Solitary foraging ants excel in following long visual routes in complex environments with limited sensory and neural resources—an ability that remains challenging for robots with minimal computational power. Here, we introduce a self-supervised, insect-inspired neural network that enables robust route-following on the compact, low-cost Antcar robot. The robot leverages key aspects of ant brain and behavior: (i) continuous, one-shot visual route learning using panoramic encoding in a mushroom body-inspired network, (ii) categorization of low-resolution egocentric panoramas via oscillatory movements, (iii) opponent-process control of angular and forward velocities based on visual familiarity, (iv) recognition of places of interest along routes, and (v) motivation-based memory modulation. Antcar autonomously followed routes between indoor or outdoor destinations, forward or backward, while remaining stable in both theoretical analysis and real-world testing despite occlusions and visual changes. Across 1.3 km of autonomous travel, Antcar achieved challenging route-following with sub-20 cm lateral error at speeds up to 150 cm/s, requiring only 148 kilobits of memory and processing panoramas every 62 ms. This efficient, brain-inspired architecture stands out from more sensor-intensive and computationally demanding methods, presenting a neuromorphic approach with valuable insights into insect navigation and practical robotic applications.