Optimal trajectories for multi robot localization

This paper considers the problem of multi robot localization. The analysis is focused on the problem of determining which are the optimal robot trajectories in order to minimize the localization error at the final robot configurations. Furthermore, the analysis takes into account several constrains expressing the maximum robot energy consumption and maximum robot speed and acceleration. The problem is formulated as an optimal control problem. For the special case of holonomic vehicles, an analytical solution is derived. In particular, this solution satisfies second order differential equations. The trajectories corresponding to this optimal control are plotted for different initial and final robot configurations and for several values of the system parameters (characterizing the precision of the robot sensors and the values of the constrains). Extensive simulations validate the derived analytical results.