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.
Bibliographical noteFunding Information:
Manuscript received October 1, 2007; revised March 31, 2008. First published November 11, 2008; current version published December 30, 2008. This work was supported in part by the University of Minnesota (DTC) and by the National Science Foundation under Grant EIA-0324864, Grant IIS-0643680, and Grant IIS-0811946. This paper was recommended for publication by Associate Editor I. Iangemma and Editor L. Parker upon evaluation of the reviewers’ comments.
- Distance measurement
- Lie derivatives
- Observability of nonlinear systems
- Relative pose estimation
- Robot kinematics