Purpose Robots with a spherical unactuated wrist can be used for minimally invasive surgery. With such a robot, positioning the wrist center controls the instrument tip position when assuming that the insertion site behaves like a lever with a fixed and known fulcrum. In practice, this assumption is not always respected. In this paper we first study the practical consequences of this problem in terms of tip precision positioning. We then propose a robotic control scheme that improves the precision compared to the fixed point assumption approach. Methods In the first part of the paper, data recorded during robot-assisted transrectal needle positioning for prostate biopsies (nine patients) are exploited to quantify the positioning error induced by the use of a fixed point hypothesis in the positioning process. In the second part of the paper advanced control techniques allow for the online identification of a locally linear system that describes a model characterized by anisotropy and center displacement. A laboratory apparatus is used to demonstrate the resulting improvement on tip positioning precision. Results Errors obtained by processing the clinical data reach 7.5 mm at the tip in average. Errors obtained with the laboratory apparatus drop from 2.4 mm in average to 0.8 mm when using real-time model update.