Information Technology Reference
In-Depth Information
sleeve
funnel
apex
path
start
Fig. 2. The path, apex, and funnel of the funnel algorithm
define
[ u, v ]= ʻu +(1
ʻ ) v,
[ u, v [=[ u, v ]
\{
v
}
,
] u, v [=[ u, v [
\{
u
}
.
Based on the idea of direct multiple shooting method for solving the optimal
control problems, the proposed method first splits the polygon
PQ
into sub-
polygons
T i ,for i =0 ,...,k , by parallel cutting segments ʾ 1 ,...,ʾ k
satisfying
following conditions:
ʾ i =[ u i ,v i ]
ↂD
such that ] u i ,v i [
int
D
,
[ u i ,v i ] strictly separates a and b ,
T i is bounded by
P
,
Q
, cutting segments ʾ i and ʾ i +1 ,
and
SP ( u i ,u i +1 )
SP ( v i ,v i +1 )
=
,
i =0 T i
where u i ∈P
and v i ∈Q
, for all i =1 ,...,k . We then have that
PQ
=
and int
= j .
We initialize a set of shooting points a 0
T i
int
T j =
,for i
i
ʾ i ,for i =1 ,...,k . The shooting
point a i
i =0 Z i
Z j :=
ʾ i
( j
0) is refined iteratively such that
tends to
SP ( a, b ), where a 0 = a and a k +1 = b and
Z i
denotes the shortest path between
a i
and a i +1 in
T i (see Fig. 3 ). This refinement is finished if the following collinear
condition
SP ( a i
,a i− 1 ) ,SP ( a i
,a i +1 )= ˀ,
Search WWH ::




Custom Search