In this paper we derive theoretical results for the problem of on-line sensor calibration for a mobile robot. We consider the case of the odometry sensor. A first series of results regards the problem of understanding if a given system (consisting of a robot with several sensors) contains the necessary information to perform the on-line self calibration of one of its sensors. We consider several cases corresponding to different odometry systems and different types of robot sensors. Finally, we also consider the problem of maximizing the calibration accuracy and we formulate this problem as an optimal control problem. For the special case of a holonomic vehicle, we derive an analytical solution, i.e. we find the best trajectory which maximizes the calibration accuracy.