基于QR分解的冗余度机械臂雅可比矩阵求逆方法

摘要

针对冗余度机械臂在轨操作实时性的需求，提出一种基于QR分解的冗余度机械臂雅克比矩阵求逆方法。根据具体的冗余度机械臂的构型特点，将运动学逆解过程划分为多个模块，采用修正施密特QR分解方法计算机械臂雅可比矩阵的伪逆，利用硬件描述语言在FPGA上对各个模块进行了实现。以机械臂直线运动为例，通过仿真实验与利用Matlab解算的方法进行了对比，并研究了定点数长度对硬件资源和误差的影响。实验结果验证了所提出雅克比矩阵求逆方法的可行性及有效性。%According to real-time requirements of the redundant robotic manipulator mission, a jacobian matrix inversion Method for the redundant robotic manipulator base on QR decomposition is proposed. On the basis of the conifguration characteristics of redundant space robotic manipulator, the processes of kinematics inverse solution are divided into several modules, the pseudo-inverse of jacobian matrix is computed by modiifed schmidt QR decomposition. Meanwhile, each module is implemented by hardware description language on FPGA. Take the linear motion of space robotic manipulator as an example, this method and the method which using Matlab to slove are contrasted in the simulated experiments. Meanwhile, ifx-point median impact on error and resources is studied. The feasibility and effectiveness of the jacobian matrix inversion method are veriifed by simulation and experiment.