Control design for robotic systems guaranteeing safety and convergence properties in cluttered environments is intrinsically challenging due to their potentially conflicting ob jectives. While several research streams tackle the problem from different angles, a general solution for nonlinear dynamical systems is still out of reach. In this paper, we tackle the problem through a dynamic extension of the controller, ensuring that the output of a system stays within the vicinity of a predefined path, ensuring safety first and then asymptotic stability of the desired point. The results rely on the forward invariance of sublevel sets of Lyapunov functions and on stabilizing dynamically updated reference points. The results are illustrated using the example of a linear double integrator and extended unicycle dynamics.