rs rrt r - - PowerPoint PPT Presentation

■♥tr♦❞✉❝t✐♦♥ P❛r❛❞✐❣♠❛t✐❝ ❛♣♣❧✐❝❛t✐♦♥✿ ❍♦s❡ tr❛♥s♣♦rt❛t✐♦♥ ❊①♣❡r✐♠❡♥ts

❚♦✇❛r❞s ❝♦♥❝✉rr❡♥t ◗✲▲❡❛r♥✐♥❣ ♦♥ ▲✐♥❦❡❞ ▼✉❧t✐✲❈♦♠♣♦♥❡♥t ❘♦❜♦t✐❝ ❙②st❡♠s

❇♦r❥❛ ❋❡r♥❛♥❞❡③✲●❛✉♥❛✱ ❏♦s❡ ▼❛♥✉❡❧ ▲♦♣❡③✲●✉❡❞❡✱ ▼❛♥✉❡❧

• r❛ñ❛

❈♦♠♣✉t❛t✐♦♥❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ●r♦✉♣ ❯♥✐✈❡rs✐t② ♦❢ t❤❡ ❇❛sq✉❡ ❈♦✉♥tr② ✭❯P❱✴❊❍❯✮

❍❆■❙ ✷✵✶✶✱ ❲r♦❝❧❛✇ ✭P♦❧❛♥❞✮

❤tt♣✿✴✴✇✇✇✳❡❤✉✳❡s✴❝❝✇✐♥t❝♦ ✭❈♦♠♣✉t❛t✐♦♥❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ●r♦✉♣ ❯♥✐✈❡rs✐t② ♦❢ t❤❡ ❇❛sq✉❡ ❈♦✉♥tr② ✭❯P❱✴❊❍❯✮✮ ❈♦♥❝✉rr❡♥t ◗✲▲❡❛r♥✐♥❣ ♦♥ ▲✲▼❈❘❙ ❍❆■❙ ✷✵✶✶ ✶ ✴ ✶✺

■♥tr♦❞✉❝t✐♦♥ P❛r❛❞✐❣♠❛t✐❝ ❛♣♣❧✐❝❛t✐♦♥✿ ❍♦s❡ tr❛♥s♣♦rt❛t✐♦♥ ❊①♣❡r✐♠❡♥ts

❖✉t❧✐♥❡

✶

■♥tr♦❞✉❝t✐♦♥

✷

P❛r❛❞✐❣♠❛t✐❝ ❛♣♣❧✐❝❛t✐♦♥✿ ❍♦s❡ tr❛♥s♣♦rt❛t✐♦♥

✸

❊①♣❡r✐♠❡♥ts

❤tt♣✿✴✴✇✇✇✳❡❤✉✳❡s✴❝❝✇✐♥t❝♦ ✭❈♦♠♣✉t❛t✐♦♥❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ●r♦✉♣ ❯♥✐✈❡rs✐t② ♦❢ t❤❡ ❇❛sq✉❡ ❈♦✉♥tr② ✭❯P❱✴❊❍❯✮✮ ❈♦♥❝✉rr❡♥t ◗✲▲❡❛r♥✐♥❣ ♦♥ ▲✲▼❈❘❙ ❍❆■❙ ✷✵✶✶ ✷ ✴ ✶✺

■♥tr♦❞✉❝t✐♦♥ P❛r❛❞✐❣♠❛t✐❝ ❛♣♣❧✐❝❛t✐♦♥✿ ❍♦s❡ tr❛♥s♣♦rt❛t✐♦♥ ❊①♣❡r✐♠❡♥ts

▲✐♥❦❡❞ ▼✉❧t✐❝♦♠♣♦♥❡♥t ❘♦❜♦t✐❝ ❙②st❡♠s

❉❡✜♥✐t✐♦♥✿ ❣r♦✉♣ ♦❢ r♦❜♦t✐❝ ✉♥✐ts ♣❤②s✐❝❛❧❧②✲❧✐♥❦❡❞ ❜② ❛ ♥♦♥✲r✐❣✐❞ ❡❧❡♠❡♥t✳ P❤②s✐❝❛❧ ❧✐♥❦ ✐♥tr♦❞✉❝❡s ♥❡✇ ♥♦♥✲❧✐♥❡❛r ❞②♥❛♠✐❝s ❛♥❞ ♣❤②s✐❝❛❧ ❝♦♥str❛✐♥ts ✐♥ t❤❡ s②st❡♠✳ ❚r❛❞✐t✐♦♥❛❧ ❝♦♥tr♦❧ t❡❝❤♥✐q✉❡s ❛r❡ ♥♦t ❛♣♣r♦♣r✐❛t❡

❤tt♣✿✴✴✇✇✇✳❡❤✉✳❡s✴❝❝✇✐♥t❝♦ ✭❈♦♠♣✉t❛t✐♦♥❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ●r♦✉♣ ❯♥✐✈❡rs✐t② ♦❢ t❤❡ ❇❛sq✉❡ ❈♦✉♥tr② ✭❯P❱✴❊❍❯✮✮ ❈♦♥❝✉rr❡♥t ◗✲▲❡❛r♥✐♥❣ ♦♥ ▲✲▼❈❘❙ ❍❆■❙ ✷✵✶✶ ✸ ✴ ✶✺

■♥tr♦❞✉❝t✐♦♥ P❛r❛❞✐❣♠❛t✐❝ ❛♣♣❧✐❝❛t✐♦♥✿ ❍♦s❡ tr❛♥s♣♦rt❛t✐♦♥ ❊①♣❡r✐♠❡♥ts

▼✉❧t✐✲❆❣❡♥t ❘❡✐♥❢♦r❝❡♠❡♥t ▲❡❛r♥✐♥❣

❘❡✐♥❢♦r❝❡♠❡♥t ▲❡❛r♥✐♥❣ ✭❘▲✮

❙❡t ♦❢ ❛❧❣♦r✐t❤♠s t❤❛t ❧❡❛r♥ ❜② ❡①♣❧♦r✐♥❣ t❤❡ st❛t❡ s♣❛❝❡ S t❛❦✐♥❣ ❛❝t✐♦♥s ❢r♦♠ s❡t A ❆ r❡✇❛r❞ ❢✉♥❝t✐♦♥ q✉❛❧✐✜❡s ❤♦✇ ❣♦♦❞ t❤❡ ♦❜s❡r✈❡❞ st❛t❡ ✐s ✭R : S → R✮

• ♦❛❧✿ ♠❛①✐♠✐③❡ t❤❡ ❛❝❝✉♠✉❧❛t❡❞ r❡✇❛r❞s ♦✈❡r t✐♠❡

◗✲▲❡❛r♥✐♥❣

❊st✐♠❛t❡s t❤❡ r❡✇❛r❞s t♦ ❜❡ ♦❜t❛✐♥❡❞ ❛❢t❡r t❛❦✐♥❣ ❛❝t✐♦♥ a ✐♥ st❛t❡ s ❜② ❧♦♦❦✐♥❣ ♦♥❡ st❡♣ ❛❤❡❛❞✿

Q(s,a) ← Q(s,a)+α

• r +γ ∗max

a′

• Q(s′,a′)−Q(s,a)
• ❤tt♣✿✴✴✇✇✇✳❡❤✉✳❡s✴❝❝✇✐♥t❝♦

✭❈♦♠♣✉t❛t✐♦♥❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ●r♦✉♣ ❯♥✐✈❡rs✐t② ♦❢ t❤❡ ❇❛sq✉❡ ❈♦✉♥tr② ✭❯P❱✴❊❍❯✮✮ ❈♦♥❝✉rr❡♥t ◗✲▲❡❛r♥✐♥❣ ♦♥ ▲✲▼❈❘❙ ❍❆■❙ ✷✵✶✶ ✹ ✴ ✶✺

■♥tr♦❞✉❝t✐♦♥ P❛r❛❞✐❣♠❛t✐❝ ❛♣♣❧✐❝❛t✐♦♥✿ ❍♦s❡ tr❛♥s♣♦rt❛t✐♦♥ ❊①♣❡r✐♠❡♥ts

▼✉❧t✐✲❆❣❡♥t ❘❡✐♥❢♦r❝❡♠❡♥t ▲❡❛r♥✐♥❣

▼❛✐♥ ❘▲ ❞r❛✇❜❛❝❦✿ ❡①♣♦♥❡♥t✐❛❧ ❣r♦✇t❤ ♦❢ t❤❡ st❛t❡✲❛❝t✐♦♥ s♣❛❝❡ ✭| S×A |✮ ▼✉❧t✐✲❆❣❡♥t ❘❡✐♥❢♦r❝❡♠❡♥t ▲❡❛r♥✐♥❣ ✭▼❆❘▲✮ ♠❛❦❡s ✐t ❡✈❡♥ ✇♦rs❡✿ | S×An | ▲✲▼❈❘❙ ♣r❡s❡♥t ❛♥ ❛❞❞✐t✐♦♥❛❧ ♣r♦❜❧❡♠✿ ♣❤②s✐❝❛❧ ❝♦♥str❛✐♥ts✳

❙♦♠❡ st❛t❡s ❢♦r❝❡ s✐♠✉❧❛t✐♦♥ t♦ st♦♣ ❛♥❞ st❛rt ♦✈❡r ❊①❛♠♣❧❡s✿

♣❤②s✐❝❛❧✲❧✐♥❦ str❡t❝❤❡❞ ❜❡②♦♥❞ ✐ts ♥♦♠✐♥❛❧ ❧❡♥❣t❤ ❝♦❧❧✐s✐♦♥ ❜❡t✇❡❡♥ r♦❜♦t✐❝ ✉♥✐ts

❤tt♣✿✴✴✇✇✇✳❡❤✉✳❡s✴❝❝✇✐♥t❝♦ ✭❈♦♠♣✉t❛t✐♦♥❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ●r♦✉♣ ❯♥✐✈❡rs✐t② ♦❢ t❤❡ ❇❛sq✉❡ ❈♦✉♥tr② ✭❯P❱✴❊❍❯✮✮ ❈♦♥❝✉rr❡♥t ◗✲▲❡❛r♥✐♥❣ ♦♥ ▲✲▼❈❘❙ ❍❆■❙ ✷✵✶✶ ✺ ✴ ✶✺

■♥tr♦❞✉❝t✐♦♥ P❛r❛❞✐❣♠❛t✐❝ ❛♣♣❧✐❝❛t✐♦♥✿ ❍♦s❡ tr❛♥s♣♦rt❛t✐♦♥ ❊①♣❡r✐♠❡♥ts

Pr♦❜❧❡♠ ❙t❛t❡♠❡♥t

A set of n linked robots (each of them represented as P

i) must

carry the tip of a hose from a starting configuration to the goal ❆✈❛✐❧❛❜❧❡ ❛❝t✐♦♥s✿ ❯♣✱ ❉♦✇♥✱ ▲❡❢t✱ ❘✐❣❤t✱ ❯♣✲▲❡❢t✱ ❯♣✲❘✐❣❤t✱ ❉♦✇♥✲▲❡❢t✱ ❉♦✇♥✲❘✐❣❤t ❛♥❞ ◆♦♥❡ ❙✐♠♣❧❡ ❤♦s❡ ♠♦❞❡❧✿ ❧✐♥❡ s❡❣♠❡♥t ❚❡r♠✐♥❛t✐♦♥ ❝♦♥❞✐t✐♦♥s✿

❆ r♦❜♦t st❡♣s ♦✈❡r t❤❡ ❤♦s❡ ❍♦s❡ s❡❣♠❡♥ts ❛r❡ str❡t❝❤❡❞ ♦✈❡r ♥♦♠✐♥❛❧ ❧❡♥❣t❤ ❆ r♦❜♦t ❣❡ts ♦✉t ♦❢ t❤❡ s✐♠✉❧❛t✐♦♥ ✇♦r❧❞ ❚✇♦ r♦❜♦ts ❝♦❧✐❞❡

❉❡❝❡♥tr❛❧✐③❡❞ ❝♦♥tr♦❧

❤tt♣✿✴✴✇✇✇✳❡❤✉✳❡s✴❝❝✇✐♥t❝♦ ✭❈♦♠♣✉t❛t✐♦♥❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ●r♦✉♣ ❯♥✐✈❡rs✐t② ♦❢ t❤❡ ❇❛sq✉❡ ❈♦✉♥tr② ✭❯P❱✴❊❍❯✮✮ ❈♦♥❝✉rr❡♥t ◗✲▲❡❛r♥✐♥❣ ♦♥ ▲✲▼❈❘❙ ❍❆■❙ ✷✵✶✶ ✻ ✴ ✶✺

■♥tr♦❞✉❝t✐♦♥ P❛r❛❞✐❣♠❛t✐❝ ❛♣♣❧✐❝❛t✐♦♥✿ ❍♦s❡ tr❛♥s♣♦rt❛t✐♦♥ ❊①♣❡r✐♠❡♥ts

❊①❛♠♣❧❡

❋✐❣✉r❡✿ ❆♥ ❡①❛♠♣❧❡ ♦❢ ❛♥ ✐♥✐t✐❛❧ ❝♦♥✜❣✉r❛t✐♦♥

❤tt♣✿✴✴✇✇✇✳❡❤✉✳❡s✴❝❝✇✐♥t❝♦ ✭❈♦♠♣✉t❛t✐♦♥❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ●r♦✉♣ ❯♥✐✈❡rs✐t② ♦❢ t❤❡ ❇❛sq✉❡ ❈♦✉♥tr② ✭❯P❱✴❊❍❯✮✮ ❈♦♥❝✉rr❡♥t ◗✲▲❡❛r♥✐♥❣ ♦♥ ▲✲▼❈❘❙ ❍❆■❙ ✷✵✶✶ ✼ ✴ ✶✺

■♥tr♦❞✉❝t✐♦♥ P❛r❛❞✐❣♠❛t✐❝ ❛♣♣❧✐❝❛t✐♦♥✿ ❍♦s❡ tr❛♥s♣♦rt❛t✐♦♥ ❊①♣❡r✐♠❡♥ts

▼✉❧t✐✲❆❣❡♥t ❈♦♦r❞✐♥❛t✐♦♥

❋♦r t❤❡ ❛❣❡♥ts t♦ ❧❡❛r♥ t❤❡ ❜❡st ♣♦❧✐❝② ❢♦r ❡❛❝❤ ♦❢ t❤❡ st❛t❡s✱ t❤❡ str❛✐❣❤t❢♦r✇❛r❞ ❛♣♣r♦❛❝❤ ✉s❡s ♦♠♥✐s❝✐❡♥t ❛❣❡♥ts ❙t❛t❡✲❛❝t✐♦♥ ❣r♦✇t❤ ♠❛❦❡s ✐t ✉♥❢❡❛s✐❜❧❡ ❡✈❡♥ ✐♥ t❤✐s s✐♠♣❧❡ ❡♥✈✐r♦♥♠❡♥t ■♥st❡❛❞ ✇❡ ✉s❡ t✉r♥s✱ s♦ t❤❡ st❛t❡ r❡♠❛✐♥s st❛t✐♦♥❛r② ❞✉r✐♥❣ ❛♥ ❛❣❡♥t✬s ♠♦✈❡ ❇❡❝❛✉s❡ ♦❢ ♣❛rt✐❝✉❧❛r✐t✐❡s ♦❢ ▲✲▼❈❘❙✱ ✇❡ ✐♥✈❡st✐❣❛t❡ t❤❡ ❜❡❤❛✈✐♦r ♦❢ ❛❣❡♥ts ❛❜❧❡ t♦ ♦❜s❡r✈❡ ♦♥❧② ❛ ❢❡✇ st❛t❡ ✈❛r✐❛❜❧❡s✿

♣♦s✐t✐♦♥ ♦❢ t❤❡ ❛❣❡♥t ❛♥❞ ✐ts ♥❡✐❣❤❜♦✉rs ❞❡t❡❝t✐♦♥ ♦❢ ❛♥ ♦❜❥❡❝t ✐♥ ❛❞❥❛❝❡♥t ❝❡❧❧s

❤tt♣✿✴✴✇✇✇✳❡❤✉✳❡s✴❝❝✇✐♥t❝♦ ✭❈♦♠♣✉t❛t✐♦♥❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ●r♦✉♣ ❯♥✐✈❡rs✐t② ♦❢ t❤❡ ❇❛sq✉❡ ❈♦✉♥tr② ✭❯P❱✴❊❍❯✮✮ ❈♦♥❝✉rr❡♥t ◗✲▲❡❛r♥✐♥❣ ♦♥ ▲✲▼❈❘❙ ❍❆■❙ ✷✵✶✶ ✽ ✴ ✶✺

■♥tr♦❞✉❝t✐♦♥ P❛r❛❞✐❣♠❛t✐❝ ❛♣♣❧✐❝❛t✐♦♥✿ ❍♦s❡ tr❛♥s♣♦rt❛t✐♦♥ ❊①♣❡r✐♠❡♥ts

❯♥❞❡s✐r❛❜❧❡ ❚❡r♠✐♥❛t✐♦♥ ❈♦♥❞✐t✐♦♥s

❘❡✇❛r❞ ❢✉♥❝t✐♦♥ ❞❡❝♦♠♣♦s✐t✐♦♥✿ ❛ ✉♥✐q✉❡ ❣♦❛❧ r❡✇❛r❞ ❢✉♥❝t✐♦♥ RG : S → R ≥ 0 ❛♥❞ s❡✈❡r❛❧ ❛✉①✐❧✐❛r② ❢✉♥❝t✐♦♥s RU

i : S → R ≤ 0

RG r❡t✉r♥s ❛ ♣♦s✐t✐✈❡ r❡✇❛r❞ ✇❤❡♥❡✈❡r t❤❡ ❣♦❛❧ ✐s r❡❛❝❤❡❞ RU

i r❡t✉r♥ ❛ ♥❡❣❛t✐✈❡ r❡✇❛r❞ ✇❤❡♥ t❤❡ i✲t❤ ❝♦♥str❛✐♥t ✐s ❜r♦❦❡♥

❤tt♣✿✴✴✇✇✇✳❡❤✉✳❡s✴❝❝✇✐♥t❝♦ ✭❈♦♠♣✉t❛t✐♦♥❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ●r♦✉♣ ❯♥✐✈❡rs✐t② ♦❢ t❤❡ ❇❛sq✉❡ ❈♦✉♥tr② ✭❯P❱✴❊❍❯✮✮ ❈♦♥❝✉rr❡♥t ◗✲▲❡❛r♥✐♥❣ ♦♥ ▲✲▼❈❘❙ ❍❆■❙ ✷✵✶✶ ✾ ✴ ✶✺

■♥tr♦❞✉❝t✐♦♥ P❛r❛❞✐❣♠❛t✐❝ ❛♣♣❧✐❝❛t✐♦♥✿ ❍♦s❡ tr❛♥s♣♦rt❛t✐♦♥ ❊①♣❡r✐♠❡♥ts

❙t❛t❡✲❆❝t✐♦♥ ▼♦❞✉❧❛r ❱❡t♦ ❛♣♣r♦❛❝❤

❆ss✉♠✐♥❣ ♥♦t ❛❧❧ RU

i ❞❡♣❡♥❞ ♦♥ ❛❧❧ t❤❡ st❛t❡ ✈❛r✐❛❜❧❡s ❜✉t ❛

s✉❜s❡t✱ t❤❡ ♦r✐❣✐♥❛❧ ♣r♦❜❧❡♠ ❝❛♥ ❜❡ ❞❡❝♦♠♣♦s❡❞ ✐♥ s❡✈❡r❛❧ ❝♦♥❝✉rr❡♥t ♠♦❞✉❧❡s ❖♥❡ ♦❢ t❤❡♠ ❧❡❛r♥s ❤♦✇ t♦ ♠❛①✐♠✐③❡ RG ❛♥❞ t❤❡ r❡st ♦❢ ♠♦❞✉❧❡s ❧❡❛r♥ st❛t❡✲❛❝t✐♦♥ ♣❛✐rs ❧❡❛❞✐♥❣ t♦ ✉♥❞❡s✐r❡❞ t❡r♠✐♥❛t✐♦♥s s♦ ❛s t♦ ✈❡t♦ t❤❡♠ ✐♥ t❤❡ ❢✉t✉r❡ ❚❤❡ r❡❞✉❝❡❞ st❛t❡ s♣❛❝❡ ♠❛❦❡s ❝♦♥s✐❞❡r❛❜❧② ❢❛st❡r ❧❡❛r♥✐♥❣ ❤♦✇ t♦ ❛✈♦✐❞ t❤❡♠

❤tt♣✿✴✴✇✇✇✳❡❤✉✳❡s✴❝❝✇✐♥t❝♦ ✭❈♦♠♣✉t❛t✐♦♥❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ●r♦✉♣ ❯♥✐✈❡rs✐t② ♦❢ t❤❡ ❇❛sq✉❡ ❈♦✉♥tr② ✭❯P❱✴❊❍❯✮✮ ❈♦♥❝✉rr❡♥t ◗✲▲❡❛r♥✐♥❣ ♦♥ ▲✲▼❈❘❙ ❍❆■❙ ✷✵✶✶ ✶✵ ✴ ✶✺

■♥tr♦❞✉❝t✐♦♥ P❛r❛❞✐❣♠❛t✐❝ ❛♣♣❧✐❝❛t✐♦♥✿ ❍♦s❡ tr❛♥s♣♦rt❛t✐♦♥ ❊①♣❡r✐♠❡♥ts

❙t❛t❡✲❆❝t✐♦♥ ▼♦❞✉❧❛r ❱❡t♦ ❛♣♣r♦❛❝❤

RL Modules

Goal-Module Goal-Module Veto-Module #m Veto-Module #m Veto-Module #1 Veto-Module #1

Sensors Sensors Module Mediator Module Mediator

 Q s

G

a  Q s 1

U

 Qsm

U

s

G

Environment Environment

s 1

U

sm

U

S

R

G

R1

U

Rm

U

❋✐❣✉r❡✿ ❙❝❤❡♠❡ ♦❢ t❤❡ ❙t❛t❡✲❆❝t✐♦♥ ▼♦❞✉❧❛r ❱❡t♦ ❛❧❣♦r✐t❤♠

❤tt♣✿✴✴✇✇✇✳❡❤✉✳❡s✴❝❝✇✐♥t❝♦ ✭❈♦♠♣✉t❛t✐♦♥❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ●r♦✉♣ ❯♥✐✈❡rs✐t② ♦❢ t❤❡ ❇❛sq✉❡ ❈♦✉♥tr② ✭❯P❱✴❊❍❯✮✮ ❈♦♥❝✉rr❡♥t ◗✲▲❡❛r♥✐♥❣ ♦♥ ▲✲▼❈❘❙ ❍❆■❙ ✷✵✶✶ ✶✶ ✴ ✶✺

■♥tr♦❞✉❝t✐♦♥ P❛r❛❞✐❣♠❛t✐❝ ❛♣♣❧✐❝❛t✐♦♥✿ ❍♦s❡ tr❛♥s♣♦rt❛t✐♦♥ ❊①♣❡r✐♠❡♥ts

❘❡s✉❧ts

■♥✐t✐❛❧ ❝♦♥✜❣✉r❛t✐♦♥s ✇❡r❡ r❛♥❞♦♠❧② ❣❡♥❡r❛t❡❞ ❖♥❡ ❡♣✐s♦❞❡ ✇❛s s✐♠✉❧❛t❡❞ ❢♦r ❡❛❝❤ ❝♦♥✜❣✉r❛t✐♦♥ ✇✐t❤ t②♣✐❝❛❧ ε −greedy ❡①♣❧♦r❛t✐♦♥ P❡r❝❡♥t ♦❢ s✉❝❝❡s❢✉❧❧ ❝♦♥✜❣✉r❛t✐♦♥s ✇❛s ♠❡❛s✉r❡❞ ✇✐t❤ ❛ 500 ❡♣✐s♦❞❡ ✇✐♥❞♦✇

❤tt♣✿✴✴✇✇✇✳❡❤✉✳❡s✴❝❝✇✐♥t❝♦ ✭❈♦♠♣✉t❛t✐♦♥❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ●r♦✉♣ ❯♥✐✈❡rs✐t② ♦❢ t❤❡ ❇❛sq✉❡ ❈♦✉♥tr② ✭❯P❱✴❊❍❯✮✮ ❈♦♥❝✉rr❡♥t ◗✲▲❡❛r♥✐♥❣ ♦♥ ▲✲▼❈❘❙ ❍❆■❙ ✷✵✶✶ ✶✷ ✴ ✶✺

■♥tr♦❞✉❝t✐♦♥ P❛r❛❞✐❣♠❛t✐❝ ❛♣♣❧✐❝❛t✐♦♥✿ ❍♦s❡ tr❛♥s♣♦rt❛t✐♦♥ ❊①♣❡r✐♠❡♥ts

❊①♣❡r✐♠❡♥t ❆✿ ◆♦ ♠♦❞✉❧❛r ✈❡t♦ s②st❡♠

❋✐❣✉r❡✿ ❘❡s✉❧ts ✇✐t❤♦✉t t❤❡ ♠♦❞✉❧❛r ✈❡t♦ s②st❡♠

❤tt♣✿✴✴✇✇✇✳❡❤✉✳❡s✴❝❝✇✐♥t❝♦ ✭❈♦♠♣✉t❛t✐♦♥❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ●r♦✉♣ ❯♥✐✈❡rs✐t② ♦❢ t❤❡ ❇❛sq✉❡ ❈♦✉♥tr② ✭❯P❱✴❊❍❯✮✮ ❈♦♥❝✉rr❡♥t ◗✲▲❡❛r♥✐♥❣ ♦♥ ▲✲▼❈❘❙ ❍❆■❙ ✷✵✶✶ ✶✸ ✴ ✶✺

■♥tr♦❞✉❝t✐♦♥ P❛r❛❞✐❣♠❛t✐❝ ❛♣♣❧✐❝❛t✐♦♥✿ ❍♦s❡ tr❛♥s♣♦rt❛t✐♦♥ ❊①♣❡r✐♠❡♥ts

❊①♣❡r✐♠❡♥t ❇✿ ▼♦❞✉❧❛r ✈❡t♦ s②st❡♠

❋✐❣✉r❡✿ ❘❡s✉❧ts ✇✐t❤♦✉t t❤❡ ♠♦❞✉❧❛r ✈❡t♦ s②st❡♠

❤tt♣✿✴✴✇✇✇✳❡❤✉✳❡s✴❝❝✇✐♥t❝♦ ✭❈♦♠♣✉t❛t✐♦♥❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ●r♦✉♣ ❯♥✐✈❡rs✐t② ♦❢ t❤❡ ❇❛sq✉❡ ❈♦✉♥tr② ✭❯P❱✴❊❍❯✮✮ ❈♦♥❝✉rr❡♥t ◗✲▲❡❛r♥✐♥❣ ♦♥ ▲✲▼❈❘❙ ❍❆■❙ ✷✵✶✶ ✶✹ ✴ ✶✺

❆♣♣❡♥❞✐①

❚❤❛♥❦s

❚❤❛♥❦ ②♦✉ ✈❡r② ♠✉❝❤ ❢♦r ②♦✉r ❛tt❡♥t✐♦♥✳

❈♦♥t❛❝t✿

❇♦r❥❛ ❋❡r♥á♥❞❡③ ●❛✉♥❛✳ ❈♦♠♣✉t❛t✐♦♥❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ●r♦✉♣✳ ❯♥✐✈❡rs✐t② ♦❢ t❤❡ ❇❛sq✉❡ ❈♦✉♥tr② ✭❯P❱✴❊❍❯✮✳ ❊✲♠❛✐❧✿ ❜♦r❥❛✳❢❡r♥❛♥❞❡③❅❡❤✉✳❡s ❲❡❜ ♣❛❣❡✿ ❤tt♣✿✴✴✇✇✇✳❡❤✉✳❡s✴❝♦♠♣✉t❛t✐♦♥❛❧✐♥t❡❧❧✐❣❡♥❝❡

❤tt♣✿✴✴✇✇✇✳❡❤✉✳❡s✴❝❝✇✐♥t❝♦ ✭❈♦♠♣✉t❛t✐♦♥❛❧ ■♥t❡❧❧✐❣❡♥❝❡ ●r♦✉♣ ❯♥✐✈❡rs✐t② ♦❢ t❤❡ ❇❛sq✉❡ ❈♦✉♥tr② ✭❯P❱✴❊❍❯✮✮ ❈♦♥❝✉rr❡♥t ◗✲▲❡❛r♥✐♥❣ ♦♥ ▲✲▼❈❘❙ ❍❆■❙ ✷✵✶✶ ✶✺ ✴ ✶✺