The use of robotic arms for fruit picking is becoming a trend in modern agriculture. However, the irregular shape of fruit trees and the uncertain positions of fruits in orchards present significant challenges. Direct grasping can lead to collisions with branches and leaves, causing damage and failed attempts. The RRT* algorithm and its variants address path planning by initially finding a path, which greatly impacts the algorithm's performance. This paper introduces the GD-RRT* algorithm for initial path acquisition. It uses a Gaussian mixed probability distribution model with real-time parameter updates, alternating between Gaussian sampling and target bias strategies, and dynamically adjusts the depth value based on collision detection success rates. Simulations show that GD-RRT* reduces path cost and planning time compared to RRT*. In comparison with the I-RRT* algorithm, it reduces planning time by 67.04% and optimal path finding time by 95.75%, with an average planning time of 263.4 Ms. Experiments demonstrate its applicability in dynamic and complex agricultural environments, achieving 100% success in obstacle avoidance, 92% in indoor picking, and 84% in orchard picking. These results indicate that GD-RRT* effectively performs obstacle avoidance and picking functions in real orchard environments.