Matrix differential expression with application in biped robot

On the basis of analyzing matrix differential expression, the tensor differential and the method for matrix differential based on the matrix vectorization in sequence of columns(vec-vecc) presented by Magnus are introduces firstly, then the method of the sum of Hadamard product that meets chain rule and the method for matrix differential based on the matrix vectorization in sequence of rows(vecr) are established, by applying the vecr method, the derivatives relative to screw axis error, axis position error or rotation angle error and pitch error etc. of twists with pitch h=0, ∞ and finite value and the configuration of a biped robot leg with 6 degrees of freedom are deduced.