Automatic Lighthouse Calibration Using Conics for Indoor Robot Localization

In this letter, we propose a technique for calibrating Lighthouse localization systems using a single view of two or more coplanar circles traced by a moving robot. The calibration method leverages conic algebra to compute the homography between the Lighthouse view and the world plane, up to similarity. This approach requires minimal user intervention and is particularly suited for automatically calibrating large-scale deployments involving hundreds of mobile robots. We validate our method using a centimeter-scale differential-drive robot, utilizing 5 cm circles to calibrate a 2 $\times \text{2 m}^{2}$ area. The proposed technique achieved a mean positional accuracy of 7.77 mm, compared to the 5.37 mm accuracy of a previous calibration method based on manual measurements and known correspondences. We demonstrate that the conics traced by the robot are accurate enough for reliable homography estimation, even under varying conditions of tire material and surface type. A camera-based motion capture system served as the ground truth for all experiments. This work represents a step toward scalable and decentralized lighthouse calibration, enabling efficient 2D localization in large-scale robotic systems.