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Link to original content: https://doi.org/10.1007/s10846-008-9302-x
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An Optimal Approach to Collaborative Target Tracking with Performance Guarantees

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Abstract

In this paper, we present a discrete-time optimization framework for target tracking with multi-agent systems. The “target tracking” problem is formulated as a generic semidefinite program (SDP) that when paired with an appropriate objective yields an optimal robot configuration over a given time step. The framework affords impressive performance guarantees to include full target coverage (i.e. each target is tracked by at least a single team member) as well as maintenance of network connectivity across the formation. Key to this work is the result from spectral graph theory that states the second-smallest eigenvalue—λ 2—of a weighted graph’s Laplacian (i.e. its inter-connectivity matrix) is a measure of connectivity for the associated graph. Our approach allows us to articulate agent-target coverage and inter-agent communication constraints as linear-matrix inequalities (LMIs). Additionally, we present two key extensions to the framework by considering alternate tracking problem formulations. The first allows us to guarantee k-coverage of targets, where each target is tracked by k or more agents. In the second, we consider a relaxed formulation for the case when network connectivity constraints are superfluous. The problem is modeled as a second-order cone program (SOCP) that can be solved significantly more efficiently than its SDP counterpart—making it suitable for large-scale teams (e.g. 100’s of nodes in real-time). Methods for enforcing inter-agent proximity constraints for collision avoidance are also presented as well as simulation results for multi-agent systems tracking mobile targets in both ℝ2 and ℝ3.

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Authors and Affiliations

  1. Computer Science and Engineering, Lehigh University, Bethlehem, PA, 18015, USA

    Jason Derenick & John Spletzer

  2. Mechanical Engineering and Mechanics, Drexel University, Philadelphia, PA, 19104, USA

    Ani Hsieh

Authors
  1. Jason Derenick
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  2. John Spletzer
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  3. Ani Hsieh
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Correspondence to Jason Derenick.

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Derenick, J., Spletzer, J. & Hsieh, A. An Optimal Approach to Collaborative Target Tracking with Performance Guarantees. J Intell Robot Syst 56, 47–67 (2009). https://doi.org/10.1007/s10846-008-9302-x

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  • DOI: https://doi.org/10.1007/s10846-008-9302-x

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