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This document considers the problem of sensor self-calibration in mobile robotics by only using a single point feature. In particular, it is introduced a simple and efficient strategy to extrinsically calibrate a bearing sensor (e.g. a vision sensor) mounted on a vehicle and simultaneously estimate the parameters describing the systematic error of its odometry system. Special attention is devoted to investigate the dependence of the observability properties of these parameters on the chosen robot trajectory. The document provides two contributions. The first one is the analytical derivation of the combinations of these parameters which are observable for a given robot trajectory. This derivation requires to perform a local decomposition of the system, based on the theory of distributions. In this respect, this document represents the first application of the distribution theory in the frame-work of mobile robotics. Then, starting from this decomposition, it is possible to analytically derive the expression of the bearing angle of the feature in the bearing sensor local frame vs the curve length of the robot trajectory as evaluated by the odometry. Starting from this expression, a method to efficiently estimate the parameters describing both the extrinsic bearing sensor calibration and the odometry calibration is derived (second contribution). Many accurate simulations and real experiments with the robot e-Puck equipped with encoder sensors and a camera show the robustness the efficiency and the accuracy of the proposed approach.

Using the distribution theory to simultaneously calibrate the sensors of a mobile robot