基于空间算子代数理论的多体系统雅可比矩阵及其逆的描述与实现

Jacobin matrix and its inverse of multibody system dynamics analysis and realization based on spatial operator algebra theory

雅可比矩阵及其逆在运动学和动力学方程的计算中有非常广泛的用途.使用空间算子代数理论来对雅可比矩阵及其逆的结构进行研究,形成了高效的速度和静力递推算法.随后对链式多体系统的D-H参数表达进行了进一步的研究,结合空间算子代数理论给出了雅可比矩阵及其逆的软件实现流程.最后,运用Matlab@符号计算库对雅可比矩阵及其逆的计算进行了实现,并通过与实际算例的对比验证了该方法的有效性.

Jacobin matrix and its inverse are widely applied in kinematics and dynamics. The high effective recursive method can be used to compute velocity and static force when using spatial operator algebra theory to carry on the research of Jacobi matrix and its inverse. The D-H parameters in chain systems were studied. It build the Jacobin matrix and its inverse software structure combined with the spatial operator algebra theory. The realization of the Jacobin matrix and its inverse based on Matlab@symbolic toolbox were achieved. The effectiveness of the proposed method was verified by some examples.