Conditions and strategies for uniqueness of the solutions to cooperative localization and mapping problems using rigidity theory

In this paper, we use the rigidity theory to address two problems encountered in cooperative localization and mapping. First, we consider the problem of map merging in scenarios where a group of mobile agents explore an environment. We establish conditions for the agents to be able to exchange the environmental information that they have gathered in their own local coordinate frames. We relate these conditions to the sensing capabilities of the agents. Second, we study a scenario where a group of mobile agents in a network need to localize their positions. It is assumed that there are not enough measurements to achieve this task at any time instance. We propose a coordinated motion strategy that enables the agents to achieve this goal over a period of time. Numerical simulations are provided to demonstrate the results.