This study describes a cognitive radar architecture with application to real‐time obstacle avoidance in mobile robotic platforms. The concept of a world memory map is introduced as a means of providing an enhanced perception of the environment around the robotic platform. This is combined with a specially designed obstacle avoidance algorithm, Nearest Steering Vector Searching, all capable of operating in real‐time. The study analytically derives the radar signal processing algorithm, starting from range‐angle maps, so that a collision free course to a set destination point can be robustly navigated. Finally, the performance of this cognitive approach is examined through a number of proof‐of‐concept experiments using a commercial off‐the‐shelf radar mounted on a mobile ground robotic platform.