Health-related limitations prohibit a human from working in hazardous environments, due to which cognitive robots are needed to work there. A robot cannot learn the spatial semantics of the environment or object, which hinders the robot from interacting with the working environment. To overcome this problem, in this work, an agent is computationally devised that mimics the grid and place neuron functionality to learn cognitive maps from the input spatial data of an environment or an object. A novel quadrant-based approach is proposed to model the behavior of the grid neuron, which, like the real grid neuron, is capable of generating periodic hexagonal grid-like output patterns from the input body movement. Furthermore, a cognitive map formation and their learning mechanism are proposed using the place-grid neuron interaction system, which is meant for making predictions of environmental sensations from the body movement. A place sequence learning system is also introduced, which is like an episodicmemory of a trip that is forgettable based on their usage frequency and helps in reducing the accumulation of error during a visit to distant places. The model has been deployed and validated in two different spatial data learning applications, one being the 2D object detection by touch, and another is the navigation in an environment. The result analysis shows that the proposed model is significantly associated with the expected outcomes. © 2020 by the authors.