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In this study, a desert ant-inspired celestial compass and a bio-inspired minimalist optic flow sensor named M(2)APix (which stands for Michaelis Menten Auto-adaptive Pixels), were embedded onboard our 2 kg-hexapod walking robot called AntBot, in order to reproduce the homing behavior observed in desert ants Cataglyphis fortis. The robotic challenge here was to make the robot come back home autonomously after being displaced from its initial location. The navigation toolkit of AntBot comprises the celestial-based heading direction, and both stride- and ventral optic flow-based odometry, as observed in desert ants. Experimental results show that our bio-inspired approach can be useful for autonomous outdoor navigation robotics in case of GPS or magnetometer failure, but also to compensate for a drift of the inertial measurement unit. In addition, our strategy requires few computational resources due to the small number of pixels (only 14 here), and a high robustness and precision (mean error of 4.8 cm for an overall path ranging from 2 m to 5 m). Finally, this work presents highly interesting field results of ant-based theoretical models for homing tasks that have not been tested yet in insectoid robots.