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.