This paper enhances prostate brachytherapy robot accuracy by developing a needle deflection prediction model and a controlled puncturing strategy, addressing current challenges and trends. The study addresses the challenges in needle deflection prediction by proposing a correction force-based prediction model. The puncture control strategy comprises two phases: preoperative needle trajectory planning and intraoperative approach adjustment, both relying on corrective force. During operative adjustment, a model predicting and counteracting needle tip deflection ensures accurate corrective force application. An adaptive PID controller, utilizing Reinforcement Learning (RL), regulates corrective force for precise puncture accuracy. A dedicated experimental platform was constructed to validate the puncture control strategy for prostate seed implantation. The seed implantation's average error was 1.96 mm, with a standard error of 0.56 mm. Experiments show that correction force in the strategy significantly reduces tip deflection, enhancing seed implantation precision.