In response to the issues of poor random sampling bias, low path search efficiency, and slow convergence speed in the path expansion of the traditional RRT* algorithm, a redefined sampling region RRT* (RTSR-RRT*) algorithm is proposed. Firstly, a target bias strategy is introduced into the RRT* algorithm to reduce the randomness of sampling and increase the bias of sampling points. Secondly, the offset angle between the expansion node and the target point, along with the density of surrounding obstacle distribution, is converted into an angle based on the duty cycle. This angle is then superimposed, and the expansion node is used as the vertex, with the line connecting to the target point as the bisector, to bisect the sum of the two angles, thereby redefining the sampling region. This redefinition narrows the sampling space and enhances the efficiency of path search. Furthermore, a secondary sampling is conducted within the redefined sampling region. By leveraging the fixed gravitational force of the target point and the variable gravitational force of the sampling points, the growth direction of new nodes is optimized, further increasing the bias of path expansion and accelerating the convergence speed of the algorithm, ultimately generating the planned path. To validate the superiority of the proposed algorithm, comparisons were made with the RRT*, informed-RRT*, GB-RRT* and AEC-RRT* algorithms. The results indicate that compared to the RRT* algorithm, planning time is reduced by 35%, and the number of sampling points is decreased by 58%; compared to the informed-RRT* algorithm, planning time is reduced by 40%, and the number of sampling points is decreased by 50%; compared to the GB-RRT* algorithm, planning time is reduced by 29%, and the number of sampling points is decreased by 54%; and compared to the AEC-RRT* algorithm, planning time is reduced by 31%, and the number of sampling points is decreased by 53%. Finally, the planned path was tested on a robotic arm platform, further verifying the effectiveness of the proposed algorithm.