powerpoint presentationarielpro/15780s18/slides/780s18-3.pdf · jorge 2009 "his path-planning...
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• 𝑥𝑓 𝑥 < 𝑓 𝑡∗ 𝑡∗
•
2
• 𝐼𝐺 ℎ
• 𝑥
• 𝑓 𝑥 < 𝑓 𝑡∗ = 𝐶∗
• 𝐵𝑥
3
𝑥
𝑠
• 𝐺′ 𝑡(𝑥, 𝑡) ℎ(𝑥)
• ℎ′ ℎ ℎ′ 𝑡 = 0
• ℎ′
o
𝑡
o (𝑦, 𝑡)ℎ′ 𝑦 = ℎ 𝑦 ≤ 𝑐 𝑦, 𝑥 + ℎ 𝑥= 𝑐 𝑦, 𝑡 = 𝑐 𝑦, 𝑡 + ℎ′ 𝑡
4
𝑠
𝑡
ℎ(𝑥)
𝑥
𝐺
𝐺′
• 𝐼′ 𝐺′ℎ′ 𝑡
𝑔 𝑡 + ℎ′ 𝑡 = 𝑔 𝑥 + ℎ 𝑥 < 𝐶∗
• 𝐵 𝑥 𝐼′𝐼 𝐵
𝐶∗
•
𝐵∎
5
𝑡
ℎ(𝑥)
𝐺
𝐺′
𝑠
𝑥
6
•
•
7
𝑎𝑎
𝑏 𝑐ℎ = 1 ℎ = 20 ℎ = 6
3 1 1
1
ℎ = 1 ℎ = 1
𝑎
11 1
𝑠
𝑡
8
•
•
•
•
9
10
•
o
o
•
11
•
•
•
12
13
•
•
o 𝑥1, … , 𝑥𝑛
o 𝑥𝑘 𝑥𝑗
o 𝑥1, … , 𝑥𝑗 , 𝑥𝑘 , … , 𝑥𝑛
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15
16
•
•
o 𝑔(𝑦) = 𝑔(𝑥) + 𝑐(𝑥, 𝑦)
o 𝑦𝑓 𝑦 = 𝑔(𝑥) + 𝑐(𝑥, 𝑦) + ℎ(𝑦)
•
o (𝑥) 𝑦 𝑦𝑓(𝑦) = 𝑔( (𝑥)) + 𝑐( (𝑥), 𝑦) + ℎ(𝑦)
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18
19
•
•
•
20
•
• ⇒ 𝑝
𝑝
• 𝑝
•
21
𝑝
•
•
•
∎
22
𝑝
𝑝
23
24
= 𝑠, 𝑡= (𝑥, 𝑦) 𝑦 𝑥
• 𝑛
1. Θ 𝑛
2. Θ 𝑛
3. Θ 𝑛2
4. Θ 𝑛3
25
•
o
o
o
•
o
o
•
o
26
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