Journal
IEEE TRANSACTIONS ON ROBOTICS
Volume 27, Issue 4, Pages 678-695Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TRO.2011.2114734
Keywords
Bearing measurement; distance measurement; Gauss-Seidel relaxation (GSR); mobile sensor; target tracking
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Funding
- Digital Technology Center, University of Minnesota
- National Science Foundation [IIS-0643680]
- Air Force Office of Scientific Research through the 2010 Multidisciplinary University Research Initiative (MURI)
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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 target's 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 fromthat 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.
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