Optimal formations for cooperative localization of mobile robots

This paper studies the effects of the geometry of a mobile robot formation on the accuracy of the robots' localization. The general case of heterogeneous (in terms of sensor accuracy) robot teams performing Cooperative Localization is considered. An analysis of the time evolution of the covariance matrix of the position estimates allows us to express the steady-state positioning uncertainty of the robots as an analytic function of the relative positions of the robots in the formation. This metric encapsulates the effect of formation geometry on the information content of the exteroceptive measurements, as well as the effect of the influx of uncertainty due to the errors in the robots' odometry. Thus, by minimizing the trace of the steady state covariance matrix with respect to the positions of the robots, the optimal robot configuration can be determined. Numerical experiments are presented, which indicate that it is possible to derive a practical rule for determining optimal formations, without the need to resort to extensive simulations, or experimentation.