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This study addresses the targeting challenges in MRI-guided transperineal needle placement for prostate cancer (PCa) diagnosis and treatment, a procedure where accuracy is crucial for effective outcomes. We introduce a parameter-agnostic trajectory correction approach incorporating a data-driven closed-loop strategy by radial displacement and an FBG-based shape sensing to enable autonomous needle steering. In an animal study designed to emulate clinical complexity and assess MRI compatibility through a PCa mock biopsy procedure, our approach demonstrated a significant improvement in targeting accuracy (p<0.05), with mean target error of only 2.2 ± 1.9 mm on first insertion attempts, without needle reinsertions. To the best of our knowledge, this work represents the first in vivo evaluation of robotic needle steering with FBG-sensor feedback, marking a significant step towards its clinical translation.