h i g h l i g h t s • Novel control strategy based on static/dynamic target reaching for autonomous navigation. • Control law is synthesized using a Lyapunov function based on a new set of variables. • Interesting properties of the control law in terms of stability and flexibility. • Sequential target assignment strategy allows performing safe navigation. • Experiments using actual vehicles and several simulations show the advantages of the proposal. a b s t r a c t This paper presents a complete framework for reactive and flexible autonomous vehicle navigation. A human driver reactively guides a vehicle to the final destination while performing a smooth trajectory and respecting the road boundaries. The objective of this paper is to achieve similar behavior in an unmanned ground vehicle to reach a static or dynamic target location. This is achieved by using a flexible control law based on a novel definition of control variables and Lyapunov synthesis. Furthermore, a target assignment strategy to enable vehicle navigation through successive waypoints in the environment is presented. An elementary waypoint selection method is also presented to perform safe and smooth trajectories. The asymptotic stability of the proposed control strategy is proved. In addition, an accurate estimation of the maximum error boundary, according to the controller parameters, is given. With this indicator, the vehicle navigation will be safe within a certain boundaries. Simulations and experiments are performed in different cases to demonstrate the flexibility, reliability and efficiency of the control strategy. Our proposal is compared with different navigation methods from the literature such as those based on trajectory following.