Journal of Intelligent and Robotic Systems

, Volume 56, Issue 1–2, pp 47–67 | Cite as

An Optimal Approach to Collaborative Target Tracking with Performance Guarantees



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—λ2—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.


Optimal target tracking Convex optimization Semidefinite programming Second-order cone programming Multi-agent systems 


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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Computer Science and EngineeringLehigh UniversityBethlehemUSA
  2. 2.Mechanical Engineering and MechanicsDrexel UniversityPhiladelphiaUSA

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