This paper describes a novel behavior-based local navigation approach for rough off-road scenarios. Trajectory candidates are generated based on vehicle kinematics and dynamics as well as the desired global trajectory. In contrast to on-road local navigation approaches, the work at hand proposes the use of a shiftable elevation grid map instead of occupancy maps since traversability in rough terrains does not only depend on location, but also on the robot's orientation. The traversability is evaluated by determining tire contact points with the terrain to take various different safety and efficiency aspects like underbody collisions and rollover risk into account. By exploiting the behavior-based control paradigm, the navigation approach can be easily extended and its robustness is shown in experimental evaluations using an Unimog U5023.