure is able to perform a variety of tasks. This paper presents the structural design of an innovative parallel robot with six degrees of freedom and its proposed configurations with five, four, three and two degrees of freedom. The kinematic analysis and the workspace representations of all the presented configurations of the parallel robot, called Recrob, are also presented.     

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.     

Kinematic analysis of a new 5-DOF modular parallel robot for brachytherapy

Cancer represents one of the main causes of the death. Huge efforts have been made by the scientific community to provide better cancer treatment solutions. An innovative option is the brachytherapy (BT), a local radiation technique for cancer treatment, which enables the delivery of high doses of radiation inside the tumors. BT usage is limited by the insufficient accuracy of the radioactive seeds placement. In order to eliminate these limitations, the authors propose an innovative modular structure which would enable the precise positioning of the BT needles in any part of the patient body. The paper presents the kinematic modeling of the new 5-DOF robotic structure. The workspace analysis and the singularities are studied and the dexterous workspace for a given insertion point inside the patient is also shown. Finally, some numerical simulations of different BT needle trajectories are included.     

Forward and inverse kinematics of a 5-DOF hybrid robot for composite material machining

Hybrid robots consist of both serial and parallel mechanisms, which have advantages in stiffness and workspace compared with serial/parallel robots when machining composite material. However, the forward and inverse kinematics of hybrid robots generally do not have analytic solutions. This paper deals with the analytic forward and inverse kinematics solutions of a 5-degree-of-freedom (DOF) hybrid robot which consists with a 3-DOF 2UPU/SP parallel mechanism (PM) and a 2-DOF rotating head. In the forward kinematic problem, a method is proposed to transfer the high order kinematic equation to a 4th-order polynomial based on the Sylvester's dialytic elimination, and the analytic solutions can be further obtained by Ferrari's method. In the inverse problem, the redundant Euler angles expressed by four rotations are firstly proposed for decoupling different motions, then, the closed-form solution of inverse kinematics can be found. Finally, a simulation trajectory is given, and the result shows that the accuracy of the solutions’ calculation reaches femtometer grade and the efficiency reaches microsecond grade; furthermore, an experiment is performed on the prototype to validate the effectiveness of the proposed forward and inverse kinematics.     

6-DOF并联机器人控制算法结构化分析与设计

为了实现对六自由度并联机器人位置速度算法的控制,针时控制算法采用了软件工程的原理和方法进行了分析,并对机器人运动特性进行了研究.根据运动特性对位置与速度的控制算法进行了解析,提出位置反解的控制策略,给出了功能分析的DFD模型和软件结构化设计模型SC图.描述了算法的详细设计及实现,采用结构化语言表达工具,并对实现中重要的部分细节进行了细致的研究,其结果达到了位置速度控制的目的及机器人控制算法的软件结构化设计.     

Comparison of four different heuristic optimization algorithms for the inverse kinematics solution of a real 4-DOF serial robot manipulator

In this study, a 4-degree-of-freedom (DOF) serial robot manipulator was designed and developed for the pick-and-place operation of a flexible manufacturing system. The solution of the inverse kinematics equation, one of the most important parts of the control process of the manipulator, was obtained by using four different optimization algorithms: the genetic algorithm (GA), the particle swarm optimization (PSO) algorithm, the quantum particle swarm optimization (QPSO) algorithm and the gravitational search algorithm (GSA). These algorithms were tested with two different scenarios for the motion of the manipulator’s end-effector. One hundred randomly selected workspace points were defined for the first scenario, while a spline trajectory, also composed of one hundred workspace points, was used for the second. The optimization algorithms were used for solving of the inverse kinematics of the manipulator in order to successfully move the end-effector to these workspace points. The four algorithms were compared according to the execution time, the end-effector position error and the required number of generations. The results showed that the QPSO could be effectively used for the inverse kinematics solution of the developed manipulator.     

Fast Implementation of forward robot kinematics of position withdistributed arithmetic architecture

This paper refers to the fast implementation of the forward kinematic equations of position of robotics manipulators, using a distributed arithmetic-based pipeline architecture. The building blocks of this pipeline architecture are the distributed arithmetic-based circuits that implement the matrix-vector multiplications involved in the calculation of the forward kinematics of position. The matrix-vector multiplications are implemented in the distributed arithmetic technique by using auxiliary binary functions, which are stored in look-up tables. The digit-serial configuration of the proposed implementation is described. The serial and the parallel configurations may result as special extreme cases of the digit-serial configuration     

连续型同心管机器人正运动学快速求解方法

针对可在受限环境中灵活运动的连续型同心管机器人传统正运动学方法计算时间较长,不利于机器人实时运行的问题,本文提出了基于机器人几何学的同心管机器人正运动学快速求解方法,能够在精度损失有限的情况下,提高正运动学模型的计算效率.先根据Cosserat杆模型对同心管机器人进行建模,再利用李代数理论建立了机器人空间位置和曲率的关系式,并结合提出的正运动学方法,对机器人进行了基于逆运动学的开环控制实验.最后通过3管机器人的仿真和实物实验验证了本文所提方法的快速性和有效性.     

6-DOF并联机器人工作空间边界分析与判定算法

6-DOF并联机器人的工作空间是控制过程研究的主要问题之一,所谓活动空间的边界分析,即指各液压缸活动过程中相互不能发生碰撞,如果碰撞发生,则该点即为边界点.对6-DOF并联机器人的机构和工作原理进行了介绍,给出了对于工作空间边界分析必要的位置算法,根据机构的特点与机器人的运动特性对6-DOF并联机器人的工作空间边界进行了细致的分析并给出了可操作的运动边界判定算法.实现了对液压缸碰撞的判定.     

An improved hybrid method for forward kinematics analysis of parallel robots

This paper combines a new structure of artificial neural networks (ANNs) with a 3rd-order numerical algorithm and proposes an improved hybrid method for solving forward kinematics problem (FKP) of parallel manipulators. In this method, an approximate solution of the FKP is first generated by the neural network. This solution is next considered as an initial guess for the 3rd-order numerical technique which solves the nonlinear forward kinematics equations and obtains the answer with a desired level of accuracy. To speed up the method, a new structure is proposed for designing the ANN which is called Same Class One Network. In this structure, the outputs of the ANN are classified into classes of similar variables with an individual network designed for each class. The proposed method is then applied to a planar 3-RPR parallel manipulator and a spatial 3-PSP parallel robot. The results show that using this method will lead to a 55% reduction in required iterations and a 20% reduction in the FKP analysis time, while maintaining a high level of solution accuracy.     

Optimal design of a 2-DOF parallel manipulator with actuation redundancy considering kinematics and natural frequency

In this paper, a planar 2-DOF parallel manipulator with actuation redundancy is proposed and the optimal design considering kinematics and natural frequency is presented. The stiffness matrix and mass matrix are derived, and the structural dynamics is modeled. The natural frequency is obtained on the basis of dynamic model. Based on the kinematic performance, the range for link length is given. Then, considering the natural frequency, the geometry is optimized. The natural frequency is simulated and compared with the corresponding non-redundant parallel manipulator. The designed redundant parallel manipulator has desired kinematic performance and natural frequency and is incorporated into a 4-DOF hybrid machine tool.     

基于牛顿-拉夫逊迭代法的6自由度机器人逆解算法

为解决一般6自由度旋转关节机器人逆运动学问题,提出了一种用牛顿一拉夫逊迭代法逐次逼近目标位姿的逆解算法.根据正运动学方程建立雅克比矩阵,采用基于豪斯霍尔德的SVD分解求其伪逆来避免雅克比矩阵的奇异性问题,通过建立迭代规则并逐次迭代找到最优的逆运动学单解,实际应用时无需再建立多解取优策略.本算法具有较好的局部快速收敛性,能够达到较好的精度和速度,并在基于ARM9的嵌人式系统上实现了此算法.相应的测试表明:算法实时性能够满足系统要求,可应用于机器人实时控制系统.     

Trajectory tracking control of a 6-DOF hydraulic parallel robot manipulator with uncertain load disturbances

This study addresses the trajectory tracking control of a 6-DOF (degrees of freedom) hydraulic parallel robot manipulator with uncertain load disturbances. As load disturbances are the main external disturbances of the parallel robot manipulators and have a significant impact on system tracking performance, many researchers have been devoted to synthesize advanced control methods for improving the system robustness under the assumption that load disturbances are bounded. However, load disturbances are uncertain and vary in a large range in real situation happening in most hydraulic parallel robot manipulators, which is opposed to the assumption. In this paper, the load disturbances are directly measured by force sensors. Then a sliding mode control with discontinuous projection-based adaptation laws is proposed to improve the tracking performance of the parallel robot manipulator. Simulations and experiments with typical desired trajectory are presented, and the results show that good tracking performance is achieved in the presence of uncertain load disturbances.     

Dynamics and elasto-dynamics optimization of a 2-DOF planar parallel pick-and-place robot with flexible links

Dynamic modeling and analysis of a 2-DOF translational parallel robot with flexible links for high-speed pick-and-place operation is presented in this paper. Optimization is implemented with the goal to improve the dynamic accuracy of the end-effector at high speed. The governing equations of flexible links within the robot are formulated in the floating reference frame using Euler–Lagrange method, leading to a global FEM model being generated using the KED (Kineto-Elasto-Dynamics) technique. The dynamic characteristics of the robot are then investigated by model analysis. A numerical dynamic index is proposed to identity the range of natural frequency when the robot reaches different configurations. The comparisons are made between the optimized and original designs in terms of dynamic stress and response.