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If the windshield of an agent is a single point (
), every agent moves directly toward its target, and we obtain a version of the classic cyclic pursuit, or
bug problem. We call this variety the direct cyclic pursuit problem to distinguish it from the Dubins car cyclic pursuit. If we are not sure whether such pursuit is cyclic, we call it direct pursuit. Such cases can be viewed as limiting cases as the windshield goes from an open interval to a point. Here we show that our approach also applies to this special case. Allowing the pursuit formation to be an arbitrary polygon and using the general form of
defined for selfintersecting polygon, (9) becomes:

(51) 
with
and
. Since for at least one
,
,
is always strictly negative for fixed
and any set of
for some fixed
. The intree and cycle plus branch cases also follow. We obtain the following corollary:
Corollary 19
Direct pursuit of
agents with lower bounded speed and arbitrary connected, singletarget assignment graph will rendezvous in finite time.
We can say a little more if
(or any constant) holds for all agents:
PROOF. Writing
as that of (13), we readily see that
for such systems. (52) is then easily obtained by substituting in (22).
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Up: Rendezvous Without Coordinates^{1}
Previous: Appendix B: Remaining Proofs
Jingjin Yu
20110118