We present a novel Deep Reinforcement Learning (DRL) based policy to compute dynamically feasible and spatially aware velocities for a robot navigating among mobile obstacles. Our approach combines the benefits of the Dynamic Window Approach (DWA) in terms of satisfying the robot’s dynamics constraints with state-of-the-art DRL-based navigation methods that can handle moving obstacles and pedestrians well. Our formulation achieves these goals by embedding the environmental obstacles’ motions in a novel low-dimensional observation space. It also uses a novel reward function to positively reinforce velocities that move the robot away from the obstacle’s heading direction leading to significantly lower number of collisions. We evaluate our method in realistic 3-D simulated environments and on a real differential drive robot in challenging dense indoor scenarios with several walking pedestrians. We compare our method with state-of-the-art collision avoidance methods and observe significant improvements in terms of success rate (up to 33% increase), number of dynamics constraint violations (up to 61% decrease), and smoothness. We also conduct ablation studies to highlight the advantages of our observation space formulation, and reward structure.