The path construction of robot task space has always been the focus of researchers,and a smoother path is particularly critical for robot motion.A method to construct a second-order smooth pose path for robot task space was proposed.The attitude path was divided into position path and attitude path.Line and arc were used to represent the basic position path,and quaternion was used to represent the attitude path.According to the transition region given by the environment,the transition curve of position and attitude path was constructed respectively based on Hermite method,and an efficient and easy to understand numerical integration algorithm was designed to calculate the length of pose path.Then the interpolation calculation of given path length was realized by using integrating numerical integration and dichotomy search algorithm.Numerical simulation analysis was made in MATLAB.The effectiveness of the algorithm in second-order smooth pose path construction for robot task space was verified.