In recent years a number of robotic steering systems have been proposed that are geared towards improving interventional radiology procedures such as tumor ablation and biopsy. These solutions have introduced new safety challenges in the physical human-robot interaction domain. This study presents a new 3D robotized needle steering algorithm compatible with CT and MR-imaging guidance. The steering algorithm is featured with an adaptive self-correction mechanism that works as a failure contingency tool that could be adapted online at each insertion step. The developed pHRI solution was designed to be compatible to ferro-magnetic issues and a reduced workspace inside the scanner bore. As far as we know, this is the first approach designed to steer rigid needles free of force sensors and which meets the challenges that prevail in our context. Our proposed approach helps overcome safety issues regarding the physical interaction between robotized needles and patients. Validation testing highlighted the feasibility of the new needle steering algorithm, while its accuracy revealed the potential of the approach under the proposed scope of application.