This paper presents a new solution for 3D steering of flexible needles guided by 3D B-mode ultrasound imaging. It aims to realize a robust steering, by accounting for uncertainties, noise and tissue heterogeneities, while limiting tissue-related disturbances. The proposed solution features interconnected state observer, automatic needle tip segmentation and path planning algorithms. Measurement quality, state uncertainties and tissue heterogeneity are considered for robust needle steering with helical paths of variable curvature. Fast replanning allows for adaptability to unexpected disturbances. An experimental validation has been done through 62 insertions of 24 Gauge bevel-tip nitinol needles in various tissue. Results are promising, characterized by mean targeting errors of less than 1 mm in homogeneous phantoms, 1.5 ± 0.9 mm in heterogeneous phantoms and 1.7 ± 0.8 mm in ex-vivo tissue. This new approach is a step towards a precise and robust patient-specific gesture.