This paper presents a new approach for a safe autonomous navigation based on reliable state space reachability analysis. This latter improves an already proposed flexible Navigation Strategy based on Sequential Waypoint Reaching (NSbSWR) framework (Vilca et al., 2015), while considering explicitly different uncertainties in modeling and/or perception. Indeed, NSbSWR is an emergent concept that exploits its flexibility and genericity to avoid frequent complex trajectories’ planning/re-planning. The paper’s main contribution is to introduce a reachability analysis scheme as a reliable risk assessment and management policy ensuring safe autonomous navigation between the successive assigned waypoints. For this aim, interval analysis is employed to propagate uncertainties influencing the vehicle’s dynamics into the navigation system states. By solving an ordinary differential equation with uncertain variables and parameters via an interval Taylor series expansion method, all the vehicle potential reachable state-space is revealed. According to the obtained bounds of the reachable sets, a decision about the navigation safety is made. Once a collision risk is captured, the risk management layer acts to update the control parameters to master the critical situation and guarantee a proper reaching of waypoint, while avoiding any risky state. Several simulation results prove the safety, efficiency and robustness of the overall navigation under uncertainties.