Local decomposition and observability properties for automatic calibration in mobile robotics

This paper considers the problem of sensor self-calibration in mobile robotics by only using a single point feature (e.g. a source of light). In particular, the problem of determining the extrinsic parameters of a bearing sensor mounted on a mobile platform (e.g. a camera) and simultaneously estimating the parameters describing the systematic error in the odometry system is discussed. Special attention is devoted to investigate the dependence of the observability properties of these parameters on the chosen robot trajectory. The main contribution provided by this paper is the introduction of a new method to deal with estimation problems in the framework of mobile robotics. Specifically, a calibration problem has been considered. However, the same method can be adopted to solve other fundamental estimation problems. The method is based on the theory of distributions which exploits all the system Lie symmetries. Regarding the considered calibration problem this method allows analytically detecting the combinations of the calibration parameters which are observable for a given robot trajectory. Experiments are provided to validate the results.