This paper proposes a new dynamic planning navigation strategy for use with mobile terrestrial robots. The strategy was applied to situations in which the environment and obstacles were unknown. After each displacement event, the robot replanned its route using a control algorithm that minimized the distance to the target and maximized the distance between the obstacles. Using a spatial localization sensor and a set of distance sensors, the proposed navigation strategy was able to dynamically plan optimum routes that were free of collisions. Simulations performed using different types of environment demonstrated that the technique offers a high degree of flexibility and robustness, and validated its potential use in real applications involving mobile terrestrial robots.