物理受限冗余机械臂逆运动学凸优化求解

针对冗余机械臂逆运动学求解结果极有可能超过机械臂物理限制的问题,提出一种基于凸优化的逆运动学求解方法使得逆解结果满足物理约束.首先分析了关节速度与力矩关系,采用机械臂动能及重复运动为优化指标,以关节速度、关节力矩为优化变量.然后将逆运动学求解问题转化为凸优化问题,进一步转化为二次规划问题,充分利用冗余特性,实现逆运动学求解时避免关节位置、关节速度、关节力矩极限.最后利用7自由度冗余机械臂KUKA LBR iiwa进行仿真,求解关节量结果符合物理极限及优化准则.结果表明本文提出的方法适用于物理受限冗余机械臂的逆运动学求解.     

基于BP神经网络的排爆机械臂逆运动学分析

机械臂逆运动学是已知末端执行器的位姿求解机械臂各关节变量,主要用于机械臂末端执行器的精确定位和轨迹规划,如何高效的求解机械臂运动学逆解是机械臂轨迹控制的难点;针对传统的机械臂逆运动学求解方法复杂且存在多解等问题,提出一种基于BP神经网络的机械臂逆运动学求解方法;以四自由度机械臂为研究对象,对其运动学原理进行分析,建立BP神经网络模型并对神经网络算法进行改进,最后使用MATLAB进行仿真验证;仿真结果表明:使用BP神经网络模型求解机械臂逆运动学问题设计过程简单,求解精度较高,一定程度上避免了传统方法的不足,是一种可行的机械臂逆运动学求解方法。     

GAMMA300型七自由度机械臂运动学仿真

针对机械臂的运动学问题以及运动路径的设计问题,以冗余度为1的美国ROBAI公司生产的7自由度冗余机械臂GAMMA300为具体研究对象,对七自由度机械臂进行运动学建模与仿真.利用Robotics Toolbox机器人工具箱编写该机械手的运动学程序.通过仿真实现了预定目标,验证了设计参数的正确性和可行性,为机械臂末端执行器的精确定位和轨迹规划提供了理论依据.对于冗余机械臂一般逆运动学封闭解的研究有一定的实用价值.     

一种求解冗余机械臂逆运动学的优化方法

基于加权最小范数法,推导出一种避免计算雅可比矩阵伪逆的优化方法.首先对加权雅可比矩阵的6维非奇异子矩阵求逆,得到逆运动学的特解和齐次解.然后用特解减去齐次解沿特解方向的分量得到运动学逆解.通过一个7自由度冗余机械臂的算例和仿真证明了方法在保证求解精度、降低求解难度以及避免关节极限方面的有效性     

机械臂的位姿分离求逆和改进RRT-connect算法研究北大核心CSCD

针对机械臂逆解求取过程中存在大量矩阵变换、计算成本高的问题,采用位姿分离法对逆运动学求解过程进行改进,并提出基于自适应步长的RRT-connect路径规划算法。首先建立六自由度机械臂连杆坐标系模型,采用Standard Denavit-Hartenberg(D-H)方法对机械臂进行正运动学分析,得到机械臂末端执行器位姿相对于基座的齐次变换矩阵。然后引入位姿分离法改进了机械臂的逆运动学求解方法,将机械臂运动学逆解分为位置逆解和姿态逆解两部分,分别用几何法和解析法进行求解,减少了整体计算量。再者提出基于自适应步长的改进RRT-connect路径规划算法,解决了扩展速度慢的问题。最后通过仿真验证所提出方法的正确性和有效性。     

基于ELM-IWO机械臂运动学逆解算法研究

为了提高机械臂控制中运动学逆解的速度和准确度,提出了一种基于入侵性杂草优化的机械臂运动学逆解方法.通过D-H法建立了工业六自由度机械臂的正向运动学模型,并利用训练速度较快的ELM(极限学习机)计算机械臂关节角度向量,即输出其逆运动学初解.利用IWO(入侵性杂草优化)算法对得到的初始逆解进行优化,取最小适应度下的杂草位置作为输出,以便得到最佳的逆运动学求解.实验结果表明,相比基于PSO-BP神经网络的求解方法,基于ELM-IWO算法的机械臂末端执行器的精度更高,实时性更好.     

新型六自由度机械臂的运动学分析与仿真验证

针对新型机器人六自由度机械臂的构型特点,采用传统的D-H法建立机械臂的连杆坐标系和运动学方程.在此基础上对传统的逆运动学求解的解析法进行改进,对得到的多组解采用能耗最小原则进行优化得出最适合的一组解.用MTALAB/SIMULINK搭建仿真模型,验证所得结果的正确性并分析所得结果的误差,仿真结果表明针对于此种构型机械臂的逆运动学求解,该方法无误差、耗能小,为类似构型的机械臂逆运动学求解提供了思路.     

自适应粒子群算法求冗余机械臂逆运动学解

以正向运动学方程为基础，冗余机械臂逆运动学解问题转换为等效最小值问题，提出一种自适应粒子群算法求解该问题。为了保持粒子群的活力，在算法内引入弹射操作。如果粒子满足设定自适应判别函数，粒子将按概率被从当前位置发射到较远区域。为了配合弹射操作，提出一种新的粒子优劣的判断机制，使得粒子可以被弹射飞出可行域。数值实验表明，算法具有较强的全局搜索能力和较快的搜索速度，是求解冗余机械臂逆运动学解的一种有效方法。     

故障容错串联机械臂设计方法研究

本文从机械臂运动学任务特性出发,定义了故障容错机械臂的相关特性,论证了运动学关节冗余也可以提高机械臂系统的可靠性,故障容错机械臂所应该具备的自由度数,以及针对不同的任务对象要求,设计故障容错机械臂的方法.将任务空间抽象简化为一系列的特征点,建立机械臂参数与理想值相关的罚函数,选择有效的优化算法,设计出了一系列故障容错平面位置机械臂和故障容错空间位置机械臂.建立起完整的故障容错机械臂的设计方法,对危险环境机器人、医疗机器人的研究设计具有重要价值.     

结合IMask R-CNN的绳驱机械臂视觉抓取方法研究

绳驱超冗余机械臂具有灵活性强、工作空间大等特点,在航天活动中可替代宇航员进行各种航空作业.以空间飞行器在轨维修为研究背景,模拟其实验环境,设计了一套基于RGB-D的可移动绳驱超冗余机械臂定位抓取系统.首先改进了Mask R-CNN算法,在保证检测精度的同时降低模型尺寸,通过Intel RealSense D435 i采集图像输入到目标检测模型得到目标的类别和位置信息,进一步利用自适应末端位置更新算法递推机械臂的正逆运动学模型,并结合轨迹规划完成目标的三维空间定位和抓取.实验结果表明,改进后的Mask R-CNN算法能在保证精度的情况下有效地降低模型尺寸,抓取系统的逆运动学求解速度快,具有较好的定位精度,能够有效地完成飞行器抓取的任务.     

A solution to the inverse kinematics of redundant manipulators

A solution to the inverse kinematics is a set of joint coordinates which correspond to a given set of task space coordinates (position and orientation of end effector). For the class of kinematically redundant robots, the solution is generically nonunique such that special methods are required for obtaining a solution. The method addressed in the paper, introduced earlier and termed “generalized inverse,” is based on a certain partitioning of the Jacobian functional corresponding to a nonlinear relationship of the inverse kinematics type. The article presents a new algorithm for solving the inverse kinematics using the method of generalized inverse based on a modified Newton-Raphson iterative technique. The new algorithm is efficient, converges rapidly, and completely generalizes the solution of the inverse kinematics problem for redundant robots. The method is illustrated by numerical examples.     

Approximation of Jacobian Inverse Kinematics Algorithms: Differential Geometric vs. Variational Approach

This paper addresses the approximation problem of Jacobian inverse kinematics algorithms for redundant robotic manipulators. Specifically, we focus on the approximation of the Jacobian pseudo inverse by the extended Jacobian algorithm. The algorithms are defined as certain dynamic systems driven by the task space error, and identified with vector field distributions. The distribution corresponding to the Jacobian pseudo inverse is non-integrable, while that associated with the extended Jacobian is integrable. Two methods of devising the approximating extended Jacobian algorithm are examined. The first method is referred to as differential geometric, and relies on the approximation of a non-integrable distribution (in fact: a codistribution) by an integrable one. As an alternative, the approximation problem has been formulated as the minimization of an approximation error functional, and solved using the methods of the calculus of variations. Performance of the obtained extended Jacobian inverse kinematics algorithms has been compared by means of computer simulations involving the kinematics model of the 7 dof industrial manipulator POLYCRANK. It is concluded that the differential geometric method offers a rapid, while the variational method a systematic tool for solving inverse kinematic problems.     

A fast approach for the robust trajectory planning of redunant robot manipulators

In this article, a fast approach for robust trajectory planning, in the task space, of redundant robot manipulators is presented. The approach is based on combining an original method for obstacle avoidance by the manipulator configuration with the traditional potential field approach for the motion planning of the end-effector. This novel method is based on formulating an inverse kinematics problem under an inexact context. This procedure permits dealing with the avoidance of obstacles with an appropriate and easy to compute null space vector; whereas the avoidance of singularities is attained by the proper pseudoinverse perturbation. Furthermore, it is also shown that this formulation allows one to deal effectively with the local minimum problem frequently associated with the potential field approaches. The computation of the inverse kinematics problem is accomplished by numerically solving a linear system, which includes the vector for obstacle avoidance and a scheme for the proper pseudoinverse perturbation to deal with the singularities and/or the potential function local minima. These properties make the proposed approach suitable for redundant robots operating in real time in a sensor-based environment. The developed algorithm is tested on the simulation of a planar redundant manipulator. From the results obtained it is observed that the proposed approach compares favorably with the other approaches that have recently been proposed. © 1995 John Wiley & Sons, Inc.     

基于解析法和遗传算法的机械手运动学逆解

研究优化机械手轨迹规划问题,机械手运动时要具有稳定性避障性能。针对平面3自由度冗余机械手优化控制问题,建立机械手的结构模型。提出用解析法和遗传算法相结合满足具有计算量小和适应性强的特点。在给定机械手末端执行器的运动轨迹,按着机械手冗余自由度,运动轨迹上每个点对应的关节角有无穷多个解。而通过算法可以找到一组最优的关节角,可得到优化机械手运动过程中柔顺性和避障点。仿真结果表明,该算法可以快速收敛到全局最优解,可用于计算冗余机械手运动学逆解,并可实现机器人的轨迹规划和避障优化控制。     

Canonical parameterization of excess motor degrees of freedom withself-organizing maps

The problem of sensorimotor control is underdetermined due to excess (or "redundant") degrees of freedom when there are more joint variables than the minimum needed for positioning an end-effector. A method is presented for solving the nonlinear inverse kinematics problem for a redundant manipulator by learning a natural parameterization of the inverse solution manifolds with self-organizing maps. The parameterization approximates the topological structure of the joint space, which is that of a fiber bundle. The fibers represent the "self-motion manifolds" along which the manipulator can change configuration while keeping the end-effector at a fixed location. The method is demonstrated for the case of the redundant planar manipulator. Data samples along the self-motion manifolds are selected from a large set of measured input-output data. This is done by taking points in the joint space corresponding to end-effector locations near "query points", which define small neighborhoods in the end-effector work space. Self-organizing maps are used to construct an approximate parameterization of each manifold which is consistent for all of the query points. The resulting parameterization is used to augment the overall kinematics map so that it is locally invertible. Joint-angle and end-effector position data, along with the learned parameterizations, are used to train neural networks to approximate direct inverse functions.     

Inverse kinematics of planar redundant manipulators via virtual links with configuration index

This article presents a new method for generating inverse kinematic solutions for planar manipulators with large redundancy (hyper-redundant manipulators). The proposed method starts by decomposing a planar redundant manipulator into a series of local planar arms that are either 2-link or 3-link manipulator modules, and connecting the conjunction points between them with virtual links. The manipulator then can be handled by a simple virtual link system, which may be conveniently divided into non-singular and singular cases depending on its configuration. When the virtual link system is no longer effective due to a singular configuration, the displacement of the end-effector is then allocated to virtual links according to a displacement distribution criterion. A dexterity index called the “configuration index” distinguishes the non-singular and singular cases. The concept of virtual link is shown by computer simulations to be simple and effective for the inverse kinematics of a planar hyper-redundant manipulator with a discrete model. In particular, it can be applied to solving the inverse kinematics of a SCARA-type spatial redundant manipulator whose redundancy is included in its planar mechanism. © 1994 John Wiley & Sons, Inc.     

Kinematic analysis of a novel 3-DOF actuation redundant parallel manipulator using artificial intelligence approach

Kinematic analysis is one of the key issues in the research domain of parallel kinematic manipulators. It includes inverse kinematics and forward kinematics. Contrary to a serial manipulator, the inverse kinematics of a parallel manipulator is usually simple and straightforward. However, forward kinematic mapping of a parallel manipulator involves highly coupled nonlinear equations. Therefore, it is more difficult to solve the forward kinematics problem of parallel robots. In this paper, a novel three degrees-of-freedom (DOFs) actuation redundant parallel manipulator is introduced. Different intelligent approaches, which include the Multilayer Perceptron (MLP) neural network, Radial Basis Functions (RBF) neural network, and Support Vector Machine (SVM), are applied to investigate the forward kinematic problem of the robot. Simulation is conducted and the accuracy of the models set up by the different methods is compared in detail. The advantages and the disadvantages of each method are analyzed. It is concluded that ν-SVM with a linear kernel function has the best performance to estimate the forward kinematic mapping of a parallel manipulator.     

Multiple tasks manipulation for a robotic manipulator

Robotic manipulators can execute multiple tasks precisely at the same time and, thus, the task-priority scheme plays an important role in implementing multiple tasks. Until now, several algorithms for task-priority have been used in solving the inverse kinematics for redundant manipulators. In this paper, through the comparative study of existing algorithms, we will propose a new method for task-priority manipulation in terms of two important criteria—algorithmic singularity and task error. This manipulation scheme will be applied to a planar three-link manipulator to demonstrate its effectiveness.     

Dynamic formulation of a planar 3-DOF parallel manipulator with actuation redundancy

In this paper, based on the conventional Newton–Euler approach, a simplification method is proposed to derive the dynamic formulation of a planar 3-DOF parallel manipulator with actuation redundancy. Closed-form solutions are developed for the inverse kinematics. Based on the kinematics, the Newton–Euler approach in simplification form is used to derive the inverse dynamic model of the redundant parallel manipulator. Then, the driving force optimization is performed by minimizing an objective function which is the square of the sum of four driving forces. The dynamic simulations are done for the parallel manipulator with both the redundant and non-redundant actuations. The result shows that the dynamic characteristics of the manipulator in the redundant case are better than that in the non-redundancy. The redundantly actuated parallel manipulator was incorporated into a 4-DOF hybrid machine tool which includes a feed worktable.     

On inverting singular kinematics and geodesic trajectory generation for robot manipulators

In this paper, a new method is proposed of solving the inverse kinematic problem for robot manipulators whose kinematics are allowed to possess singularities. The method is based upon the so-called generalized Newton algorithm, introduced by S. Smale, and can be adopted to both nonredundant and redundant kinematics. Moreover, given a pair of points in the external space of a manipulator, the method is capable of generating a minimum-length trajectory joining the points (a geodesic), in particular a straight-line trajectory. Results of representative computer experiments, including those with the PUMA 560 kinematics, are reported in order to illustrate the performance of the method.