Determining the robot-to-robot relative pose using range-only measurements

In this paper we address the problem of determining the relative pose of pairs robots that move on a plane while measuring the distance to each other. We show that the minimum number of distance measurements required for the 3 degrees of freedom robot-to-robot transformation to become locally observable is 3. Furthermore, we prove that the maximum number of possible solutions in this case is 6, while a minimum of 5 distance measurements is necessary in order to uniquely determine the robots' relative pose. Finally, we present efficient algorithms for computing all possible solutions and evaluate the validity of our theoretical results both in simulation and experimentally.