Abstract-In this paper, we address the problem of determining the 2-D relative pose of pairs of communicating robots from 1) robot-to-robot distance measurements and 2) displacement estimates expressed in each robot's reference frame. Specifically, we prove that for nonsingular configurations, the minimum number of distance measurements required for determining all six possible solutions for the 3 degree-of-freedom (3-DOF) robot-to-robot transformation is 3. Additionally, we show that given four distance measurements, the maximum number of solutions is 4, while five distance measurements are sufficient for uniquely determining the robot-to-robot transformation. Furthermore, we present an efficient algorithm for computing the unique solution in closed form and describe an iterative least-squares process for improving its accuracy. Finally, we derive necessary and sufficient observability conditions based on Lie derivatives and evaluate the performance of the proposed estimation algorithms both in simulation and via experiments. Index Terms-Distance measurement, Lie derivatives, observability of nonlinear systems, relative pose estimation.
The work in REF provides non-iterative algorithms for computing the initial relative pose in 2D.
Robot-to-Robot Relative Pose Estimation From Range Measurements
IEEE Transactions on Robotics
IEEE Transactions on Robotics
Mathematics Computer Science