This paper proposes the use of a behavior-based control strategy for collision-free navigation of a two-wheel differential drive mobile robot in partially unknown environments. The proposed strategy is hierarchical, and the design of the high-level control layer (behavioral space) is based on Mamdani fuzzy logic inference, while the design of the low-level control layer (joint space) is based on Lyapunov stability theory. The collision and deadlock avoidance technique is based on subgoals that are evaluated in the behavioral space and supplied as references to the joint space controller. The in silico test study was executed by using the CoppeliaSim which is a simulation framework used for the prototyping, development and verification of robot systems and algorithms that is widely used by the robotics community. Several (robot initial and final poses, walls and loose objects placement) test scenarios, and a comparative study with previous and related work were performed. The test results show the proposed strategy provided a smooth and shorter path in all cases. This improvement is basically related with the combined use of the subgoal technique and a Lyapunov based controller. In summary, the results corroborate the correctness of the methodology adopted in the design of collision-free navigation for differential drive mobile robots.