This paper studies the accuracy of position estimation for groups of mobile robots performing cooperative localization. We consider the case of teams comprised of possibly heterogeneous robots and provide analytical expressions for the upper bound on their expected positioning uncertainty. This bound is determined as a function of the sensors' noise covariance and the eigenvalues of the relative position measurement graph (RPMG), i.e., the weighted directed graph which represents the network of robot-to-robot exteroceptive measurements. The RPMG is employed as a key element in this analysis, and its properties are related to the localization performance of the team. It is shown that, for a robot group of a certain size, the maximum expected rate of uncertainty increase is independent of the accuracy and number of relative position measurements and depends only on the accuracy of the proprioceptive and orientation sensors on the robots. Additionally, the effects of changes in the topology of the RPMG are studied, and it is shown that, at steady-state, these reconfigurations do not inflict any loss in localization precision. Experimental data, as well as simulation results that validate the theoretical analysis, are presented.
- Cooperative localization (CL)
- Kalman filtering
- Multirobot localization
- Positioning accuracy
- Relative position measurement graph (RPMG)
- Sensor sharing