A Mixed Integer Linear Programming approach to pursuit evasion problems with optional connectivity constraints

Authors:
Johan Thunberg;Petter Ögren
Affiliations:
Division of Optimization and Systems Theory, Department of Mathematics, Royal Institute of Technology (KTH), Stockholm, Sweden 100 44;Department of Aeronautical and Systems Technology, Swedish Defence Research Agency (FOI), Stockholm, Sweden 164 94
Venue:
Autonomous Robots
Year:
2011

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Abstract

In this paper, we address the multi pursuer version of the pursuit evasion problem in polygonal environments. By discretizing the problem, and applying a Mixed Integer Linear Programming (MILP) framework, we are able to address problems requiring so-called recontamination and also impose additional constraints, such as connectivity between the pursuers. The proposed MILP formulation is less conservative than solutions based on graph discretizations of the environment, but still somewhat more conservative than the original underlying problem. It is well known that MILPs, as well as multi pursuer pursuit evasion problems, are NP-hard. Therefore we apply an iterative Receding Horizon Control (RHC) scheme where a number of smaller MILPs are solved over shorter planning horizons. The proposed approach is implemented in Matlab/Cplex and illustrated by a number of solved examples.