Drawing inspiration from biology, the Psikharpax project aims at endowing a robot with a sensori-motor equipment and a neural control architecture that will afford some of the capacities of autonomy and adaptation that are exhibited by real rats. The paper summarizes the current state of achievement of the project. It successively describes the robot's future sensors and actuators, and several biomimetic models of the anatomy and physiology of structures in the rat's brain, like the hippocampus and the basal ganglia, which have already been at work on various robots, and that make navigation and action selection possible. Preliminary results on the implementation of learning mechanisms in these structures are also presented. Finally, the article discusses the potential benefits that a biologically-inspired approach affords to traditional autonomous robotics.