1 research outputs found
Matching-Based Capture Strategies for 3D Heterogeneous Multiplayer Reach-Avoid Differential Games
This paper studies a 3D multiplayer reach-avoid differential game with a goal
region and a play region. Multiple pursuers defend the goal region by
consecutively capturing multiple evaders in the play region. The players have
heterogeneous moving speeds and the pursuers have heterogeneous capture radii.
Since this game is hard to analyze directly, we decompose the whole game as
many subgames which involve multiple pursuers and only one evader. Then, these
subgames are used as a building block for the pursuer-evader matching. First,
for multiple pursuers and one evader, we introduce an evasion space (ES) method
characterized by a potential function to construct a guaranteed pursuer winning
strategy. Then, based on this strategy, we develop conditions to determine
whether a pursuit team can guard the goal region against one evader. It is
shown that in 3D, if a pursuit team is able to defend the goal region against
an evader, then at most three pursuers in the team are necessarily needed. We
also compute the value function of the Hamilton-Jacobi-Isaacs (HJI) equation
for a special subgame of degree. To capture the maximum number of evaders in
the open-loop sense, we formulate a maximum bipartite matching problem with
conflict graph (MBMC). We show that the MBMC is NP-hard and design a
polynomial-time constant-factor approximation algorithm to solve it. Finally,
we propose a receding horizon strategy for the pursuit team where in each
horizon an MBMC is solved and the strategies of the pursuers are given. We also
extend our results to the case of a bounded convex play region where the
evaders escape through an exit. Two numerical examples are provided to
demonstrate the obtained results.Comment: 17 pages, 8 figure