To address the difficulty of predicting the future states of dynamic obstacles and the increased decision uncertainty caused by incomplete perception and sensor noise for mobile robots in complex dynamic environments, this paper proposes Forward-dynamics-assisted Asymmetric Navigation (FANav), an autonomous navigation framework that integrates environment forward-dynamics prediction with asymmetric reinforcement learning. Specifically, an Environment Forward Dynamics Model (E-FDM) is introduced to learn the short-term evolution of robot–environment interactions during training, while predicted environmental changes and collision risks are incorporated into policy optimization to promote anticipatory decision-making. During deployment, the E-FDM generates online short-term environment predictions from local observations and the current action to assist real-time obstacle avoidance. To mitigate the safety risks induced by model prediction errors and perception noise, a Control Barrier Function (CBF)-based safety filter incorporating short-term risk prediction is further introduced at the execution layer. Using predictive risk information, the filter adjusts safety constraint strength online and applies minimally invasive corrections to policy outputs via quadratic programming, thereby ensuring formal safety guarantees. In addition, an asymmetric Proximal Policy Optimization (PPO) framework is adopted, where privileged information such as forward predictions is used to optimize the value network, improving learning efficiency and training stability. Experimental results show that the proposed method significantly outperforms baseline methods in obstacle-avoidance safety, decision robustness, and motion smoothness