This paper introduces a method for robotic steering of a flexible needle inside moving and deformable tissues. The method relies on a set of objective functions allowing to automatically steer the needle along a predefined path. In order to follow the desired trajectory, an inverse problem linking the motion of the robot end effector with the objective functions is solved using a Finite Element simulation. The main contribution of the article is the new constraint-based formulation of the objective functions allowing to: 1) significantly reduce the computation time; 2) increase the accuracy and stability of the simulation-guided needle insertion. The method is illustrated, and its performances are characterized in a realistic framework, using a direct simulation of the respiratory motion generated from in vivo data of a pig. Despite the highly non-linear behavior of the numerical simulation and the significant deformations occurring during the insertion, the obtained performances enable the possibility to follow the trajectory with the desired accuracy for medical purpose.