When applying the RRT algorithm to obstacle avoidance path planning for mobile robots, there are planning efficiency issues such as large search space, long calculation time, and uneven path. This paper proposes an enhanced algorithm that takes map information, starting and ending coordinates as inputs, and outputs an optimized smooth path to address the shortcomings of the original algorithm. This algorithm uses a low-discrepancy Sobol sequence with a probabilistic target bias strategy to optimize the sampling points. Additionally, the concept of target gravity is utilized to adjust the expansion direction of the new nodes, with the gravity coefficient being adaptively adjustable. The original obstacle avoidance path is optimized by pruning optimization removal combined with cubic B-spline curve. In a complex map setting, the improved algorithm demonstrates reductions in running time of 87.71%, 88.59%, and 67.82% compared to RRT, RRT*, and target-biased RRT, respectively. Compared with the other three algorithms, the improved approach reduces the planned path distance by 18.53%, 8.43%, and 15.28%, respectively, demonstrating its efficacy in enhancing path planning efficiency and maintaining path quality.