Observability Properties and Optimal Trajectories for On-line Odometry Self-Calibration

In this paper we derive theoretical results for the problem of on-line odometry self-calibration for a mobile robot. 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 the odometry. 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 second order differential equations characterizing the solution, i.e. defining the best trajectory which maximizes the calibration accuracy