In this paper, we study the problem of optimal trajectory generation for a team of heterogeneous robots moving in a plane and tracking a moving target by processing relative observations, i.e., distance and/or bearing. Contrary to previous approaches, we explicitly consider limits on the robots speed and impose constraints on the minimum distance at which the robots are allowed to approach the target. We first address the case of a single tracking sensor and seek the next sensing location in order to minimize the uncertainty about the targets position. We show that although the corresponding optimization problem involves a nonconvex objective function and a nonconvex constraint, its global optimal solution can be determined analytically. We then extend the approach to the case of multiple sensors and propose an iterative algorithm, i.e., the Gauss-Seidel relaxation (GSR), to determine the next best sensing location for each sensor. Extensive simulation results demonstrate that the GSR algorithm, whose computational complexity is linear in the number of sensors, achieves higher tracking accuracy than gradient descent methods and has performance that is indistinguishable from that of a grid-based exhaustive search, whose cost is exponential in the number of sensors. Finally, through experiments, we demonstrate that the proposed GSR algorithm is robust and applicable to real systems.
|Original language||English (US)|
|Number of pages||18|
|Journal||IEEE Transactions on Robotics|
|State||Published - Aug 2011|
Bibliographical noteFunding Information:
Manuscript received May 2, 2010; revised November 8, 2010; accepted February 7, 2011. Date of publication March 22, 2011; date of current version August 10, 2011. This paper was recommended for publication by Associate Editor D. Song and Editor L. Parker upon evaluation of the reviewers’ comments. This work was supported by the Digital Technology Center, University of Minnesota, the National Science Foundation through Grant IIS-0643680, and the Air Force Office of Scientific Research through the 2010 Multidisciplinary University Research Initiative (MURI), Topic 18: Control of Information Collection and Fusion.
- Bearing measurement
- Gauss-Seidel relaxation (GSR)
- distance measurement
- mobile sensor
- target tracking