基于旋转子矩阵正交的6R机器人运动学逆解研究

以机器人运动学方程为基础,基于变换矩阵中旋转子矩阵正交的特性,提出一种6R机器人运动学逆解算法.通过矢量运算,得到含有4个未知变量的4个常系数非线性方程,辅以其它方程,最终得到8组封闭解.通过对钱江一号焊接机器人的实例求解,验证了该算法解决逆解问题仅需0.087 ms,比传统的反变换法具有更优的实时性能;平面工况的运动仿真验证了该算法的有效性.该算法可应用于6R机器人的强实时在线控制系统.     

机器人逆运动学求解的可视化算法

机器人逆运动学求解的可视化算法包含两部分，数值求解两个(或一个)非线性方程和4(或5)自由度机器人封闭解，实现了任意结构的6自由度机器人的逆运动学方程的求解，根据D-H参数表生成机器人三维模型实现机器人结构的可视化，有效地判断逆解的合理性，并为机器人学习提供了辅助工具。     

冗余自由度超声检测机器人的逆运动学分析

针对一类冗余自由度超声检测机器人的传统逆运动学求解算法耗时长且准确度低的问题,提出了一种基于集合划分和解析解法相结合的逆运动学求解算法。首先采用De-navit-Hartenberg方法建立检测机器人的运动学方程;其次,利用解析解法求出机器人逆解的解析表达式,并提出三种自由度分配方案;最后,选择合适的自由度分配方案,据此对超声波探头位姿集合作划分,结合逆解解析式求出运动学逆解。实际应用中,借助十一轴超声波检测机器人,利用该算法对具有复杂外形的飞机螺旋桨叶片进行检测。结果表明,与传统的纯数值解法相比,该算法能够快速得到精确的运动学逆解。     

基于Paden-kahan子问题的冗余度机器人运动学求解

针对7DOF机器人的逆运动学求解问题,提出了一种可提高运动控制精度的混合算法.这种算法使用 旋量理论来描述机器人的运动.它首先求出对运动学性能指标进行优化的速度级逆解;然后固定一个特殊关节,将 问题转化为非冗余度机器人的运动控制,应用Paden-Kahan子问题法得到逆运动学封闭解.通过仿真实例,证实了 这种混合算法的有效性.     

一种运动旋量逆解子问题的求解及其应用

旋量理论在机器人运动学逆解过程中将运动方程分解为若干子问题,目前常见的子问题组合并不能完成所有机器人的逆解问题．本文提出了在机器人逆解过程中会遇到的另一种子问题的解法,并给出构造该子问题的限定条件．运用该解法,给出具有RTS运动链并联机器人的运动学逆解方法,并归纳出利用未知量组中对参考点起相同作用的旋量组合来简化计算的方法．该子问题的解决扩充、便利了旋量理论在机器人运动学逆解中的应用．     

结合MPGA-RBFNN的一般机器人逆运动学求解

针对一般机器人逆运动学求解过程中存在的求解速度慢、精度低的问题，将多种群遗传算法（multiple population genetic algorithm，MPGA）引入径向基函数神经网络（radial basis functions neural network，RBFNN），提出一种适用于一般机器人的高精度MPGA-RBFNN算法。该算法采用3层结构的RBFNN进行一般机器人逆运动学求解，结合一般机器人的正运动学模型，采用MPGA优化RBFNN的网络结构和连接权值的方法，同时应用混合编码和演化的方式，实现了从机器人工作空间位姿到关节角度的非线性映射，从而避免了复杂的公式推导并提高了求解速度。采用6R一般机器人作为实验平台进行实验，实验结果表明:MPGA-RBFNN算法不仅提高了一般机器人在逆运动学中的求解速度，而且MPGA-RBFNN算法的训练成功率和逆解的计算准确率也得到了提高。     

面向冗余机器人实时控制的逆运动学求解有效方法

针对7自由度冗余机器人实时运动控制,对机器人逆运动学提出了一种新的求解方法.采用位姿分解方式,使7自由度冗余机器人逆运动学简化为4自由度位置逆运动学求解.在梯度投影法得到位置优化解的基础上,利用机器人封闭解公式求得一组优化解.通过对7自由度机器人仿真分析,表明了该方法的有效性.     

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.     

面向冗余机器人实时控制的逆运动学求解有效方法

针对-自由度冗余机器人实时运动控制,对机器人逆运动学提出了一种新的求解方法.采用位姿分解方式,使-自由度冗余机器人逆运动学简化为,自由度位置逆运动学求解.在梯度投影法得到位置优化解的基础上,利用机器人封闭解公式求得一组优化解.通过对-自由度机器人仿真分析,表明了该方法的有效性.

     

6R关节型机器人运动学建模

为满足新开发的多机器人实验系统编程需要,研究了6R机器人运动学逆解问题.推导了代数逆解结果,并研究了将其用于实际控制系统时,逆解的漏解、增根和多解问题.与传统方法比较,采用了便于程序模块化的坐标系设置方式,在需要经常更换作业工具的多机器人系统中更为适用.推导过程只需2次矩阵逆乘,步骤简单.基于VC++和OpenGL技术编制了系统程序,检验了方法的有效性.以其中一个位姿为例,对比几何方法得出的结果,验证了算法的正确性.研究的结果适用于MOTOMAN-UP6和PUMA560等相似构型的所有机器人.     

Efficient closed-form solution of inverse kinematics for a specific six-DOF arm

Inverse kinematics solutions for multi-DOF arms can be classified as analytical or numerical. In general, analytical solutions are preferable to numerical solutions because analytical ones yield complete solutions and are computationally fast and reliable. However, analytical closed-form solutions for inverse kinematics of 6-DOF arms rarely exist for real-time control purposes of fast moving arms. In this paper, we propose a fast inverse kinematics algorithm with a closed-form solution for a specific 6-DOF arm. The proposed algorithm is verified using simulation modules developed by us for demonstrations.     

Cartesian path generation of robot manipulators using continuous genetic algorithms

In this paper, the authors describe a novel technique based on continuous genetic algorithms (CGAs) to solve the path generation problem for robot manipulators. We consider the following scenario: given the desired Cartesian path of the end-effector of the manipulator in a free-of-obstacles workspace, off-line smooth geometric paths in the joint space of the manipulator are obtained. The inverse kinematics problem is formulated as an optimization problem based on the concept of the minimization of the accumulative path deviation and is then solved using CGAs where smooth curves are used for representing the required geometric paths in the joint space through out the evolution process. In general, CGA uses smooth operators and avoids sharp jumps in the parameter values. This novel approach possesses several distinct advantages: first, it can be applied to any general serial manipulator with positional degrees of freedom that might not have any derived closed-form solution for its inverse kinematics. Second, to the authors’ knowledge, it is the first singularity-free path generation algorithm that can be applied at the path update rate of the manipulator. Third, extremely high accuracy can be achieved along the generated path almost similar to analytical solutions, if available. Fourth, the proposed approach can be adopted to any general serial manipulator including both nonredundant and redundant systems. Fifth, when applied on parallel computers, the real time implementation is possible due to the implicit parallel nature of genetic algorithms. The generality and efficiency of the proposed algorithm are demonstrated through simulations that include 2R and 3R planar manipulators, PUMA manipulator, and a general 6R serial manipulator.     

A New Geometric Subproblem to Extend Solvability of Inverse Kinematics Based on Screw Theory for 6R Robot Manipulators

Geometric inverse kinematics procedures that divide the whole problem into several subproblems with known solutions, and make use of screw motion operators have been developed in the past for 6R robot manipulators. These geometric procedures are widely used because the solutions of the subproblems are geometrically meaningful and numerically stable. Nonetheless, the existing subproblems limit the types of 6R robot structural configurations for which the inverse kinematics can be solved. This work presents the solution of a novel geometric subproblem that solves the joint angles of a general anthropomorphic arm. Using this new subproblem, an inverse kinematics procedure is derived which is applicable to a wider range of 6R robot manipulators. The inverse kinematics of a closed curve were carried out, in both simulations and experiments, to validate computational cost and realizability of the proposed approach. Multiple 6R robot manipulators with different structural configurations were used to validate the generality of the method. The results are compared with those of other methods in the screw theory framework. The obtained results show that our approach is the most general and the most efficient.

     

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.     

Closed-form forward kinematics solutions of a 4-DOF parallel robot

It is well known that the forward kinematics of parallel robots is a very difficult problem. Closed-form forward kinematics solutions have been reported only to a few special classes of parallel robots. This paper presents closed-form forward kinematics solutions of a 4-DOF parallel robot H4. A 16th order polynomial in a single variable is derived to solve the forward kinematics of the H4. The 16 roots of the polynomial lead to at most 16 different forward kinematics solutions. A numerical verification is also presented.     

On inverse kinematics with inequality constraints: new insights into minimum jerk trajectory generation

The problem of inverse kinematics is revisited in the present paper. The paper is focusing on the problem of solving the inverse kinematics problem while minimizing the jerk of the joint trajectories. Even though the conventional inverse kinematics algorithms have been proven to be efficient in many applications, it has been proven that constraints on the accelerations or the jerk cannot be guaranteed, and even yields to divergence or makes the problem unsolvable. The proposed algorithm yields smooth velocity and acceleration trajectories, which are highly desired features for industrial robots. The algorithm uses the joint jerk as the control parameter instead of the classical use of the joint velocity as result constraints on the jerk function can be easily incorporated. To validate the proposed approach, we have conducted several simulations scenarios. The simulation results have revealed that the proposed method can efficiently solve the inverse kinematics problem while considering constraints on the joint acceleration and jerk.     

A neuro-simulated annealing approach to the inverse kinematics solution of redundant robotic manipulators

The neural-network-based inverse kinematics solution is one of the recent topics in the robotics because of the fact that many traditional inverse kinematics problem solutions such as geometric, iterative and algebraic are inadequate for redundant robots. However, since the neural networks work with an acceptable error, the error at the end of inverse kinematics learning should be minimized. In this study, simulated annealing (SA) algorithm was used together with the neural-network-based inverse kinematics problem solution robots to minimize the error at the end effector. The solution method is applied to Stanford and Puma 560 six-joint robot models to show the efficiency. The proposed algorithm combines the characteristics of neural network and an optimization technique to obtain the best solution for the critical robotic applications. Three Elman neural networks were trained using separate training sets and different parameters, since one of them can give better results than the others can. The best result is selected within three neural network results by computing the end effector error via direct kinematics equation of the robotic manipulator. The decimal part of the neural network result was improved up to 10 digits using simulated annealing algorithm. The obtained best solution is given to the simulated annealing algorithm to find the best-fitting 10 digits for the decimal part of the solution. The end effector error was reduced significantly.