Simultaneous localization and mapping (SLAM) is an essential capability for Unmanned Ground Vehicles (UGVs) travelling in unknown environments where globally accurate position data as GPS is not available. It is an important topic in the autonomous mobile robot research. This paper presents an Adaptive Decentralized Cooperative Vision-based SLAM solution for multiple UGVs, using the Adaptive Covariance Intersection (ACI) supported by a stereo vision sensor.
❱❖▲❯▼❊✿ ✷ | ■❙❙❯❊✿ ✸ | ✷✵✶✽ | ❙❡♣t❡♠❜❡r ❈♦♦♣❡r❛t✐✈❡ ❱✐s✉❛❧ ❙▲❆▼ ❆❧❣♦r✐t❤♠ ❜❛s❡❞ ♦♥ ❆❞❛♣t✐✈❡ ❈♦✈❛r✐❛♥❝❡ ■♥t❡rs❡❝t✐♦♥ ❋❡t❤✐ ❉❊▼■▼ 1,∗ ✱ ❆❜❞❡❧❦r✐♠ ◆❊▼❘❆ ❆❜❞❡❧❣❤❛♥✐ ❇❖❯❈❍❊▲❖❯❑❍ ✱ ❑❛❤✐♥❛ ▲❖❯❆❉❏ ✱ ▼✉st❛♣❤❛ ❍❆▼❊❘▲❆■◆ ❆❜❞❡❧♦✉❛❤❛❜ ❇❆❩❖❯▲❆ ✱ ✱ ▲❛❜♦r❛t♦✐r❡ ❱❡❤✐❝✉❧❡s ❆✉t♦♥♦♠❡s ■♥t❡❧❧✐❣❡♥ts✱ ❊❝♦❧❡ ▼✐❧✐t❛✐r❡ P♦❧②t❡❝❤♥✐q✉❡✱ ❊▼P✱ ❇♦r❞❥ ❊❧ ❇❛❤r✐✱ ❆❧❣✐❡rs✱ ❆❧❣❡r✐❛✳ ▲❛❜♦r❛t♦✐r❡ ❞✬■♥❢♦r♠❛t✐q✉❡ ❞❡ ▼❛t❤❡♠❛t✐q✉❡s ❡t ❞❡ P❤②s✐q✉❡ ♣♦✉r ❆❣r✐❝✉❧t✉r❡ ❡t ❧❡s ❋♦r❡ts✱ ▲■▼P❆❋✱ ❯♥✐✈❡rs✐t❡ ❞❡ ❇♦✉✐r❛✱ ❆❧❣❡r✐❛✳ ◆❛t✐♦♥❛❧ P♦❧②t❡❝❤♥✐❝ ❙❝❤♦♦❧✱ ❊◆P✱ ❊❧ ❍❛rr❛❝❤✱ ❆❧❣✐❡rs✱ ❆❧❣❡r✐❛✳ ❈❡♥t❡r ❢♦r ❉❡✈❡❧♦♣♠❡♥t ♦❢ ❆❞✈❛♥❝❡❞ ❚❡❝❤♥♦❧♦❣✐❡s✱ ❈❉❚❆✱ ❇❛❜❛ ❍❛ss❡♥✱ ❆❧❣✐❡rs✱ ❆❧❣❡r✐❛✳ ✯❈♦rr❡s♣♦♥❞✐♥❣ ❆✉t❤♦r✿ ❋❡t❤✐ ❉❊▼■▼ ✭❡♠❛✐❧✿ ❞❡♠✐❢❡t❤✐❅❣♠❛✐❧✳❝♦♠✮ ✭❘❡❝❡✐✈❡❞✿ ✵✽✲▼❛r❝❤✲✷✵✶✽❀ ❛❝❝❡♣t❡❞✿ ✶✷✲❖❝t✲✷✵✶✽❀ ♣✉❜❧✐s❤❡❞✿ ✸✶✲❖❝t✲✷✵✶✽✮ ❉❖■✿ ❤tt♣✿✴✴❞①✳❞♦✐✳♦r❣✴✶✵✳✷✺✵✼✸✴❥❛❡❝✳✷✵✶✽✷✸✳✾✶ ❙✐♠✉❧t❛♥❡♦✉s ❧♦❝❛❧✐③❛t✐♦♥ ❛♥❞ ♠❛♣✲ ♣✐♥❣ ✭❙▲❆▼✮ ✐s ❛♥ ❡ss❡♥t✐❛❧ ❝❛♣❛❜✐❧✐t② ❢♦r ❯♥✲ ♠❛♥♥❡❞ ●r♦✉♥❞ ❱❡❤✐❝❧❡s ✭❯●❱s✮ tr❛✈❡❧❧✐♥❣ ✐♥ ✉♥❦♥♦✇♥ ❡♥✈✐r♦♥♠❡♥ts ✇❤❡r❡ ❣❧♦❜❛❧❧② ❛❝❝✉r❛t❡ ♣♦s✐t✐♦♥ ❞❛t❛ ❛s ●P❙ ✐s ♥♦t ❛✈❛✐❧❛❜❧❡✳ ■t ✐s ❛♥ ✐♠♣♦rt❛♥t t♦♣✐❝ ✐♥ t❤❡ ❛✉t♦♥♦♠♦✉s ♠♦❜✐❧❡ r♦❜♦t r❡s❡❛r❝❤✳ ❚❤✐s ♣❛♣❡r ♣r❡s❡♥ts ❛♥ ❆❞❛♣t✐✈❡ ❉❡✲ ❝❡♥tr❛❧✐③❡❞ ❈♦♦♣❡r❛t✐✈❡ ❱✐s✐♦♥✲❜❛s❡❞ ❙▲❆▼ s♦✲ ❧✉t✐♦♥ ❢♦r ♠✉❧t✐♣❧❡ ❯●❱s✱ ✉s✐♥❣ t❤❡ ❆❞❛♣t✐✈❡ ❈♦✈❛r✐❛♥❝❡ ■♥t❡rs❡❝t✐♦♥ ✭❆❈■✮ s✉♣♣♦rt❡❞ ❜② ❛ st❡r❡♦ ✈✐s✐♦♥ s❡♥s♦r✳ ■♥ r❡❝❡♥t ②❡❛rs✱ ❙▲❆▼ ♣r♦❜❧❡♠ ❤❛s ❣♦tt❡♥ ❛ s♣❡❝✐✜❝ ❝♦♥s✐❞❡r❛t✐♦♥✱ t❤❡ ♠♦st ❝♦♠♠♦♥❧② ✉s❡❞ ❛♣♣r♦❛❝❤❡s ❛r❡ t❤❡ ❊❑❋✲ ❙▲❆▼ ❛❧❣♦r✐t❤♠ ❛♥❞ t❤❡ ❋❆❙❚✲❙▲❆▼ ❛❧❣♦✲ r✐t❤♠✳ ❚❤❡ ♣r✐♠❛r②✱ ✇❤✐❝❤ r❡q✉✐r❡s ❛♥ ❛❝❝✉✲ r❛t❡ ♣r♦❝❡ss ❛♥❞ ❛♥ ♦❜s❡r✈❛t✐♦♥ ♠♦❞❡❧✱ s✉✛❡rs ❢r♦♠ t❤❡ ❧✐♥❡❛r✐③❛t✐♦♥ ♣r♦❜❧❡♠✳ ❚❤❡ ❧❛st ♠❡♥✲ t✐♦♥❡❞ ✐s ♥♦t s✉✐t❛❜❧❡ ❢♦r r❡❛❧✲t✐♠❡ ✐♠♣❧❡♠❡♥t❛✲ t✐♦♥✳ ■♥ ♦✉r ✇♦r❦✱ t❤❡ ❱✐s✉❛❧ ❙▲❆▼ ✭❱❙▲❆▼✮ ♣r♦❜❧❡♠ ❝♦✉❧❞ ❜❡ s♦❧✈❡❞ ❜❛s❡❞ ♦♥ t❤❡ ❙♠♦♦t❤ ❱❛r✐❛❜❧❡ ❙tr✉❝t✉r❡ ❋✐❧t❡r ✭❙❱❙❋✮ ✐s ♣r♦♣♦s❡❞✳ ❚❤✐s ♥❡✇ ✜❧t❡r ✐s r♦❜✉st ❛♥❞ st❛❜❧❡ t♦ ♠♦❞❡❧❧✐♥❣ ✉♥❝❡rt❛✐♥t✐❡s ♠❛❦✐♥❣ ✐t s✉✐t❛❜❧❡ ❢♦r ❯●❱ ❧♦❝❛❧✲ ✐③❛t✐♦♥ ❛♥❞ ♠❛♣♣✐♥❣ ♣r♦❜❧❡♠✳ ❚❤✐s ♥❡✇ str❛t✲ ❡❣② r❡t❛✐♥s t❤❡ ♥❡❛r ♦♣t✐♠❛❧ ♣❡r❢♦r♠❛♥❝❡ ♦❢ t❤❡ ❙❱❙❋ ✇❤❡♥ ❛♣♣❧✐❡❞ t♦ ❛♥ ✉♥❝❡rt❛✐♥ s②st❡♠✱ ✐t ❤❛s t❤❡ ❛❞❞❡❞ ❜❡♥❡✜t ♦❢ ♣r❡s❡♥t✐♥❣ ❛ ❝♦♥s✐❞❡r✲ ❆❜str❛❝t✳ ❛❜❧❡ ✐♠♣r♦✈❡♠❡♥t ✐♥ t❤❡ r♦❜✉st♥❡ss ♦❢ t❤❡ ❡s✲ t✐♠❛t✐♦♥ ♣r♦❝❡ss✳ ❆❧❧ ❯●❱s ✇✐❧❧ ❛❞❞ ❞❛t❛ ❢❡❛✲ t✉r❡s s♦rt❡❞ ❜② t❤❡ ❆❈■ t❤❛t ❡st✐♠❛t❡ ♣♦s✐t✐♦♥ ♦♥ t❤❡ ❣❧♦❜❛❧ ♠❛♣✳ ❚❤✐s s♦❧✉t✐♦♥ ❣✐✈❡s✱ ❛s ❛ r❡✲ s✉❧t✱ ❛ ❧❛r❣❡ r❡❧✐❛❜❧❡ ♠❛♣ ❝♦♥str✉❝t❡❞ ❜② ❛ ❣r♦✉♣ ♦❢ ❯●❱s ♣❧♦tt❡❞ ♦♥ ✐t✳ ❚❤✐s ♣❛♣❡r ♣r❡s❡♥ts ❛ ❈♦♦♣❡r❛t✐✈❡ ❙❱❙❋✲❱❙▲❆▼ ❛❧❣♦r✐t❤♠ t❤❛t ❝♦♥✲ tr✐❜✉t❡s t♦ s♦❧✈❡ t❤❡ ❆❞❛♣t✐✈❡ ❈♦♦♣❡r❛t✐✈❡ ❱✐s✐♦♥ ❙▲❆▼ ♣r♦❜❧❡♠ ❢♦r ♠✉❧t✐♣❧❡ ❯●❱s✳ ❚❤❡ ❛❧❣♦✲ r✐t❤♠ ✇❛s ✐♠♣❧❡♠❡♥t❡❞ ♦♥ t❤r❡❡ ♠♦❜✐❧❡ r♦❜♦ts P✐♦♥❡❡r ✸✲❆❚✱ ✉s✐♥❣ st❡r❡♦ ✈✐s✐♦♥ s❡♥s♦rs✳ ❙✐♠✲ ✉❧❛t✐♦♥ r❡s✉❧ts s❤♦✇ ❡✣❝✐❡♥❝② ❛♥❞ ❣✐✈❡ ❛♥ ❛❞✲ ✈❛♥t❛❣❡ t♦ ♦✉r ♣r♦♣♦s❡❞ ❛❧❣♦r✐t❤♠✱ ❝♦♠♣❛r❡❞ t♦ t❤❡ ❈♦♦♣❡r❛t✐✈❡ ❊❑❋✲❱❙▲❆▼ ❛❧❣♦r✐t❤♠ ♠❛✐♥❧② ❝♦♥❝❡r♥✐♥❣ t❤❡ ♥♦✐s❡ q✉❛❧✐t②✳ ❑❡②✇♦r❞s ▲♦❝❛❧✐③❛t✐♦♥✱ ▼❛♣ ❇✉✐❧❞✐♥❣✱ ❆✉t♦♥♦♠♦✉s ◆❛✈✐❣❛t✐♦♥✱ ❉❛t❛ ❙❡♥s♦r ❋✉s✐♦♥✱ ▼♦❜✐❧❡ ❘♦❜♦t✳ ❝ ✷✵✶✼ ❏♦✉r♥❛❧ ♦❢ ❆❞✈❛♥❝❡❞ ❊♥❣✐♥❡❡r✐♥❣ ❛♥❞ ❈♦♠♣✉t❛t✐♦♥ ✭❏❆❊❈✮ ✶✺✶ ❱❖▲❯▼❊✿ ✷ ✶✳ ■♥tr♦❞✉❝t✐♦♥ ■♥ t❤❡ ❧❛st ❢❡✇ ②❡❛rs✱ t❤❡ s✐♠✉❧t❛♥❡♦✉s ❧♦❝❛❧✐③❛✲ t✐♦♥ ❛♥❞ ♠❛♣♣✐♥❣ ✭❙▲❆▼✮ ❜❡❝❛♠❡ ❛♥ ✐♠♣♦r✲ t❛♥t t♦♣✐❝ ♦❢ r❡s❡❛r❝❤ ✐♥ t❤❡ r♦❜♦t✐❝s ❝♦♠♠✉✲ ♥✐t②✳ ❆❝❝✉r❛t❡ ♥❛✈✐❣❛t✐♦♥ ❝❛♥ ❜❡ ❛❝❤✐❡✈❡❞ ❜② ❛❝❝✉r❛t❡ ❧♦❝❛❧✐③❛t✐♦♥ ✇✐t❤✐♥ ❛♥ ❛❝❝✉r❛t❡ ♠❛♣✳ ❙▲❆▼ ✐s t❤❡ ♣r♦❝❡ss t❤❛t ❡♥❛❜❧❡s ❛ ♠♦❜✐❧❡ r♦❜♦t t♦ ❧♦❝❛❧✐③❡ ❛♥❞ ❜✉✐❧❞ ❛ ♠❛♣ ♦❢ ❛♥ ✉♥❦♥♦✇♥ ❡♥✈✐✲ r♦♥♠❡♥t ✉s✐♥❣ ♦♥❧② ♦❜s❡r✈❛t✐♦♥s r❡❧❛t✐✈❡ t♦ t❤❡ ♠♦st r❡❧❡✈❛♥t ❢❡❛t✉r❡s ❞❡t❡❝t❡❞ ❜② ✐ts s❡♥s♦rs✳ ❚❤❡ ❜❡❛✉t② ♦❢ t❤❡ ❑❛❧♠❛♥ ❋✐❧t❡r ✭❑❋✮ ❝♦♠❡s ❢r♦♠ t❤❡ ❢❛❝t t❤❛t t❤❡② ❡st✐♠❛t❡ ❛ ❢✉❧❧② ❝♦r✲ r❡❧❛t❡❞ ♣♦st❡r✐♦r ♦✈❡r ❢❡❛t✉r❡ ♠❛♣s ❛♥❞ r♦❜♦t ♣♦s❡s✳ ❚❤❡✐r ✇❡❛❦♥❡ss ❧✐❡s ✐♥ t❤❡ str♦♥❣ ❛ss✉♠♣✲ t✐♦♥s t❤❛t ❤❛✈❡ t♦ ❜❡ ♠❛❞❡ ♦♥ ❜♦t❤ t❤❡ r♦❜♦t ♠♦t✐♦♥ ♠♦❞❡❧ ❛♥❞ t❤❡ s❡♥s♦r ♥♦✐s❡✳ ■♥ ❛❞❞✐t✐♦♥✱ t❤❡ ❊❑❋✲❙▲❆▼ ❛❧❣♦r✐t❤♠ ♦♥❧② ✇♦r❦s ✇✐t❤ ❢❡❛✲ t✉r❡ ♠❛♣s✳ ❆♥❞ ✐t ✐s ♥♦t ❛❧✇❛②s ❡❛s② t♦ ❞❡✜♥❡ ❛♥❞ ❡①tr❛❝t ❢❡❛t✉r❡s ✐♥ ✉♥str✉❝t✉r❡❞ ❛♥❞ ♦✉t✲ ❞♦♦r ❡♥✈✐r♦♥♠❡♥ts✳ ❚❤❡ ❊❑❋ ❛♣♣r♦①✐♠❛t❡s t❤❡ ❙▲❆▼ ♣♦st❡r✐♦r ❛s ❛ ❤✐❣❤✲❞✐♠❡♥s✐♦♥❛❧ ●❛✉ss✐❛♥ ♦✈❡r❛❧❧ ❢❡❛t✉r❡ ✐♥ t❤❡ ♠❛♣ ❛♥❞ t❤❡ r♦❜♦t ♣♦s❡✳ ❚❤❡ s✐♥❣❧❡ ❤②♣♦t❤❡s✐s ❛♥❞ q✉❛❞r❛t✐❝ ❝♦♠♣❧❡①✲ ✐t② ❞✉❡ t♦ t❤❡ ❤✐❣❤ ❞✐♠❡♥s✐♦♥❛❧ ●❛✉ss✐❛♥ ❛♣✲ ♣r♦①✐♠❛t✐♦♥s ❢♦r st❛t❡s ♦❢ t❤❡ r♦❜♦t ❛♥❞ ❧❛♥❞✲ ♠❛r❦s ❧♦❝❛t✐♦♥s ♠❛❦❡s t❤❡ ♦✛✲❞✐❛❣♦♥❛❧ ❡❧❡♠❡♥ts ♦❢ t❤❡ ❝♦✈❛r✐❛♥❝❡ ♠❛tr✐① ✈❡r② ❧❛r❣❡✳ ❚❤✐s ❝❛✉s❡s ♠♦r❡ ❝♦♠♣❧❡①✐t② ❛♥❞ ❝♦st ✐♥❝r❡❛s❡ ♦❢ ❝♦♠♣✉t❛✲ t✐♦♥ ❛♥❞✱ ✐♥ ♠♦st ❝❛s❡s✱ ❞✐✈❡r❣❡s t❤❡ ✜❧t❡r ❬✶✵❪✳ ■♥ ❛❞❞✐t✐♦♥✱ t❤❡ ❊❑❋ ❝♦✈❛r✐❛♥❝❡ ♠❛tr✐❝❡s ❛r❡ q✉❛❞r❛t✐❝ ✐♥ t❤❡ s✐③❡ ♦❢ t❤❡ ♠❛♣✱ ❛♥❞ ✉♣❞❛t✲ ✐♥❣ t❤❡♠ r❡q✉✐r❡s t✐♠❡ q✉❛❞r❛t✐❝ ✐♥ t❤❡ ♥✉♠✲ ❜❡r ♦❢ ❧❛♥❞♠❛r❦s ❬✶✷❪✳ ▼♦r❡♦✈❡r✱ ✇❤❡♥ ❛ ❧❛r❣❡ ♥✉♠❜❡r ♦❢ ❧❛♥❞♠❛r❦s ❛r❡ ♣r❡s❡♥t ✐♥ t❤❡ ❡♥✈✐✲ r♦♥♠❡♥t✱ t❤❡ ❝♦♠♣✉t❛t✐♦♥ ❜❡❝♦♠❡s ❛❧♠♦st ✐♠✲ ♣♦ss✐❜❧❡✳ ◗✉❛❞r❛t✐❝ ❝♦♠♣❧❡①✐t② ✐s ❛ ❝♦♥s❡q✉❡♥❝❡ ♦❢ t❤❡ ●❛✉ss✐❛♥ r❡♣r❡s❡♥t❛t✐♦♥ ❡♠♣❧♦②❡❞ ❜② t❤❡ ❊❑❋✳ ❚❤❡r❡ ✐s ❛♥♦t❤❡r t②♣❡ ♦❢ ✜❧t❡r st❛rt❡❞ t♦ r✐s❡ ❛♥❞ t❛❦❡ ♣❧❛❝❡ ✐♥ ❡st✐♠❛t✐♦♥ ✉t✐❧✐③✐♥❣ t❤❡ ♣r✐♥❝✐✲ ♣❧❡s ♦❢ t❤❡ ❯♥s❝❡♥t❡❞ ❑❛❧♠❛♥ ❋✐❧t❡r ✭❯❑❋✮ ✉s❡s ❛ ✉♥✐q✉❡ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ❛ ●❛✉ss✐❛♥ r❛♥❞♦♠ ✈❛r✐❛❜❧❡ ✐♥ N ❞✐♠❡♥s✐♦♥s ✉s✐♥❣ 2N + s❛♠♣❧❡s✱ ❝❛❧❧❡❞ s✐❣♠❛ ♣♦✐♥ts✳ ❚❤❡ r❡♣r❡s❡♥t❛t✐♦♥ ✉t✐❧✐③❡s t❤❡ ♣r♦♣❡rt✐❡s ♦❢ t❤❡ ♠❛tr✐① sq✉❛r❡ r♦♦t ❛♥❞ t❤❡ ❝♦✈❛r✐❛♥❝❡ ❞❡✜♥✐t✐♦♥s t♦ s❡❧❡❝t t❤❡s❡ ♣♦✐♥ts ✐♥ s✉❝❤ ❛ ✇❛② t❤❛t t❤❡② ❤❛✈❡ t❤❡ s❛♠❡ ❝♦✈❛r✐❛♥❝❡ ❛s t❤❡ ●❛✉ss✐❛♥ t❤❡② ❛♣♣r♦①✐♠❛t❡ ❬✷✵❪✳ ❚❤❡ ❯❑❋✲❙▲❆▼ r❡s✉❧ts ❝♦♠♣❛r❛❜❧❡ t♦ ❛ t❤✐r❞✲♦r❞❡r ✶✺✷ | ■❙❙❯❊✿ ✸ | ✷✵✶✽ | ❙❡♣t❡♠❜❡r ❚❛②❧♦r s❡r✐❡s ❡①♣❛♥s✐♦♥ ♦❢ t❤❡ st❛t❡✲♠♦❞❡❧✱ ✇❤✐❧❡ ❊❑❋ ❛r❡ ♦♥❧② ❛❝❝✉r❛t❡ t♦ ❛ ✜rst✲♦r❞❡r ❧✐♥❡❛r✐③❛✲ t✐♦♥✳ ❚❤❡ ❯♥s❝❡♥t❡❞ tr❛♥s❢♦r♠ ❛♣♣r♦❛❝❤ ❛❧s♦ ❤❛s ❛♥♦t❤❡r ❛❞✈❛♥t❛❣❡✿ ♥♦✐s❡ ❝❛♥ ❜❡ tr❡❛t❡❞ ✐♥ ❛ ♥♦♥❧✐♥❡❛r ❢❛s❤✐♦♥ t♦ ❛❝❝♦✉♥t ❢♦r ♥♦♥✲●❛✉ss✐❛♥ ♦r ♥♦♥✲❛❞❞✐t✐✈❡ ♥♦✐s❡s✳ ❚❤❡ ❯❑❋ s✉✛❡rs ❧❡ss ❢r♦♠ ❧✐♥❡❛r✐③❛t✐♦♥✱ t❤♦✉❣❤ ✐t ✐s ♥♦t ❡①❡♠♣t✳ ❚❤❡ ❯❑❋ ❞♦❡s ♥♦t ❢✉❧❧② r❡❝♦✈❡r ❢r♦♠ ♣♦♦r ❧❛♥❞♠❛r❦s✱ ✐s t❤❡ s❛♠❡ ❛s ✐♥ t❤❡ ❊❑❋ ❝❛s❡✳ ❋❛st✲❙▲❆▼ ✐s ❛♥ ❛❧❣♦r✐t❤♠ ✇❤✐❝❤ ✉s❡s t❤❡ ♠✉❧t✐✲❤②♣♦t❤❡s✐s ❞❛t❛ ❛ss♦❝✐❛t✐♦♥ ❛♥❞ ❧♦❣❛r✐t❤✲ ♠✐❝ ❝♦♠♣❧❡①✐t② ✐♥st❡❛❞ ♦❢ q✉❛❞r❛t✐❝✳ ❚❤✐s ❛♣✲ ♣r♦❛❝❤✱ ❦♥♦✇♥ ❛s ❋❛st✲❙▲❆▼ ✉t✐❧✐③❡s ❘❛♦✲❇❧❛❝❦ ✇❡❧❧✐s❡❞ ♣❛rt✐❝❧❡ ✜❧t❡r t♦ s♦❧✈❡ t❤❡ ❙▲❆▼ ♣r♦❜✲ ❧❡♠ ❡✣❝✐❡♥t❧②✳ ❯s✐♥❣ ❋❛st✲❙▲❆▼ ❛❧❣♦r✐t❤♠✱ t❤❡ ♣♦st❡r✐♦r ❡st✐♠❛t✐♦♥ ✇✐❧❧ ❜❡ ♦✈❡r t❤❡ r♦❜♦t✬s ♣♦s❡ ❛♥❞ ❧❛♥❞♠❛r❦s ❧♦❝❛t✐♦♥s ❬✶✶❪✳ ❚❤❡ ❋❛st✲ ❙▲❆▼ ❛❧❣♦r✐t❤♠ ❤❛s ❜❡❡♥ ✐♠♣❧❡♠❡♥t❡❞ s✉❝❝❡ss✲ ❢✉❧❧② ♦✈❡r t❤♦✉s❛♥❞s ♦❢ ❧❛♥❞♠❛r❦s ❛♥❞ ❝♦♠♣❛r❡ t♦ ❊❑❋✲❙▲❆▼ t❤❛t ❝❛♥ ♦♥❧② ❤❛♥❞❧❡ ❛ ❢❡✇ ❤✉♥✲ ❞r❡❞s ♦❢ ❧❛♥❞♠❛r❦s✱ ✐t ❤❛s ❛♣♣❡❛r❡❞ ✇✐t❤ ❝♦♥✲ s✐❞❡r❛❜❧❡ ❛❞✈❛♥t❛❣❡s ❬✾✱ ✶✶❪✳ ❚❤❡ ❋❛st✲❙▲❆▼ s❤❛r❡s t❤❡ ❢❛♥❝② ♣r♦♣❡rt② ✇✐t❤ ❑❋ ❛♣♣r♦❛❝❤ ✇❤❡♥ ✐t ♠❛✐♥t❛✐♥s t❤❡ ❢✉❧❧ ♣♦st❡r✐♦r ❜✉t ✐s ♠✉❝❤ ❢❛st❡r ❝♦♠♣❛r❡❞ t♦ t❤❡ ❝❧❛ss✐❝❛❧ ❑❋✲❙▲❆▼✳ ■t ❝❛♥ ❜❡ ❛♣♣❧✐❡❞ ❢♦r ❢❡❛t✉r❡✲❜❛s❡❞ ❛♥❞ ❣r✐❞✲❜❛s❡❞ ♠❛♣♣✐♥❣ s♦ t❤❛t ✐t ✐s ❛❧s♦ s✉✐t❛❜❧❡ ❢♦r ♦✉t❞♦♦r ❛♣♣❧✐❝❛t✐♦♥s✳ ■♥ ♣r❛❝t✐❝❡✱ ❢♦r ❛♣♣❧✐❝❛t✐♦♥s ✇❤❡r❡ ❛ ❝♦♥s✐st❡♥t ❣❧♦❜❛❧ ♠❛♣ ✐s r❡q✉✐r❡❞ ❛♥❞ ❛ r❡❛❧✲ t✐♠❡ ♣❡r❢♦r♠❛♥❝❡ ✐s ♥♦t ♥❡❝❡ss❛r② ✭❢♦r ❡①❛♠♣❧❡ t❤❡ ❛♣♣❧✐❝❛t✐♦♥s ❢♦❝✉s✐♥❣ ♦♥ ❝♦♥str✉❝t✐♥❣ ❛❝❝✉✲ r❛t❡ ♠❛♣s✮✱ ❋❛st✲❙▲❆▼ ✐s ❛ ❜❡tt❡r ❝❤♦✐❝❡✳ ❍♦✇✲ ❡✈❡r✱ ❢♦r ❛♣♣❧✐❝❛t✐♦♥s ✇❤❡r❡ ♦♥❧② ❛♥ ✐♥st❛♥t❛✲ ♥❡♦✉s ♠❛♣ ✐s r❡q✉✐r❡❞ ✭♦❜st❛❝❧❡ ❛✈♦✐❞❛♥❝❡ ❛♣♣❧✐✲ ❝❛t✐♦♥s✮✳ ❚❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ ❛ ♥❡✇ ❛❧❣♦r✐t❤♠ ❜❛s❡❞ ♦♥ t❤❡ ❙♠♦♦t❤ ❱❛r✐❛❜❧❡ ❙tr✉❝t✉r❡ ❋✐❧t❡r ✭❙❱❙❋✮ ✐s ♣r♦♣♦s❡❞ ❢♦r st❛t❡ ❛♥❞ ♣❛r❛♠❡t❡r ❡s✲ t✐♠❛t✐♦♥ ✇❤✐❝❤ ✐s r♦❜✉st ❛♥❞ st❛❜❧❡ t♦ ♠♦❞✲ ❡❧❧✐♥❣ ✉♥❝❡rt❛✐♥t✐❡s ♠❛❦✐♥❣ ✐t s✉✐t❛❜❧❡ ❢♦r ❆✉✲ t♦♥♦♠♦✉s ❯♥♠❛♥♥❡❞ ❱❡❤✐❝❧❡ ❧♦❝❛❧✐③❛t✐♦♥ ❛♥❞ ♠❛♣♣✐♥❣ ♣r♦❜❧❡♠ ❬✶✹❪✲❬✶✾❪✳ ▼❛♥② ❛❧❣♦r✐t❤♠s ❡①✐st t♦❞❛② t♦ s♦❧✈❡ ❙▲❆▼ ♣r♦❜❧❡♠s ❢♦r t❤❡ s✐♥❣❧❡ ♠♦❜✐❧❡ r♦❜♦t✱ t❤❡r❡ ✐s st✐❧❧ ❛ ❝❤❛❧❧❡♥❣❡ t♦ ♣❡r❢♦r♠ ❝♦♦♣❡r❛t✐✈❡ ❙▲❆▼✱ ❡s♣❡✲ ❝✐❛❧❧② ✇✐t❤ ❛ r♦❜✉st ✜❧t❡r✳ ❈♦♦♣❡r❛t✐✈❡ ❙✐♠✉❧✲ t❛♥❡♦✉s ▲♦❝❛❧✐③❛t✐♦♥ ❛♥❞ ▼❛♣♣✐♥❣ ✭❈❙▲❆▼✮ st✉❞② r❡q✉✐r❡s t❤❡ ✉s❡ ♦❢ ♠✉❧t✐♣❧❡ ❛✉t♦♥♦♠♦✉s ❯●❱s ❬✶❪✳ ❚❤❡② s❤♦✇ ♠❛♥② ❛❞✈❛♥t❛❣❡s✱ ❛♠♦♥❣ t❤❡♠ ✇❡ ❤❛✈❡✿ ✐♥❝r❡❛s✐♥❣ t❤❡ ❡✣❝✐❡♥❝② ♦❢ t❤❡ ♦✈❡r❛❧❧ s②st❡♠✱ ❡①t❡♥❞✐♥❣ t❤❡ ❡rr♦r t♦❧❡r❛♥❝❡✱ ✐♠♣r♦✈✐♥❣ r❡❧✐❛❜✐❧✐t② ❛♥❞✴♦r ♣❡r❢♦r♠❛♥❝❡✱ r❛✲ ❝ ✷✵✶✼ ❏♦✉r♥❛❧ ♦❢ ❆❞✈❛♥❝❡❞ ❊♥❣✐♥❡❡r✐♥❣ ❛♥❞ ❈♦♠♣✉t❛t✐♦♥ ✭❏❆❊❈✮ ❱❖▲❯▼❊✿ ✷ ♣✐❞✐t②✱ ✢❡①✐❜✐❧✐t②✱ ❛♥❞ r❡❞✉❝t✐♦♥ ♦❢ ❝♦st✳ ❚❤❡ ✐♥t❡r❛❝t✐♦♥ ♦❢ ♥❛✈✐❣❛t✐♦♥❛❧ ❛♥❞ s❡♥s✐t✐✈✐t② ✐♥✲ ❢♦r♠❛t✐♦♥ ♣r♦✈✐❞❡s ❜❡tt❡r ❢❡❛t✉r❡s ♦❢ ❛ ❞❡✜♥❡❞ ❛r❡❛✳ ▼❛♥② st✉❞✐❡s✱ ❡①♣❡r✐♠❡♥ts ❛♥❞ r❡s❡❛r❝❤❡s ✇❡r❡ ♠❛❞❡ ❝♦✈❡r✐♥❣ t❤✐s t♦♣✐❝✳ ❋♦r ✐♥st❛♥❝❡✱ ❙t♦② ✐♥ ❬✷❪ ♣❡r❢♦r♠❡❞ s✐♠♣❧❡ r❡❧❛t✐✈❡ ❧♦❝❛❧✐③❛✲ t✐♦♥ ❜❡t✇❡❡♥ ❝♦❧❧❛❜♦r❛t♦rs✳ ■♥ ❬✸❪ ❛♥❞ ❬✹❪✱ r❡✲ s❡❛r❝❤ tr❡❛ts t❤❡ ♣r♦❜❧❡♠ ♦❢ ❈❙▲❆▼ ✇✐t❤ t❤❡ ❣r♦✇✐♥❣ ✉♥❝❡rt❛✐♥t✐❡s s✉♣♣♦rt❡❞ ❜② s✐♠✉❧❛t✐♦♥ ❛♥❞ ❡①♣❡r✐♠❡♥t❛❧ ✈❛❧✐❞❛t✐♦♥✳ ❆❧s♦✱ ❡♥tr♦♣② ♠✐♥✐♠✐③❛t✐♦♥ ❬✺❪✱ ❛♥❞ ✐♥❢♦r♠❛t✐♦♥ t❤❡♦r② ❜❛s❡❞ t❡❝❤♥✐q✉❡s ✇❡r❡ ❞❡✈❡❧♦♣❡❞ t♦ s♦❧✈❡ ❈♦♦♣❡r❛t✐✈❡ ❙▲❆▼ ♣r♦❜❧❡♠s ❬✻❪✳ ❚❤❡ ●P❙ ❞❡♥✐❡❞ ❡♥✈✐r♦♥♠❡♥t✱ t❤❡ ❡①♣❡♥s✐✈❡ ❝♦st ♦❢ s❡♥s♦rs❀ ❝♦♠♣✉t❛t✐♦♥❛❧ ❡✣❝✐❡♥❝②✱ s♦❢t✲ ✇❛r❡✴♥❡t✇♦r❦ ♣❡r❢♦r♠❛♥❝❡✱ ❛♥❞ ♠♦❞❡❧❧✐♥❣ ❡r✲ r♦rs ❛♥❞ ✉♥❝❡rt❛✐♥t✐❡s ❛r❡ ❝r✉❝✐❛❧ ❦❡② ♣♦✐♥ts ✐♥ s♦❧✈✐♥❣ ❈❙▲❆▼ ♣r♦❜❧❡♠✳ ❘❡s❡❛r❝❤ ✐s ❝♦♥s✐❞❡r✲ ✐♥❣ ❝♦♦♣❡r❛t✐✈❡ ❞❛t❛ ❢✉s✐♦♥✱ s❡♥s♦r ♠❛♣♣✐♥❣ ✐♥ ♠✉❧t✐♣❧❡ ✈❡❤✐❝❧❡s✱ ♥❛✈✐❣❛t✐♦♥ s❝❡♥❡ ❬✼❪✳ ■♥ ❬✽❪ ✇❡ ✜♥❞ t❤❡ ❊①t❡♥❞❡❞ ❑❛❧♠❛♥ ❋✐❧t❡r ❜❛s❡❞ s♦❧✉t✐♦♥ ❢♦r s♦♠❡ ❝♦♦♣❡r❛t✐✈❡ ❙▲❆▼ ❛♥❞ s♣❡❝✐✜❝❛❧❧② ❝♦✲ ♦♣❡r❛t✐✈❡ ✈✐s✉❛❧ ❙▲❆▼ ✐♥ ❬✾✱ ✶✵❪✳ ❆❧s♦ ✐♥ ❬✶✶✱ ✶✷❪ t❤❡ ❝♦♦♣❡r❛t✐✈❡ ❱✐s✉❛❧ ❙▲❆▼ tr❡❛t❡❞ ❜❛s❡❞ ♦♥ ♣❛rt✐❝❧❡ ✜❧t❡r ❡st✐♠❛t✐♦♥ s❝❤❡♠❡✳ ❚❤❡ ✇♦r❦ ♣r❡✲ s❡♥t❡❞ ✐♥ ❬✶✷❪ ✐s ❛ ♣❛rt ♦❢ r❡s❡❛r❝❤ ✇♦r❦ ❞♦♥❡ ♦♥ ❛✉t♦♥♦♠♦✉s ♥❛✈✐❣❛t✐♦♥ ❢♦r ▼✐❝r♦ ❆❡r✐❛❧ ❱❡❤✐❝❧❡ ✭▼❆❱✮✱ ✇✐t❤ ❙❱❙❋ ✜❧t❡r✳ ❚♦ s♦❧✈❡ ❙▲❆▼ ❢♦r ♠✉❧t✐♣❧❡ ❯●❱s✱ ✇❡ ❝❛♥ ❝♦♥s✐❞❡r t✇♦ ♠❛✐♥ ❢❛♠✲ ✐❧✐❡s ♦❢ s♦❧✉t✐♦♥s✿ ❈❡♥tr❛❧✐③❡❞ ❛r❝❤✐t❡❝t✉r❡ ❛♥❞ ❉❡❝❡♥tr❛❧✐③❡❞ ❛r❝❤✐t❡❝t✉r❡✳ ■♥ t❤✐s ♣❛♣❡r✱ ✇❡ ♣r❡s❡♥t❡❞ ❛ ❞❡✈❡❧♦♣♠❡♥t ♦❢ ❛ ♥❡✇ ♣r❡❞✐❝t♦r✲❝♦rr❡❝t♦r ❝❛❧❧❡❞ t❤❡ ❆❞❛♣✲ t✐✈❡ ❙♠♦♦t❤ ❱❛r✐❛❜❧❡ ❙tr✉❝t✉r❡ ❋✐❧t❡r ✭❆❙❱❙❋✮ ❜❛s❡❞ ♦♥ s❧✐❞✐♥❣ ♠♦❞❡❧ t❤❡♦r②✱ ✉s✐♥❣ ❝♦✈❛r✐❛♥❝❡ ♠❛tr✐❝❡s t♦ ❡✈❛❧✉❛t❡ t❤❡ ✉♥❝❡rt❛✐♥t② ♦❢ t❤❡ ❡st✐✲ ♠❛t✐♦♥ ✇✐t❤ ♦♣t✐♠❛❧ ❛❞❛♣t✐✈❡ s♠♦♦t❤✐♥❣ ❜♦✉♥❞✲ ❛r② ❧❛②❡r ✈❡❝t♦r t♦ s♦❧✈❡ t❤❡ ✈✐s✉❛❧ ❙▲❆▼ Pr♦❜✲ ❧❡♠ ❬✷✾✱ ✸✵❪✳ ■t ♣r❡s❡♥ts st❛❜❧❡ ❛♥❞ r♦❜✉st ❢❛❝✉❧✲ t✐❡s ✐♥ ♠♦❞❡❧❧✐♥❣ ✉♥❝❡rt❛✐♥t✐❡s ❬✶✸✱ ✶✹❪✱ ✇❤✐❝❤ ✐s s✉✐t❛❜❧❡ ❢♦r t❤❡ ❧♦❝❛❧✐③❛t✐♦♥ ❛♥❞ ♠❛♣♣✐♥❣ ♣r♦❜✲ ❧❡♠ ♦❢ ❛ ❝♦♦♣❡r❛t✐✈❡ ❯●❱s✳ ❚❤❡ ❛❞❛♣t✐✈❡ ❙❱❙❋ ✐s ❛ r♦❜✉st r❡❝✉rs✐✈❡ ❡st✐♠❛t✐♦♥ ♠❡t❤♦❞ t❤❛t ❞❡❛❧s ❡✣❝✐❡♥t❧② ✇✐t❤ ✐♥✐t✐❛❧ ❝♦♥❞✐t✐♦♥s ❛♥❞ ♠♦❞✲ ❡❧❧✐♥❣ ❡rr♦rs ♦❢ t❤❡ ♦❞♦♠❡t❡r✴st❡r❡♦ ✈✐s✐♦♥ s②s✲ t❡♠✳ Pr❡✈✐♦✉s st✉❞✐❡s ✉t✐❧✐③❡❞ s✐♥❣❧❡ ❝❛♠❡r❛ ❛s t❤❡ ❜❡st s♦❧✉t✐♦♥ ❢♦r ❙▲❆▼ ♣r♦❜❧❡♠✱ ✉s✲ ✐♥❣ ❙❱❙❋ ✜❧t❡r✱ ❜✉t ✐♥ t❤✐s ♣❛♣❡r✱ ♠✉❧t✐♣❧❡ ❯●❱s s②st❡♠ ❜❛s❡❞ ♦♥ t❤❡ ❆❞❛♣t✐✈❡ ❉❡❝❡♥tr❛❧✲ ✐③❡❞ ❈♦♦♣❡r❛t✐✈❡ ❛r❝❤✐t❡❝t✉r❡ ✐s ❝♦♥s✐❞❡r❡❞ ✉s✲ ✐♥❣ ❛ st❡r❡♦ ✈✐s✐♦♥ s❡♥s♦r ❬✷✽❪✲❬✸✶❪✳ ❚❤❡ s✉❝✲ | ■❙❙❯❊✿ ✸ | ✷✵✶✽ | ❙❡♣t❡♠❜❡r ❝❡ss ♦❢ t❤✐s ❛♣♣❧✐❝❛t✐♦♥ ❞❡♣❡♥❞s ❤✐❣❤❧② ♦♥ t❤❡ ❛❝❝✉r❛❝② ❛♥❞ r♦❜✉st♥❡ss ♦❢ t❤❡ str❛t❡❣② ♦❢ t❤❡ ❙♠♦♦t❤ ❱❛r✐❛❜❧❡ ❙tr✉❝t✉r❡ ❋✐❧t❡r ❙▲❆▼ ✐♠♣❧❡✲ ♠❡♥t❛t✐♦♥✳ ❚❤❡ ✇♦r❦ ♣r❡s❡♥t❡❞ ✐♥ t❤✐s ♣❛♣❡r ✐s ♦r❣❛♥✐③❡❞ ❛s ❢♦❧❧♦✇s✿ ❙❡❝t✐♦♥ ✷ ✐❧❧✉str❛t❡s t❤❡ ♣r♦❝❡ss ♠♦❞❡❧s ♦❢ ❯●❱ ❛♥❞ st❡r❡♦ ✈✐s✐♦♥ s❡♥s♦r✳ ❙❡❝t✐♦♥ ✸ ❞❡s❝r✐❜❡s t❤❡ ❙❱❙❋✲❙▲❆▼ ❛❧❣♦r✐t❤♠ ❛♥❞ t❤❡ ❆❞❛♣t✐✈❡ ❙❱❙❋✲❙▲❆▼ ❛❧❣♦r✐t❤♠ ✐♥ ❞❡✲ t❛✐❧s✳ ❚❤❡ ❝♦♦♣❡r❛t✐✈❡ ❙▲❆▼ ♦❢ ♠✉❧t✐♣❧❡ ❯●❱s ✇✐t❤ ❞❡❝❡♥tr❛❧✐③❡❞ ❛r❝❤✐t❡❝t✉r❡ ✐s ❞❡s❝r✐❜❡❞ ✐♥ ❙❡❝t✐♦♥ ✹✳ ❙✐♠✉❧❛t✐♦♥ ❛♥❞ ❞✐s❝✉ss✐♦♥ ❛r❡ ♣r❡✲ s❡♥t❡❞ ✐♥ ❙❡❝t✐♦♥ ✺ ❛♥❞ ❝♦♥❝❧✉❞✐♥❣ ✐♥ ❙❡❝t✐♦♥ ✻✳ ✷✳ Pr♦❝❡ss ♠♦❞❡❧s ❖❋ ❯●❱ ❛♥❞ st❡r❡♦ ✈✐s✐♦♥ s❡♥s♦r ✷✳✶✳ Pr♦❝❡ss ♠♦❞❡❧ ❚❤❡ ❯●❱ ✉s❡❞ ✐♥ ♦✉r ✇♦r❦ ✐s t❤❡ P✐♦♥❡❡r P✸✲ ❆❚✳ ❚❤❡ P✸✲❆❚ ✐s ❛ ♥♦♥✲❤♦❧♦♥♦♠✐❝ r♦❜♦t ✇✐t❤ ❢♦✉r ✇❤❡❡❧s ❬✷✸❪✳ ❆❝❝♦r❞✐♥❣ t♦ ❬✶✺❪✱ ✇✐t❤ t❤✐s ❝♦♥tr♦❧ ✐♥♣✉t ❛♥❞ t❤❡ ❧♦❝❛t✐♦♥ ♦❢ t❤❡ r♦❜♦t ❛t t❤❡ ♣r❡✈✐♦✉s t✐♠❡ st❡♣✱ ✇❡ ❝❛♥ ❡st✐♠❛t❡ t❤❡ r♦❜♦t ❝✉rr❡♥t ❧♦❝❛t✐♦♥ ❜② Xr,k+1 Xr,k + ∆T vk cos(θr,k ) Yr,k+1 = Yr,k + ∆T vk sin(θr,k ) θr,k + ∆T wk θr,k+1 εxr + εyr ✭✶✮ εθr ❚❤❡ r♦❜♦t ❡✈♦❧✉t✐♦♥ ♠♦❞❡❧ r❡✢❡❝ts t❤❡ r❡❧❛t✐♦♥✲ s❤✐♣ ❜❡t✇❡❡♥ t❤❡ r♦❜♦t ♣r❡✈✐♦✉s st❛t❡s XR,k ❛♥❞ ✐ts ❝✉rr❡♥t st❛t❡ XR,k+1 ✳ ■♥ ❙▲❆▼✱ t❤❡ s②st❡♠ st❛t❡ ✈❡❝t♦r ❤❛s ❛ ♣♦s✐t✐♦♥ ♦❢ t❤❡ ❯●❱ (XR ) ■t ✐s r❡♣r❡s❡♥t❡❞ ❜② XR = [Xr , Yr , θr ]T ∈ R3 , ❛♥❞ ✇❡ ❝❛❧❧ ❛ ❝♦❧❧❡❝t✐♦♥ ♦❢ M ❢❡❛t✉r❡s ❛ ♠❛♣ s✉❝❤ t❤❛t L = [L1 , , LM ]T ∈ R3M ✱ ∆T ✐s t❤❡ s❛♠♣❧❡ ♣❡r✐♦❞✱ εxr ,yr ,θr ❛r❡ t❤❡ ♥♦✐s❡ t❤❛t ❛r✐s❡ ❢r♦♠ t❤❡ ❡♥❝♦❞❡r ❛♥❞ ✇❤❡❡❧s s❧✐♣♣✐♥❣✱ ❡t❝✳ ■♥ t❤✐s ✇♦r❦✱ ✇❡ ✇✐❧❧ ✉s❡ ❛ ♣♦✐♥t ❢❡❛t✉r❡ s✉❝❤ t❤❛t ❢♦r t❤❡ ith ❢❡❛t✉r❡✿ Li = [xi , yi , zi]T ✳ ❲❤❡r❡ x, y ❛♥❞ z ❛r❡ t❤❡ ❝♦♦r❞✐♥❛t❡s ♦❢ t❤❡ ♣♦✐♥t ✐♥ ❛ ❣❧♦❜❛❧ ❢r❛♠❡ ♦❢ r❡❢❡r❡♥❝❡✳ ❲❡ ❝❛♥ ✇r✐t❡ ❡q✉❛t✐♦♥ ✶ ❛s ❢♦❧❧♦✇ ❝ ✷✵✶✼ ❏♦✉r♥❛❧ ♦❢ ❆❞✈❛♥❝❡❞ ❊♥❣✐♥❡❡r✐♥❣ ❛♥❞ ❈♦♠♣✉t❛t✐♦♥ ✭❏❆❊❈✮ ✶✺✸ ❱❖▲❯▼❊✿ ✷ XR,k+1 = f (XR,k , Uk , k) + εxr ,yr ,θr ✷✳✷✳ ✭✷✮ | ■❙❙❯❊✿ ✸ | ✷✵✶✽ | ❙❡♣t❡♠❜❡r ❛♥❞ t❤❡ r♦❜♦t ❝♦♥✜❣✉r❛t✐♦♥ R = (xr , yr , 0)T ✐s ❝❛❧❧❡❞ t❤❡ ❞✐r❡❝t ♠♦❞❡❧ ♦❜s❡r✈❛t✐♦♥ ❛♥❞ ✇✐❧❧ ❜❡ ♥♦t❡❞ ❬✶✻❪ ❙t❡r❡♦ ✈✐s✐♦♥ s❡♥s♦r ♠♦❞❡❧ Z = h(R, Lg ) + εx,y,z g Lx − xr εx Z = MGR Lgy − yr + εy εz Lgz − ✭✸✮ ❚❤❡ ♣❡rs♣❡❝t✐✈❡ ❝❛♠❡r❛ ♠♦❞❡❧ ✐♥❝❧✉❞❡s ✐♥tr✐♥s✐❝ ✭✹✮ ❛♥❞ ❡①tr✐♥s✐❝ ♣❛r❛♠❡t❡rs✳ ❚❤✐s ♠♦❞❡❧ ❡♥s✉r❡s t❤❡ ❣❡♦♠❡tr✐❝ tr❛♥s❢♦r♠❛t✐♦♥ ❜❡t✇❡❡♥ ❝❛♠✲ ❡r❛✴✐♠❛❣❡ ❛♥❞ ✇♦r❧❞✴❝❛♠❡r❛ r❡❢❡r❡♥❝❡ ❢r❛♠❡s ✇❤❡r❡ t❤❡ ❣❧♦❜❛❧ t♦ t❤❡ r♦❜♦t ♣r♦❥❡❝t✐♦♥ ♠❛tr✐① r❡s♣❡❝t✐✈❡❧② ❬✷✷❪✳ MGR ✐s ❞❡♥♦t❡❞ ❜② (cos(θr ) sin(θr ) • ❖❜s❡r✈❛t✐♦♥ P♦✐♥t ❜❛s❡❞ ▼♦❞❡❧ MGR = −sin(θr ) cos(θr ) ✭✺✮ 0 ❛♥❞ εx,y,z ♣r❡s❡♥ts t❤❡ ♠❡❛s✉r❡♠❡♥t ♥♦✐s❡✳ ■♥ ♦r❞❡r t♦ ♣❡r❢♦r♠ t❤❡ ❙▲❆▼✱ t❤❡ r♦❜♦t ♥❡❡❞s t♦ ❜❡ ❛❜❧❡ t♦ s❡❧❡❝t ❛♥❞ tr❛❝❦ t❤❡ ❧❛♥❞♠❛r❦s • ■♥✈❡rs❡ ♦❜s❡r✈❛t✐♦♥ P♦✐♥t ❜❛s❡❞ ✐♥ ✐ts ❡♥✈✐r♦♥♠❡♥t t♦ ❧♦❝❛❧✐③❡ ✐ts❡❧❢✳ ■♥ t❤✐s ▼♦❞❡❧ ♣❛♣❡r✱ ✇❡ ♦♣t ❢♦r ❛ ♣♦✐♥t ❧❛♥❞♠❛r❦ ✐♥ 3D s♣❛❝❡✳ ❚♦ ❝♦♠♣✉t❡ t❤❡ r❡❧❛t✐✈❡ ♠❡❛s✉r❡♠❡♥t ♦❢ t❤❡ ❧❛♥❞♠❛r❦s ♦❜t❛✐♥❡❞ ❢r♦♠ t❤❡ ✐♠❛❣❡s ❛❝q✉✐r❡❞ ❚❤❡ ♥❡✇ ♦❜s❡r✈❡❞ ❧❛♥❞♠❛r❦ ♠✉st ❜❡ ✐♥✐t✐❛❧✐③❡❞ ❢r♦♠ t❤❡ st❡r❡♦ ✈✐s✐♦♥ s❡♥s♦r ✭❋✐❣✳ ✶✮✳ ❋♦r t❤❡ s✐♠✉❧❛t✐♦♥ t❤❡ ❙❱❙❋ ✈✐s✉❛❧ ❙▲❆▼ ♣r❡✈✐♦✉s❧② t♦ ❜❡ ❛❞❞❡❞ t♦ t❤❡ st❛t❡ ✈❡❝t♦r ❬✶✼❪✳ ❚❤❡ ✐♥✐t✐❛❧✐③❛t✐♦♥ ♣r♦❝❡ss ✐s✱ ✐♥ ❢❛❝t✱ t❤❡ ❜❡st ❡st✐♠❛t✐♦♥ ♦❢ t❤❡ ❧❛♥❞♠❛r❦ ♣♦s✐t✐♦♥✱ ❛♥❞ ✐t ✐s ❛ ❢✉♥❞❛♠❡♥t❛❧ ♣♦✐♥t t♦ ❙▲❆▼ ✐♠♣❧❡♠❡♥t❛t✐♦♥✳ ❚❤❡ ♦❜s❡r✈❛t✐♦♥ ♠♦❞❡❧ st❛t❡❞ ✐♥ (4) ❣✐✈❡s t❤r❡❡ ❡q✉❛t✐♦♥s ❢♦r t❤r❡❡ ❞✐♠❡♥s✐♦♥ ✈❛r✐❛❜❧❡ Lg ✳ ❚❤❡ ✸❉ ❝♦♦r❞✐♥❛t❡s ♦❢ ❛ ♥❡✇ ❧❛♥❞♠❛r❦ (Lgx , Lgy , Lgz )T ✇✐t❤ r❡s♣❡❝t t♦ t❤❡ ❣❧♦❜❛❧ ❢r❛♠❡✇♦r❦ ❛r❡ ✐♥✐t✐❛❧✲ ✐③❡❞ ❜② s♦❧✈✐♥❣ (3) ❛s ❢♦❧❧♦✇s ❋✐❣✳ ✶✿ ❖❜s❡r✈❛t✐♦♥ s②st❡♠ ❣❡♦♠❡tr②✳ ✸✳ ❛❧❣♦r✐t❤♠✱ ✇❡ ✉s❡ t❤❡♦r❡t✐❝❛❧ ❞❛t❛ s❡ts ✭❛ s❡t ♦❢ ✸❉ ♣♦✐♥ts✮ ♣r❡✈✐♦✉s❧② ❣❡♥❡r❛t❡❞ ✐♥st❡❛❞ ♦❢ ✉s✐♥❣ r❡❛❧ ❞❛t❛✳ ❉✉r✐♥❣ t❤❡ r♦❜♦t ♠♦t✐♦♥✱ t❤❡ ♣♦✐♥t ❧❛♥❞♠❛r❦s ✐♥❝❧✉❞❡❞ ✐♥ t❤❡ ✈✐s✐♦♥ s❡♥s♦r ✜❡❧❞ ❛r❡ ❞❡t❡❝t❡❞ ✐♥ 3D s♣❛❝❡ ❬✶✻❪✳ ❆s s❛✐❞ ♣r❡✈✐♦✉s❧②✱ t❤❡ st❡r❡♦ ✈✐s✐♦♥ s❡♥s♦r ♣r♦✈✐❞❡s r❡❧❛t✐✈❡ ♠❡❛s✉r❡♠❡♥t Z = (Lrx , Lry , Lrz )T ♦❢ t❤❡ ❧❛♥❞♠❛r❦s ✇✐t❤ r❡s♣❡❝t t♦ t❤❡ r♦❜♦t ❢r❛♠❡✱ t❤✐s ♠❡❛s✉r❡♠❡♥t ✭♦❜s❡r✈❛t✐♦♥✮ ✇✐❧❧ ❜❡ ♥♦t❡❞ Z ✳ ❚❤❡ ♠♦❞❡❧ r❡♣r❡s❡♥t✐♥❣ t❤❡ r♦❜♦t ❢r❛♠❡ ❝♦♦r❞✐✲ ♥❛t❡s ♦❢ ❛♥ ✐♥❞✐✈✐❞✉❛❧ ❧❛♥❞♠❛r❦✱ ❛❝❝♦r❞✐♥❣ t♦ ✐ts ❣❧♦❜❛❧ ❢r❛♠❡ ❝♦♦r❞✐♥❛t❡s Lg = (Lgx , Lgy , Lgz )T ✶✺✹ Lg = h−1 (R, Z) ✭✻✮ Lg = (MGR )−1 Z + R ✭✼✮ ❱✐s✉❛❧ ❆❞❛♣t✐✈❡ ❙❱❙❋✲❙▲❆▼ ❛❧❣♦r✐t❤♠ ■♥ ✷✵✵✼✱ t❤❡ s♠♦♦t❤ ✈❛r✐❛❜❧❡ str✉❝t✉r❡ ✜❧t❡r ✇❛s ✐♥tr♦❞✉❝❡❞✳ ❚❤✐s ✜❧t❡r ✐s ❜❛s❡❞ ♦♥ t❤❡ s❧✐❞✐♥❣ ♠♦❞❡ ❝♦♥tr♦❧ ❛♥❞ ❡st✐♠❛t✐♦♥ t❡❝❤♥✐q✉❡s ❛♥❞ ✐s ❢♦r♠✉❧❛t❡❞ ✐♥ ❛ ♣r❡❞✐❝t♦r✲❝♦rr❡❝t♦r ❢❛s❤✐♦♥ ❬✶✺✱ ✶✽❪✳ ❚❤❡ ❡st✐♠❛t✐♦♥ ♣r♦❝❡ss ♠❛② ❜❡ s✉♠♠❛✲ r✐③❡❞ ❜② ✭✽✮ t♦ ✭✶✸✮✱ ❛♥❞ ✐s r❡♣❡❛t❡❞ ✐t❡r❛t✐✈❡❧②✳ ❆♥ ❛ ♣r✐♦r✐ st❛t❡ ❡st✐♠❛t❡ ✐s ❝❛❧❝✉❧❛t❡❞ ✉s✐♥❣ ❛♥ ❡st✐♠❛t❡❞ ♠♦❞❡❧ ♦❢ t❤❡ s②st❡♠ ❬✶✽✱ ✷✼❪✳ ❚❤❡ ❝♦rr❡❝t t❡r♠ ❝❛❧❝✉❧❛t❡❞ ✐♥ ✭✶✵✮ ✐s t❤❡♥ ✉s❡❞ ✐♥ ✭✶✸✮ t♦ ✜♥❞ t❤❡ ♣♦st❡r✐♦r✐ st❛t❡ ❡st✐♠❛t❡✳ ❚✇♦ ❝ ✷✵✶✼ ❏♦✉r♥❛❧ ♦❢ ❆❞✈❛♥❝❡❞ ❊♥❣✐♥❡❡r✐♥❣ ❛♥❞ ❈♦♠♣✉t❛t✐♦♥ ✭❏❆❊❈✮ ❱❖▲❯▼❊✿ ✷ | ■❙❙❯❊✿ ✸ | ✷✵✶✽ | ❙❡♣t❡♠❜❡r ❝r✐t✐❝❛❧ ✈❛r✐❛❜❧❡s ✐♥ t❤✐s ♣r♦❝❡ss ❛r❡ t❤❡ ♣r✐♦r✐ ❙▲❆▼ ✐s t❤❡ ♣r♦❜❧❡♠ ♦❢ ❝♦♥str✉❝t✐♥❣ ❛ ♠♦❞❡❧ ♦❢ ❛♥❞ ❛ ♣♦st❡r✐♦r✐ ♦✉t♣✉t ❡rr♦r ❡st✐♠❛t❡✱ ❞❡✜♥❡❞ t❤❡ ❡♥✈✐r♦♥♠❡♥t ❜❡✐♥❣ tr❛✈❡rs❡❞ ✇✐t❤ ♦♥ ❜♦❛r❞ ❜② ✭✶✶✮ ❛♥❞ ✭✶✷✮ r❡s♣❡❝t✐✈❡❧② ❬✶✽✱ ✷✺❪✳ s❡♥s♦rs✱ ✇❤✐❧❡ ❛t t❤❡ s❛♠❡ t✐♠❡ ♠❛✐♥t❛✐♥✐♥❣ ❛♥ ❡st✐♠❛t❡ ♦❢ t❤❡ ✈❡❤✐❝❧❡ ❧♦❝❛t✐♦♥ ✇✐t❤✐♥ t❤❡ ˆ k+1 = f (X ˆ k , Uk ) X ✭✽✮ ♠♦❞❡❧ ❬✶✺✱ ✷✵❪✳ ❆s ❛♥ ❛❧t❡r♥❛t✐✈❡ ❛♣♣r♦❛❝❤✱ t❤❡r❡ ✐s ❛ ♥♦✈❡❧ ✜❧t❡r✱ ❦♥♦✇♥ ❛s t❤❡ ❆❞❛♣t✐✈❡ ˆk ) Zˆk+1 = h(X ✭✾✮ s♠♦♦t❤ ✈❛r✐❛❜❧❡ str✉❝t✉r❡ ✜❧t❡r ✭❆❙❱❙❋✮✳ ❚❤✐s ❚❤❡ ❣❛✐♥ ✐s ❝♦♠♣✉t❡❞ ✉s✐♥❣ t❤❡ ♣r✐♦r✐✱ t❤❡ ♣♦st❡✲ r❡s❡❛r❝❤ ❢♦❝✉s❡❞ ♦♥ ❛❞✈❛♥❝✐♥❣ t❤❡ ❞❡✈❡❧♦♣♠❡♥t r✐♦r✐ ♠❡❛s✉r❡♠❡♥t ❡rr♦r✱ t❤❡ s♠♦♦t❤✐♥❣ ❜♦✉♥❞✲ ❛♥❞ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ♦❢ t❤❡ ❆❞❛♣t✐✈❡ ❙❱❙❋✲ ❛r② ❧❛②❡r ✇✐❞t❤s ϕ ✱ ❝♦♥✈❡r❣❡♥❝❡ r❛t❡ γ ❛♥❞ ♠❡❛✲ ❱❙▲❆▼ ❛❧❣♦r✐t❤♠ ✉s✐♥❣ ♠❛tr✐① ❝♦✈❛r✐❛♥❝❡ t♦ ❡✈❛❧✉❛t❡ t❤❡ ✉♥❝❡rt❛✐♥t② ♦❢ ❡st✐♠❛t✐♥❣ ✇✐t❤ s✉r❡♠❡♥t ♠❛tr✐① Hk+1 ❛s ❢♦❧❧♦✇s ❬✶✺✱ ✷✻❪✿ ♦♣t✐♠❛❧ s♠♦♦t❤✐♥❣ ❜♦✉♥❞❛r② ❧❛②❡r ✈❡❝t♦r✳ SV SF ˆ + diag[(|ez ■♥ t❤✐s s❡❝t✐♦♥ ✇❡ ✐♥✈❡st✐❣❛t❡ t❤❡ ❆❙❱❙❋✲ Kk+1 =H | + γ|ezk/k |Abs ) k+1/k Abs k+1 ❱❙▲❆▼ ♣r♦♣♦s❡❞ ❛❧❣♦r✐t❤♠ ❛s ❛ ♥❡✇ ❛♣♣r♦❛❝❤✳ ◦ −1 −1 Sat(ϕ¯ ezk+1/k )][diag(ezk+1/k )] ❲❡ ✇✐❧❧ s❤♦✇ t❤❡ ♥♦♥❧✐♥❡❛r ❆❙❱❙❋ ✇❤✐❝❤ ✭✶✵✮ ✐s ♥❡❝❡ss❛r② t♦ s♦❧✈❡ ♦✉r ❯♥♠❛♥♥❡❞ ●r♦✉♥❞ ❱❡❤✐❝❧❡ ❙▲❆▼ ♣r♦❜❧❡♠✳ ✇❤❡r❡ ❚❤❡ ✐♥✐t✐❛❧ ❝♦♥❞✐t✐♦♥s ✉s❡❞ ❜② t❤❡ ❆❙❱❙❋✲ ❱❙▲❆▼ ❛❧❣♦r✐t❤♠ ✇❡r❡ t❤❡ s❛♠❡ ❛s t❤♦s❡ • ◦ r❡♣r❡s❡♥ts ✧❙❝❤✉r✧ ♠✉❧t✐♣❧✐❝❛t✐♦♥ ✉s❡❞ ❜② t❤❡ ❊❑❋✴❙❱❙❋✲❙▲❆▼ ❛❧❣♦r✐t❤♠✳ ❡❧❡♠❡♥t✲❜②✲❡❧❡♠❡♥t❀ ❚❤❡ ❆❞❛♣t✐✈❡ ❙❱❙❋✲❱❙▲❆▼ ❛❧❣♦r✐t❤♠ ❝❛♥ ❜❡ • + r❡❢❡rs t♦ t❤❡ ♣s❡✉❞♦ ✐♥✈❡rs❡ ♦❢ ❛ ♠❛tr✐①❀ ❞❡s❝r✐❜❡❞ ❛s ❢♦❧❧♦✇s✿ • Hk+1,j = hk+1,j (FX,i ) ✐s t❤❡ ❞❡r✐✈❛t✐✈❡ ♦❢ h ✇✐t❤ r❡s♣❡❝t t♦ t❤❡ st❛t❡ ✈❡❝t♦r Xk+1 ✱ ✇❡ ♥♦t❡ t❤❛t h ❞❡♣❡♥❞s ♦♥❧② ♦❢ t❤❡ r♦❜♦t ♣♦s❡ Rk+1 ❛♥❞ t❤❡ ❧♦❝❛t✐♦♥ ♦❢ t❤❡ ith ❧❛♥❞♠❛r❦✱ ✇❤❡r❡ i ✐s t❤❡ ✐♥❞❡① ♦❢ t❤❡ ♦❜s❡r✈❡❞ ❧❛♥❞✲ ♠❛r❦ ❛t t✐♠❡ k ❛♥❞ j ✐s t❤❡ ✐♥❞❡① ♦❢ ❛♥ ✐♥❞✐✈✐❞✉❛❧ ❧❛♥❞♠❛r❦ ♦❜s❡r✈❛t✐♦♥ ✐♥ hk+1,j ✳ FX,i ✐s ❝❛❧❝✉❧❛t❡❞ ✐♥ ❬✶✻❪✳ • ϕ¯−1 ✐s ❛ ❞✐❛❣♦♥❛❧ ♠❛tr✐① ❝♦♥str✉❝t❡❞ ❢r♦♠ t❤❡ s♠♦♦t❤✐♥❣ ❜♦✉♥❞❛r② ❧❛②❡r ✈❡❝t♦r ϕ✱ s✉❝❤ t❤❛t 1 0 ϕ1 ϕ¯−1 = [diag(ϕ)]−1 = ✳ ✳ ✳ ✱ 0 ϕM i ✇✐t❤ Mi r❡♣r❡s❡♥ts t❤❡ ♥✉♠❜❡r ♦❢ ♠❡❛s✉r❡✲ ♠❡♥ts✳ • Sat(ϕ¯−1 ezk+1 ) r❡♣r❡s❡♥ts t❤❡ s❛t✉r❛t✐♦♥ ❢✉♥❝t✐♦♥ ❬✷✸✱ ✷✽❪✳ ezk+1/k = Zk+1 − Zˆk+1/k ✭✶✶✮ ezk+1/k+1 = Zk+1 − Zˆk+1/k+1 ✭✶✷✮ ❚❤❡ ✉♣❞❛t❡ ♦❢ t❤❡ st❛t❡ ❡st✐♠❛t❡s ❝❛♥ ❜❡ ❝❛❧❝✉✲ ❧❛t❡❞ ❛s ❢♦❧❧♦✇s SV SF ˆ k+1/k+1 = X ˆ k+1/k + Kk+1 X eˆzk+1/k ✭✶✸✮ • ■♥✐t✐❛❧✐③❛t✐♦♥ ❚❤❡ ♣r♦❝❡ss ❡st✐♠❛t✐♦♥ ♥❡❡❞s t❤❡ ✐♥✐t✐❛❧✐③❛✲ ˆ t✐♦♥ ♦❢ t❤❡ ♦r✐❣✐♥❛❧ ♣♦s❡ X(0) ♦❢ t❤❡ ❝♦♦r✲ ❞✐♥❛t❡ s②st❡♠ ❛♥❞ ❝♦✈❛r✐❛♥❝❡ ♠❛tr✐① P (0)✳ ❚❤❡ ♣♦st❡r✐♦r✐ ♠❡❛s✉r❡♠❡♥t ❡rr♦r ✈❡❝t♦r eZ ❝❛♥ ❜❡ ✐s ✐♥✐t✐❛❧✐③❡❞ ❛r❜✐tr❛r② ✐♥ t❤❡ ❆❙❱❙❋✲ ❱❙▲❆▼ ❛❧❣♦r✐t❤♠✳ ¯ = [R ¯0, L ¯ f,0 , , L ¯ f,0 ]T ❛♥❞ X M0 Z M0 T Z1 eZ ] 0/0 = [e0 e0 ˆ ✇❤❡r❡ X(0) = [0, 0, 0]T ✐s t❤❡ ✐♥✐t✐❛❧ ♣♦s❡ ♦❢ t❤❡ ❯●❱✱ P0 ✐s t❤❡ ❝♦✈❛r✐❛♥❝❡ ♠❛tr✐① ❛♥❞ N0 ✐s t❤❡ ♥✉♠❜❡r ♦❢ ✐♥✐t✐❛❧ ❢❡❛t✉r❡✳ Zk = [Z1 , Z2 , , ZM ]T ❜❡ ❛ s❡t ♦❢ s②st❡♠ ♠❡❛s✉r❡♠❡♥ts✳ • Pr❡❞✐❝t✐♦♥ ❚❤❡ ♣r❡❞✐❝t✐♦♥ st❛❣❡ ✐s ❛ ♣r♦❝❡ss✱ ✇❤✐❝❤ ❞❡❛❧s ✇✐t❤ ✈❡❤✐❝❧❡ ♠♦t✐♦♥ ❜❛s❡❞ ♦♥ ✐♥✲ ❝r❡♠❡♥t❛❧ ❞❡❛❞ r❡❝❦♦♥✐♥❣ ❡st✐♠❛t❡s ❛♥❞ ✐♥❝r❡❛s❡s t❤❡ ✉♥❝❡rt❛✐♥t② ♦❢ t❤❡ ✈❡❤✐❝❧❡ ♣♦s❡ ❡st✐♠❛t❡✳ ❚❤❡ st❛t❡ ✈❡❝t♦r ✐s ❛✉❣♠❡♥t❡❞ ✇✐t❤ ❛ ❝♦♥tr♦❧ ✐♥♣✉t Uk ✳ ❲❡ ❝♦♥s✐❞❡r t❤❡ ❢♦❧❧♦✇✐♥❣ ♣r♦❝❡ss ❢♦r t❤❡ ❆❙❱❙❋ ❡st✐♠❛t✐♦♥ str❛t❡❣②✱ ❛s ❛♣♣❧✐❡❞ t♦ ❛ ♥♦♥❧✐♥❡❛r s②st❡♠✳ ❚❤❡ ♣r❡❞✐❝t❡❞ st❛t❡ ❡st✐♠❛t❡s Xk+1/k ❛♥❞ t❤❡ ♣r❡❞✐❝t❡❞ ❝♦✈❛r✐❛♥❝❡ ♠❛tr✐① Pk+1/k ❛r❡ ✜rst ❝❛❧❝✉❧❛t❡❞ ❛s ❢♦❧❧♦✇s✿ ❝ ✷✵✶✼ ❏♦✉r♥❛❧ ♦❢ ❆❞✈❛♥❝❡❞ ❊♥❣✐♥❡❡r✐♥❣ ❛♥❞ ❈♦♠♣✉t❛t✐♦♥ ✭❏❆❊❈✮ ✶✺✺ ❱❖▲❯▼❊✿ ✷ ˆk , U ˆk ) = f (Rk+1 , Lf,k+1 ) − Xk+1 = f (X i − Pk+1/k = ∇FX Pk/k ∇FX T + ∇FU Qk ∇FU T ✇❤❡r❡ ∇FX ❛♥❞ ∇FU ❜❡ t❤❡ ❏❛❝♦❜✐❛♥ ♠❛tr✐❝❡s ♦❢ f (.) ✇✐t❤ r❡s♣❡❝t t♦ Xk+1 ❡✈❛❧✉❛t❡❞ ❛t ❛♥ ❡❧s❡✇❤❡r❡ s♣❡❝✐✜❡❞ ♣♦✐♥t✱ ❞❡♥♦t❡❞ ❜② J1 ❛♥❞ ∇FX = ✳✳ ✳✳ ✳ ✳ ✳ ✱ ✳ ✳ ✳ ✳✳ ∇FU = J2 ✳✳ ✳ ✇❤❡r❡ PR ∈ R3∗3 ✱ PLf,k+1 ,R ∈ 03∗3 ✱ i PR,Lf,k+1 ∈ 03∗3 ❛♥❞ PLf,k+1 ∈ R3∗3 ✳ i i ❚❤❡ ❛rr❛② ✇✐❞t❤ ♦❢ t❤❡ ❜♦✉♥❞❛r② ❧❛②❡r 2∗2 ϕ¯opt ♠❛② ❜❡ ❝❛❧❝✉❧❛t❡❞ ❜② k+1 ∈ R opt ϕ ¯ − ϕ¯k+1 = (∇hk+1 Pk+1/k (∇hk+1 )T + Rk )(∇hk+1 ϕ ¯ (∇hk+1 )T )−1 [diag(|ˆ ezk+1,i |Abs + Pk+1/k γ|ˆ ezk,i |Abs )] ✇❤❡r❡ ˆ k+1/k ) ˆ k+1/k ) ∂h(X ∂h(X , ∂Lf,k+1 ] ∇hk+1 = [ ∂X R i ❯s❡ t❤❡ ϕ¯opt t♦ ❝❛❧❝✉❧❛t❡ ❙❱❙❋ ❣❛✐♥ ASV SF Kk+1 ∈ R6∗3 ASV SF − Kk+1 = + (Hk+1,j ) diag[(|ezk+1,i |Abs + −1 γ|ezk,i |Abs )◦ Sat((ϕ¯opt ) k+1 eˆzk+1,i )][diag(ˆ ezk+1,i )]−1 (Hk+1,j )+ = (FX,i )T (hk+1,j )+ ✿ ✉s❡❞ ✭✷✶✮ t♦ ❝❛❧❝✉❧❛t❡ (Hk+1,j )+ ◆♦t❡ t❤❛t t❤❡ ✇❤❡r❡ ∂f (.) ∂f (.) ∂f (.) [ ; ; ] ∂xr ∂yr ∂θr −vsin(θr )∆T = vcos(θr )∆T 0 cos(θr )∆T 0 J2 = [ ∂f∂v(.) ; ∂f∂w(.) ] = sin(θr )∆T ∆T J1 = Qk σv2 = σx2i 0 Rk • = σw yi2 ✶✺✻ ♠❛tr✐① hk+1,j = ˆ k+1/k ) ∂h(X Xk+1 ✐s t❤❡ ❏❛❝♦❜✐❛♥ ♦❢ ✇✐t❤ r❡s♣❡❝t t♦ Rk+1 ❛♥❞ Lf,k+1 ✳ i ASV SF ❚❤❡ ❣❛✐♥ ✈❡❝t♦r Kk+1 ✐s ✉s❡❞ t♦ ❢♦r✲ ♠✉❧❛t❡ ❛ ♣♦st❡r✐♦r✐ st❛t❡ ❡st✐♠❛t❡ ❛♥❞ t❤❡ ✉♣❞❛t❡ ♦❢ t❤❡ st❛t❡ ❡st✐♠❛t❡ ❝❛♥ ❜❡ ❝❛❧❝✉❧❛t❡❞ ❛s ❢♦❧❧♦✇s ˆ k+1/k+1 = X ˆ k+1/k + K ASV SF eˆz 10 − X k+1,i k+1 ❯♣❞❛t❡ Pk+1/k+1 ∈ R6∗6 11 − Pk+1/k+1 = (I6∗6 − ϕ ¯ ASV SF Kk+1 ∇hk+1 )Pk+1/k ASV SF (I6∗6 − Kk+1 ∇hk+1 )T + ASV SF ASV SF T Kk+1 Rk (Kk+1 ) ❚❤❡ ♣r✐♦r✐ ♠❡❛s✉r❡♠❡♥ts ❡rr♦r ✈❡❝t♦r ezk+1/k ∈ R3∗1 ♠❛② ❜❡ ❝❛❧❝✉❧❛t❡❞ ❜② ˆ k+1 , Lf,k+1 ) 12 − ezk+1,i = Zk+1,j − h(R i 13−❊♥❞ ✐❢ 14−❊♥❞ ❋♦r ˆ k+1/k+1 = X ˆ k+1/k ✱ 15 − X Pk+1/k+1 = Pk+1/k , 0 zi2 ❉❛t❛ ❛ss♦❝✐❛t✐♦♥ ❛♥❞ ✉♣❞❛t❡ ❚❤❡ ❢❡❛t✉r❡ ❛❧r❡❛❞② st♦r❡❞ ✐♥ t❤❡ ♠❛♣ ✐s ♦❜s❡r✈❡❞ ❜② ❛ ✈✐s✐♦♥ s❡♥s♦r ✇✐t❤ t❤❡ ♠❡❛s✉r❡♠❡♥t Zk+1 ✳ 3−❋♦r ❛❧❧ ❢❡❛t✉r❡s ♦❜s❡r✈❛t✐♦♥s Zk+1,j ˆ k+1 ) = h(R ˆ k+1 , Lf,k+1 ) − Zˆk+1,i = h(X i 5− ✐❢ t❤❡ t❤❡ ❧❛♥❞♠❛r❦ j ✐s s❡❡♥ ❜❡❢♦r❡ ✭❝♦rr❡s♣♦♥❞❡♥❝❡ ✐s ❢♦✉♥❞❡❞✮✳ ❚❤❡ ♣♦st❡r✐♦r✐ ♠❡❛s✉r❡♠❡♥ts ❡rr♦r ✈❡❝t♦r eˆzk+1,i ∈ R3∗1 ♠❛② ❜❡ ❝❛❧❝✉❧❛t❡❞ ❜② − eˆzk+1,i = Zk+1,j − Zˆk+1,i ϕ ¯ Pk+1/k ∈ R6∗6 ♠❛tr✐① t❤❛t ✐s ❡①tr❛❝t❡❞ ❢r♦♠ Pk+1/k ✐s ❝❛❧❝✉❧❛t❡❞ ❜② PR PLf,k+1 ,R ϕ ¯ i − Pk+1/k = PR,Lf,k+1 PLf,k+1 i | ■❙❙❯❊✿ ✸ | ✷✵✶✽ | ❙❡♣t❡♠❜❡r • ▼❛♣ ▼❛♥❛❣❡♠❡♥t ❆s t❤❡ ❡♥✈✐r♦♥♠❡♥t ✐s ❡①♣❧♦r❡❞✱ ♥❡✇ ❢❡❛t✉r❡s ❛r❡ ♦❜s❡r✈❡❞ ❛♥❞ s❤♦✉❧❞ ❜❡ ❛❞❞❡❞ t♦ t❤❡ st♦r❡❞ ♠❛♣✳ ■♥ t❤✐s ❝❛s❡✱ t❤❡ st❛t❡ ✈❡❝t♦r ❛♥❞ t❤❡ ♦✉t♣✉t ❡rr♦r ❡st✐♠❛t❡ ♠❛tr✐① ❛r❡ ❝❛❧❝✉❧❛t❡❞ ❢r♦♠ t❤❡ ♥❡✇ ♦❜s❡r✈❛t✐♦♥ ❬✷✶✱ ✷✸❪✳ i ❝ ✷✵✶✼ ❏♦✉r♥❛❧ ♦❢ ❆❞✈❛♥❝❡❞ ❊♥❣✐♥❡❡r✐♥❣ ❛♥❞ ❈♦♠♣✉t❛t✐♦♥ ✭❏❆❊❈✮ ❱❖▲❯▼❊✿ ✷ ✹✳ | ■❙❙❯❊✿ ✸ | ✷✵✶✽ | ❙❡♣t❡♠❜❡r ❉❡❝❡♥tr❛❧✐③❡❞ ❈♦♦♣❡r❛t✐✈❡ ❱✐s✉❛❧ ❙▲❆▼ ❈♦♠♠✉♥✐❝❛t✐♦♥ ✐s ❛ ❝❡♥tr❛❧ ✐ss✉❡ ❢♦r ♠✉❧t✐♣❧❡ ✈❡❤✐❝❧❡ s②st❡♠s ❜❡❝❛✉s❡ ✐t ❞❡t❡r♠✐♥❡s t❤❡ ♣♦s✲ s✐❜❧❡ ♠♦❞❡s ♦❢ ✐♥t❡r❛❝t✐♦♥ ❛♠♦♥❣ ✈❡❤✐❝❧❡s✱ ❛s ✇❡❧❧ ❛s t❤❡✐r ❛❜✐❧✐t② t♦ s✉❝❝❡ss❢✉❧❧② ❜✉✐❧❞ ❛ ✇♦r❧❞ ♠♦❞❡❧ ❬✷✵❪✳ ■t ✐s ❡①❝✐t✐♥❣ t♦ ❦♥♦✇ ❤♦✇ t❤❡ ♠✉❧✲ ❋✐❣✳ ✸✿ ❆❈■ ❉❡❝❡♥tr❛❧✐③❡❞ ❈♦♦♣❡r❛t✐✈❡ ❱❙▲❆▼ str❛t✲ ❡❣②✳ ❋✐❣✳ ✷✿ ❉❡❝❡♥tr❛❧✐③❡❞ ❈♦♦♣❡r❛t✐✈❡ ❙▲❆▼ ❛r❝❤✐t❡❝t✉r❡✳ t✐♣❧❡ ❯●❱s ❝❛♥ ❤❡❧♣ ❡❛❝❤ ♦t❤❡r t♦ s♦❧✈❡ t❤❡ ❈♦♦♣❡r❛t✐✈❡ ✈✐s✐♦♥ ❙▲❆▼ ♣r♦❜❧❡♠✳ ❋✐❣✉r❡ ✷ s❤♦✇s t❤❡ ❛r❝❤✐t❡❝t✉r❡ ♦❢ t❤❡ ❉❡❝❡♥tr❛❧✐③❡❞ ❈♦✲ ♦♣❡r❛t✐✈❡ ❙▲❆▼ ✭❉❈✲❙▲❆▼✮✳ ❊❛❝❤ ❯●❱ ✇❤❡♥ s❤❛r❡❞ ❢❡❛t✉r❡s ❛r❡ ♦❜s❡r✈❡❞ ✐♥ t❤❡✐r ♣♦s✐t✐♦♥s ❛♥❞ ✉♥❝❡rt❛✐♥t✐❡s ❛r❡ ✉♣❞❛t❡❞ ✉s✐♥❣ ❞✐str✐❜✉t❡❞ ❡st✐♠❛t✐♦♥✳ ❚❤❡ ♣r♦♣♦s❡❞ ❉❈✲❙▲❆▼ ✇✐❧❧ ❜❡ ♠❛✐♥❧② ❜❛s❡❞ ♦♥ t❤❡ t❤✐r❞ ❢♦r♠ ♦❢ ✐♥t❡r❛❝t✐♦♥ ✇❤✐❝❤ ✐s ✈✐❛ ❡①♣❧✐❝✐t ❝♦♠♠✉♥✐❝❛t✐♦♥✳ ❚❤❡ ♠♦st r❡str✐❝t✐✈❡ ❝♦♥str❛✐♥t ❢♦r ❡①♣❧✐❝✐t ❝♦♠♠✉♥✐❝❛✲ t✐♦♥ ✐s t❤❡ ❧✐♠✐t❡❞ ❛♠♦✉♥t ♦❢ ❞❛t❛ t♦ ❝♦♠♠✉✲ ♥✐❝❛t❡ ❜❡t✇❡❡♥ ❯●❱s✳ ❆s ❛ r❡s✉❧t✱ t❤❡ ❝♦❧✲ ❧❡❝t✐✈❡ ❞❛t❛ t♦ s❤❛r❡ s❤♦✉❧❞ ❜❡ s❡❧❡❝t❡❞ ❝❛r❡✲ ❢✉❧❧② ✐♥ ♦r❞❡r t♦ ♠❛①✐♠✐③❡ t❤❡ ❣❛✐♥ ✇✐t❤ ❛ ♠✐♥✲ ✐♠✉♠ ❝♦♠♠✉♥✐❝❛t✐♦♥ ❬✷✵❪✳ ❆ss✉♠❡ ✇❡ ❤❛✈❡ N ❯●❱s (U GV1 , U GV2 , , U GVN )✳ ❆t t = ti ❡❛❝❤ U GVi ♦❜s❡r✈❡s Mi ❢❡❛t✉r❡ f eati (xi , y i , z i )✳ ❖✉r str❛t❡❣② ✐s t❤❡♥ t♦ ❞❡t❡❝t ♣♦ss✐❜❧❡ s❤❛r❡❞ r❡❣✐♦♥ ✇❤✐❝❤ ✐s ❛s ❢♦❧❧♦✇s ✭❋✐❣✳ ✸✮✿ ❋♦r ❡❛❝❤ U GVi ✇❡ ❝❛❧❝✉❧❛t❡ t❤❡ ♠❡❛♥ (µi ) ❛♥❞ t❤❡ st❛♥❞❛r❞ ❞❡✈✐❛t✐♦♥ (σ i ) ♦❢ t❤❡ ♦❜s❡r✈❡❞ ❢❡❛t✉r❡s (f eati )✳ ❚❤❡♥✱ ❡❛❝❤ s❡t ♦❢ ♦❜s❡r✈❡❞ ❢❡❛t✉r❡s ✇✐❧❧ ❜❡ ❛♣✲ ♣r♦①✐♠❛t❡❞ ❜② ❛♥ ❡❧❧✐♣s♦✐❞ (ξ i ) ❝❡♥t❡r❡❞ ❛t (µi ) ✇✐t❤ ❛①❡s (σ i )✳ ❚❤❡r❡❢♦r❡ U GVi ❛♥❞ U GVj ✇✐❧❧ ❝♦♦♣❡r❛t❡ (Cooperation(i, j) = 1) ✐❢ ❛♥❞ ♦♥❧② ✐❢✿ ξ i ∩ ξ j = ∅ ❬✷✵❪✳ ❚❤❡ ♣r♦♣♦s❡❞ ❉❈✲❙▲❆▼ str❛t❡❣② ✐s ❞❡✜♥❡❞ ❛s ❢♦❧❧♦✇s✿ ❛ss✉♠❡ ✇❡ ❤❛✈❡ t❤r❡❡ ❯●❱s✭U GVi ✱ U GVj ❛♥❞ U GVk ) ♦❜s❡r✈✐♥❣ ❛ ♥✉♠❜❡r ♦❢ ❢❡❛t✉r❡s✭Ni ✱ Ni ❛♥❞ Nk ✮ r❡s♣❡❝✲ t✐✈❡❧②✳ ❊❛❝❤ ♦❜s❡r✈❡❞ ❢❡❛t✉r❡ ❤❛s ❛ ❞❡s❝r✐♣t✐♦♥ ♦r ❛♥ ✐♥❞❡①✳ ❚❤❡ ❆❞❛♣t✐✈❡ ❈♦✈❛r✐❛♥❝❡ ■♥t❡r✲ s❡❝t✐♦♥ ✭❆❈■✮ ❛♣♣r♦❛❝❤ ✐s ✉s❡❞ t♦ ❡st✐♠❛t❡ t❤❡ ♣♦s✐t✐♦♥ ❛♥❞ ❝♦✈❛r✐❛♥❝❡ ♦❢ s❤❛r❡❞ ❢❡❛t✉r❡s ❜❡❢♦r❡ ❛❞❞✐♥❣ t❤❡♠ t♦ t❤❡ ❣❧♦❜❛❧ ♠❛♣ ❬✷✵✱ ✷✹❪✳ ✺✳ ❙■▼❯▲❆❚■❖◆✱ ❊❳P❊❘■▼❊◆❚❙ ❆◆❉ ❉■❙❈❯❙❙■❖◆ ■♥ ♦r❞❡r t♦ ✈❡r✐❢② t❤❡ ❡✣❝✐❡♥❝② ♦❢ t❤❡ ❆❞❛♣✲ t✐✈❡ ❈♦♦♣❡r❛t✐✈❡ ❙❱❙❋✲❙▲❆▼ ❝♦♠♣❛r✐♥❣ ✇✐t❤ t❤❡ ❝♦♦♣❡r❛t✐✈❡ ❊❑❋✲❙▲❆▼✳ ❙✉♣♣♦s❡ t❤❛t t❤❡ ♦❜s❡r✈❛t✐♦♥ ♥♦✐s❡ ♦❜❡②s t❤❡ ♠✐①t✉r❡ ●❛✉ss ❞✐s✲ tr✐❜✉t✐♦♥ ❛s σx = σy = 10−3 ♠✱ σθ = 10−4 r❛❞✳ ❚❤❡ ❝♦♥✈❡r❣❡♥❝❡ r❛t❡ ♠❛tr✐① γ = diag(0.8, 0.8, 0.8) ❛♥❞ t❤❡ ✇✐❞t❤ ♦❢ t❤❡ s♠♦♦t❤✐♥❣ ❜♦✉♥❞❛r② ❧❛②❡r ✈❡❝t♦r ✉s❡❞ ✐s ϕ = [21; 21; 15]✳ ❚❤❡ s❛♠♣❧✐♥❣ r❛t❡s ✉s❡❞ ❢♦r ❡❛❝❤ ✜❧✲ t❡r ❛♥❞ s❡♥s♦rs ✉s❡❞ ✐♥ t❤✐s st✉❞② ❛r❡ ❛s ❢♦❧❧♦✇s fOdom = fCamera = fEKF = fSV SF = fASV SF = 10 ❍③✳ ❲❡ s✉♣♣♦s❡ t❤❛t t❤❡ ♦❜s❡r✈❛t✐♦♥ ♥♦✐s❡ ♦❜❡②s t❤❡ ♠✐①t✉r❡ ●❛✉ss ❞✐str✐❜✉t✐♦♥ ❛s ❬✶✻❪ εxr ,yr ,θr ∼ 0.5N (0, R1 ) + 0.5N (0, R2 ) ❛♥❞ t❤❡ ♠♦t✐♦♥ ♥♦✐s❡ ♦❜❡②s t❤❡ ●❛✉ss ❞✐str✐❜✉t✐♦♥ ❛s N (0, Qk )✱ ❝ ✷✵✶✼ ❏♦✉r♥❛❧ ♦❢ ❆❞✈❛♥❝❡❞ ❊♥❣✐♥❡❡r✐♥❣ ❛♥❞ ❈♦♠♣✉t❛t✐♦♥ ✭❏❆❊❈✮ ✶✺✼ ❱❖▲❯▼❊✿ ✷ ❋✐❣✳ ✹✿ ❱✐s✉❛❧ ❊❑❋✲❙▲❆▼ s✐♠✉❧❛t✐♦♥ r❡s✉❧ts ✇✐t❤ ❋✐❣✳ ✺✿ ❱✐s✉❛❧ ❆❙❱❙❋✲❙▲❆▼ s✐♠✉❧❛t✐♦♥ r❡s✉❧ts ✇✐t❤ ✇❤✐t❡ ❝❡♥t❡r❡❞ ●❛✉ss✐❛♥ ♥♦✐s❡✳ ✇❤✐t❡ ❝❡♥t❡r❡❞ ●❛✉ss✐❛♥ ♥♦✐s❡✳ 0.02 0 0.01 ❚❤❡ ❝♦♥✈❡r❣❡♥❝❡ diag(0.8, 0.8, 0.8) | ■❙❙❯❊✿ ✸ | ✷✵✶✽ | ❙❡♣t❡♠❜❡r Qk = • r❛t❡ ♠❛tr✐① γ = ❚❡st ✶ ✿ ✇✐t❤ ✇❤✐t❡ ❝❡♥t❡r❡❞ ●❛✉ss✐❛♥ ♥♦✐s❡ ■♥ t❤❡ ✜rst ❡①♣❡r✐♠❡♥t✱ ✇❡ ❛ss✉♠❡ ❛ ✇❤✐t❡ ❝❡♥t❡r❡❞ ●❛✉ss✐❛♥ ♥♦✐s❡✱ ❢♦r ♣r♦❝❡ss ❛♥❞ ♦❜s❡r✲ ✈❛t✐♦♥ ♠♦❞❡❧ ✇❤❡r❡ σv = 0.02 ♠✴s✱ σw = 0.01 r❛❞✴s✱ σx = 0.1 ♠✱ σy = 0.1 ♠ ❛♥❞ σz = 0.1 ♠✳ 0.02 Qk = Rk = 0.01 0 0.02 0.01 , ✇❤✐t❡ ❝❡♥t❡r❡❞ ●❛✉ss✐❛♥ ♥♦✐s❡ ✇❡ ❝❛♥ ♦❜s❡r✈❡ t❤❛t ❛t ♠❛♥② ❧♦♦♣ ❝❧♦s✐♥❣ ❛r❡ ❞❡t❡❝t❡❞ ✇❤❡♥ t❤❡ ❯●❱s ♦❜s❡r✈❡s t❤❡♠s❡❧✈❡s✱ ❛❧s♦ ✇❤❡♥ t❤❡ ❯●❱s ♦❜s❡r✈❡s ❢❡❛t✉r❡s ❛❧r❡❛❞② ♦❜s❡r✈❡❞ ♣r❡✈✐♦✉s❧②✳ 0 0.01 ❋✐❣✉r❡s ✹✱ ✺✱ ✻ ❛♥❞ ✼ ♣r❡s❡♥t t❤❡ r❡s✉❧ts ♦❢ ❛ ❝♦♠♣❛r✐s♦♥ ♦❢ t❤❡ ❡st✐♠❛t❡❞ ♣♦s✐t✐♦♥ ❛♥❞ ❡r✲ r♦rs ♦❢ t❤❡ ❯●❱s ❣✐✈❡♥ ❜② t❤❡ ❊❑❋✲❱❙▲❆▼ ❛♥❞ ❆❙❱❙❋✲❱❙▲❆▼✳ ❆s ❝❛♥ ❜❡ s❡❡♥ ❢r♦♠ t❤❡s❡ ✜❣✉r❡s ✇❤❡♥ t❤❡ ♣r♦❝❡ss ❛♥❞ ♦❜s❡r✈❛t✐♦♥ ♥♦✐s❡s ❛r❡ ❝❡♥t❡r❡❞ ✇❤✐t❡ ●❛✉ss✐❛♥ ♥♦✐s❡s t❤❡ ❝♦♦♣❡r❛✲ t✐✈❡ ❊❑❋✲❱❙▲❆▼ ♣❡r❢♦r♠s ♠✉❝❤ ❜❡tt❡r t❤❛♥ t❤❡ ❝♦♦♣❡r❛t✐✈❡ ❆❙❱❙❋✲❱❙▲❆▼✳ ❚❤❡ ❯●❱s ♣♦s❡s ❡rr♦rs ❛r❡ s❤♦✇♥ ✐♥ ❋✐❣✳ ✻✳ ❚❤✐s ✜❣✲ ✉r❡ ❝♦♥✜r♠s t❤❡ ♣r❡✈✐♦✉s ❝♦♥❝❧✉s✐♦♥✱ ❛♥❞ ✐t ✐s ❝❧❡❛r t❤❛t t❤❡ ❝♦♦♣❡r❛t✐✈❡ ❊❑❋✲❱❙▲❆▼ ❛❧❣♦✲ r✐t❤♠ r❡q✉✐r❡s ③❡r♦✲♠❡❛♥ ✇❤✐t❡ ♥♦✐s❡✱ ♦t❤❡r✇✐s❡✱ t❤❡ ❡rr♦rs ♣♦s❡ ❞❡❝r❡❛s❡ s✐❣♥✐✜❝❛♥t❧② ❢♦❧❧♦✇✐♥❣ x✱ y ❛♥❞ θ ❝♦♠♣❛r✐♥❣ t♦ ❝♦♦♣❡r❛t✐✈❡ ❆❙❱❙❋✲ ❱❙▲❆▼ ❛❧❣♦r✐t❤♠✳ ▼♦r❡♦✈❡r✱ ❢r♦♠ t❤❡ ❋✐❣✳ ✼✱ ✶✺✽ ❋✐❣✳ ✻✿ P♦s✐t✐♦♥ ❡rr♦rs ♦❢ ❝♦♦♣❡r❛t✐✈❡ ❱✐s✉❛❧ ❙▲❆▼ ✇✐t❤ • ❚❡st ✷ ✿ ✇✐t❤ ♥♦♥✲❝❡♥t❡r❡❞ ●❛✉ss✐❛♥ ♥♦✐s❡ ■♥ t❤✐s ❡①♣❡r✐♠❡♥t ✇❡ ❛ss✉♠❡ ❛ ✇❤✐t❡ ♥♦✐s❡ ✇✐t❤ ❜✐❛s✱ ❢♦r ♣r♦❝❡ss ❛♥❞ ♦❜s❡r✈❛t✐♦♥ ♠♦❞❡❧ ✇❤❡r❡ σv = 0.02 ♠✴s✱ σw = 0.01 r❛❞✴s✱ σx = 0.1 ♠✱ σy = σz = 0.1 ♠✳ 0.02 0 0.02 , 0.01 Rk = 0 0.01 0 0.01 Qk = ❝ ✷✵✶✼ ❏♦✉r♥❛❧ ♦❢ ❆❞✈❛♥❝❡❞ ❊♥❣✐♥❡❡r✐♥❣ ❛♥❞ ❈♦♠♣✉t❛t✐♦♥ ✭❏❆❊❈✮ ❱❖▲❯▼❊✿ ✷ ❋✐❣✳ ✼✿ ❘▼❙❊ ❘❡s✉❧ts ✇✐t❤ ✇❤✐t❡ ❝❡♥t❡r❡❞ ●❛✉ss✐❛♥ ❋✐❣✳ ✾✿ ❱✐s✉❛❧ ❆❙❱❙❋✲❙▲❆▼ s✐♠✉❧❛t✐♦♥ r❡s✉❧ts ✇✐t❤ ♥♦✐s❡✳ ❋✐❣✳ ✽✿ ❱✐s✉❛❧ ❊❑❋✲❙▲❆▼ s✐♠✉❧❛t✐♦♥ r❡s✉❧ts ✇✐t❤ ♥♦♥✲ ♥♦♥✲❝❡♥t❡r❡❞ ●❛✉ss✐❛♥ ♥♦✐s❡✳ ❋✐❣✳ ✶✵✿ P♦s✐t✐♦♥ ❡rr♦rs ♦❢ ❝♦♦♣❡r❛t✐✈❡ ❱✐s✉❛❧ ❙▲❆▼ ❝❡♥t❡r❡❞ ●❛✉ss✐❛♥ ♥♦✐s❡✳ ❋✐❣✉r❡s ✽ ❛♥❞ ✾ ♣r❡s❡♥t t❤❡ ♣♦s❡ ❡st✐♠❛t✐♦♥ ✉s✲ ✐♥❣ t❤❡ ❝♦♦♣❡r❛t✐✈❡ ❊❑❋✴❆❙❱❙❋✲❱❙▲❆▼ ✇✐t❤ ♥♦♥✲❝❡♥t❡r❡❞ ●❛✉ss✐❛♥ ♥♦✐s❡ ♦❢ t❤❡ ❯●❱s✳ ❆s s❤♦✇♥ ✐♥ ❋✐❣✉r❡s ✽✱ ✾✱ ✶✵ ❛♥❞ ✶✶✱ t❤❡ s✐❣♥✐✜❝❛♥t ❞❡❝r❡❛s❡ ♦❢ ♣❡r❢♦r♠❛♥❝❡ ♦❢ t❤❡ ❊❑❋✲❱❙▲❆▼ ❡s✲ t✐♠❛t♦r ✐s ♦❜s❡r✈❡❞ ✇❤❡♥ t❤❡ ♣r♦❝❡ss ❛♥❞ ♦❜✲ s❡r✈❛t✐♦♥ ♥♦✐s❡s ❛r❡ ♥♦♥✲❝❡♥t❡r❡❞✳ ■♥ t❤✐s ❝❛s❡✱ ❛s s❤♦✇♥ ✐♥ ❋✐❣✉r❡s ✽ ❛♥❞ ✾✱ t❤❡ ✈❛❧✉❡s ❡st✐✲ ♠❛t❡❞ ❜② t❤❡ ❈♦♦♣❡r❛t✐✈❡ ❆❙❱❙❋✲❱❙▲❆▼ ❛r❡ ❧❡ss ❛❝❝✉r❛t❡ t❤❛♥ t❤❡ ❝♦rr❡❝t❡❞ ✈❛❧✉❡s x✱ y ❛♥❞ θ✳ ❉❡❝❡♥tr❛❧✐③❡❞ ❈♦♦♣❡r❛t✐✈❡ ❙▲❆▼ ❜② ❆❙❱❙❋ s❤♦✇s ♠✉❝❤ ❜❡tt❡r ♥❛✈✐❣❛t✐♦♥ ❛♥❞ ♠❛♣♣✐♥❣ ♣❡r✲ ❢♦r♠❛♥❝❡s t❤❛♥ ❊❑❋✲❱❙▲❆▼ ❛♥❞ ♣r♦✈✐❞❡s ❛♥ ❛❝❝✉r❛t❡ ♣♦s✐t✐♦♥ ♦❢ t❤❡ ❯●❱s✳ ❋r♦♠ ❋✐❣✳ ✶✵✱ ✇❡ ❝❛♥ ♦❜s❡r✈❡ ❛ ❧♦♦♣ ❝❧♦s✐♥❣ ✐s ❞❡t❡❝t❡❞ ❛♥❞ t❤❡ ❯●❱s ♦❜s❡r✈❡ ❛ ❝♦♠♠♦♥ ❢❡❛t✉r❡✳ ❆t t❤✐s ♠♦✲ ♠❡♥t ✇❡ ♦❜s❡r✈❡ ❛ s✐❣♥✐✜❝❛♥t ✐♠♣r♦✈❡♠❡♥t ✐♥ t❤❡ ❛❝❝✉r❛❝② ♦❢ t❤❡ ❆❞❛♣t✐✈❡ ❙❱❙❋✲❱❙▲❆▼ ❛s ✇❡❧❧ ❛s t❤❡ ❊❑❋✲❱❙▲❆▼✳ ❚❤❡ ❙❱❙❋✲❙▲❆▼ ♣r♦✲ | ■❙❙❯❊✿ ✸ | ✷✵✶✽ | ❙❡♣t❡♠❜❡r ✇✐t❤ ♥♦♥✲❝❡♥t❡r❡❞ ●❛✉ss✐❛♥ ♥♦✐s❡✳ ✈✐❞❡s t❤❡ ❜❡st ❘▼❙❊ ✐♥ ❝♦♠♣❛r✐s♦♥ ✇✐t❤ t♦ t❤❡ ❊❑❋✲❙▲❆▼ ✇❤❡♥ ✇❡ ✉s❡ ♥♦♥✲❝❡♥t❡r❡❞ ●❛✉ss✐❛♥ ♥♦✐s❡ ❛s s❤♦✇♥ ✐♥ ❋✐❣✳ ✶✶✳ ■♥ t❤❡ r❡s✉❧ts ♦❢ t❤❡ ✜rst ❡①♣❡r✐♠❡♥t✱ ✐♥ t❤❡ ❝❛s❡ ♦❢ ✇❤✐t❡ ❝❡♥t❡r❡❞ ●❛✉ss✐❛♥ ♥♦✐s❡✱ t❤❡ ❊❑❋✲ ❙▲❆▼ ❛❧❣♦r✐t❤♠ ❣✐✈❡s t❤❡ ❜❡st r❡s✉❧ts ♣♦s✐✲ t✐♦♥ ❛♥❞ ✐s ♠♦r❡ ❛❝❝✉r❛t❡ t❤❛♥ t❤❡ ❛❞❛♣t✐✈❡ ❙❱❙❋✲❙▲❆▼ ❛❧❣♦r✐t❤♠✳ ❚❤✐s ❝❛♥ ❜❡ ✐♥t❡r♣r❡t❡❞ ❛s ❢♦❧❧♦✇s✿ t❤❡ s②st❡♠ ❛♥❞ ♦❜s❡r✈❛t✐♦♥ ♠♦❞✲ ❡❧s ❛r❡ ❛❝❝✉r❛t❡ ❜❡s✐❞❡s✱ ✇❤❡♥ t❤❡ ♣r♦❝❡ss ❛♥❞ ♦❜s❡r✈❛t✐♦♥ ♥♦✐s❡s ❛r❡ ✉♥❝♦rr❡❧❛t❡❞ ③❡r♦✲♠❡❛♥ ●❛✉ss✐❛♥ ✇✐t❤ ❦♥♦✇♥ ❝♦✈❛r✐❛♥❝❡ t❤❡♥ t❤❡ ❊❑❋ ❣✐✈❡s ❛ ❣♦♦❞ ❛❝❝✉r❛❝② ❢♦r ♣♦s✐t✐♦♥ ❡st✐♠❛t✐♦♥✳ ■t ♠❡❛♥s t❤❛t t❤❡ ❊❑❋✲❙▲❆▼ ❛❧❣♦r✐t❤♠ ❜❡✲ ❝♦♠❡s t❤❡ ♦♣t✐♠❛❧ ✜❧t❡r✳ ❍♦✇❡✈❡r✱ t❤❡ ❛❞❛♣✲ t✐✈❡ ❙❱❙❋✲❙▲❆▼ ♣r♦✈✐❞❡ ❛ ♠♦r❡ ❛❝❝✉r❛t❡ ❡st✐✲ ♠❛t❡ t❤❛♥ t❤❡ ❊❑❋✲❙▲❆▼ ✇❤❡♥ ✇❡ ✉s❡ ♥♦♥✲ ❝❡♥t❡r❡❞ ●❛✉ss✐❛♥ ♥♦✐s❡✳ ❚❤❡s❡ r❡s✉❧ts ❝❧❡❛r❧② ✈❛❧✐❞❛t❡ t❤❡ ❛❞✈❛♥t❛❣❡ ♦❢ t❤❡ ❛❞❛♣t✐✈❡ ❙❱❙❋✲ ❝ ✷✵✶✼ ❏♦✉r♥❛❧ ♦❢ ❆❞✈❛♥❝❡❞ ❊♥❣✐♥❡❡r✐♥❣ ❛♥❞ ❈♦♠♣✉t❛t✐♦♥ ✭❏❆❊❈✮ ✶✺✾ ❱❖▲❯▼❊✿ ✷ | ■❙❙❯❊✿ ✸ | ✷✵✶✽ | ❙❡♣t❡♠❜❡r ❘❡❢❡r❡♥❝❡s ❬✶❪ ❨❛♠❛s❤✐t❛✱ ❆✳✱ ❆r❛✐✱ ❚✳✱ ❖t❛✱ ❏✳✱ ✫ ❆s❛♠❛✱ ❍✳ ✭✷✵✵✸✮✳ ▼♦t✐♦♥ ♣❧❛♥♥✐♥❣ ♦❢ ♠✉❧t✐♣❧❡ ♠♦✲ ❜✐❧❡ r♦❜♦ts ❢♦r ❝♦♦♣❡r❛t✐✈❡ ♠❛♥✐♣✉❧❛t✐♦♥ ❛♥❞ tr❛♥s♣♦rt❛t✐♦♥✳ ■❊❊❊ ❚r❛♥s❛❝t✐♦♥s ♦♥ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♠❛t✐♦♥✱ ✶✾✱ ✷✷✸✲✷✸✼✳ ❬✷❪ ❙tø②✱ ❑✳ ✭✷✵✵✶✮✳ ❯s✐♥❣ ❙✐t✉❛t❡❞ ❈♦♠♠✉♥✐✲ ❝❛t✐♦♥ ✐♥ ❉✐str✐❜✉t❡❞ ❆✉t♦♥♦♠♦✉s ▼♦❜✐❧❡ ❘♦❜♦t✐❝s✳ ■♥ ❙❈❆■✱ ✶✱ ✹✹✲✺✷✳ ❋✐❣✳ ✶✶✿ ❘▼❙❊ ❘❡s✉❧ts ✇✐t❤ ♥♦♥✲❝❡♥t❡r❡❞ ●❛✉ss✐❛♥ ♥♦✐s❡✳ ❙▲❆▼ ♦✈❡r t❤❡ ❊❑❋✲❙▲❆▼ ❡s♣❡❝✐❛❧❧② ✇❤❡♥ t❤❡ s②st❡♠ ♦r ♦❜s❡r✈❛t✐♦♥ ♠♦❞❡❧s ❛r❡ ♥♦t ❛❝❝✉r❛t❡ ❡♥♦✉❣❤ ❛♥❞ t❤❡ ♣r♦❝❡ss ❛♥❞ ♦❜s❡r✈❛t✐♦♥ ♥♦✐s❡s ❛r❡ ♥♦♥✲❝❡♥t❡r❡❞ ●❛✉ss✐❛♥ ♥♦✐s❡✳ ✻✳ ❈♦♥❝❧✉s✐♦♥ ❚❤❡ ❛✐♠ ♦❢ t❤✐s ✇♦r❦ ✐s t♦ ❝♦♠❡ ✉♣ ✇✐t❤ t♦♦❧s t❤❛t ❛r❡ ❝❛♣❛❜❧❡ ♦❢ ♣r♦❞✉❝✐♥❣ ❛♥ ❛❝❝✉r❛t❡ ❛✉t♦♠❛t✐❝ ❧♦❝❛❧✐③❛t✐♦♥ ✇❤✐❝❤ ❝♦✉❧❞ ❜❡ ✉s❡❞ ✐♥ ❛♥ ❛❝❝✉r❛t❡ ♠❛♣ ♠❛♥❛❣❡♠❡♥t✳ ❯●❱s ❛r❡ ❛ ❝♦r❡ t♦♦❧ ✐♥ t❤✐s st✉❞②❀ ✇❡ ✇♦r❦❡❞ t♦ ✐♠♣r♦✈❡ t❤❡✐r ❛✉t♦♥♦♠② ❜② s♦❧✈✐♥❣ s♦♠❡ ♦❢ t❤❡✐r t❡❝❤✲ ♥✐❝❛❧ ♣r♦❜❧❡♠s✳ ❲❡ ♠❛❞❡ ❛♥ ✐♥✈❡st✐❣❛t✐♦♥ ♦❢ t❤❡ ❯●❱s ❧♦❝❛❧✐③❛t✐♦♥✱ ✐❧❧✉str❛t❡❞ ❯●❱s ♠❛♣ ❜✉✐❧❞✐♥❣✱ ❛♥❞ ✐♠♣❧❡♠❡♥t❡❞ ❛ s✐♠✉❧t❛♥❡♦✉s ❧♦❝❛❧✲ ✐③❛t✐♦♥ ❛♥❞ ♠❛♣♣✐♥❣ s♦❧✉t✐♦♥ ✉s✐♥❣ st❡r❡♦ ✈✐s✐♦♥ s❡♥s♦rs ❜② t✇♦ ❛❧❣♦r✐t❤♠s✱ ❈♦♦♣❡r❛t✐✈❡ ❊❑❋✲ ❱❙▲❆▼ ❛♥❞ ❈♦♦♣❡r❛t✐✈❡ ❆❙❱❙❋✲❱❙▲❆▼✳ ❚❤❡ ♣r♦♣♦s❡❞ s♦❧✉t✐♦♥ ✐s ❡①t❡♥❞❡❞ t♦ t❤❡ ❉❡❝❡♥tr❛❧✐③❡❞ ❈♦♦♣❡r❛t✐✈❡ ❱✐s✐♦♥ ❙▲❆▼✳ ❖✉r ♣r♦♣♦s❛❧ ✐s ❛ ♥❡✇ s♦❧✉t✐♦♥ ❢♦r ❆❞❛♣t✐✈❡ ❉❡❝❡♥✲ tr❛❧✐③❡❞ ❈♦♦♣❡r❛t✐✈❡ ❙❱❙❋✲❙▲❆▼ ❢♦r ♠✉❧t✐♣❧❡ ❯●❱s ✇✐t❤ st❡r❡♦ ✈✐s✐♦♥ s❡♥s♦rs✳ ❚❤❡ ❛❞♦♣t❡❞ ❛♣♣r♦❛❝❤ ✐s t❡st❡❞ ✇✐t❤ ❞✐✛❡r❡♥t s❝❡♥❛r✐♦s✳ ❆❢t❡r ✈❛❧✐❞❛t✐♦♥ ♦❢ t❤❡ ♣r♦♣♦s❡❞ ❛❧❣♦r✐t❤♠s ✇✐t❤ s✐♠✉❧❛t✐♦♥ ♦♥ t❤r❡❡ ♠♦❜✐❧❡ r♦❜♦ts P✐♦♥❡❡r 3AT ✱ s❛t✐s❢❛❝t♦r② r❡s✉❧ts ✭❣♦♦❞ ❛❝❝✉r❛❝② ❛♥❞ r♦❜✉st♥❡ss✮ ✇❡r❡ ♦❜t❛✐♥❡❞ ✇✐t❤ ❛❞❛♣t✐✈❡ ❙❱❙❋ ❋✐❧t❡r ✇✐t❤♦✉t ❛♥② ❛ss✉♠♣t✐♦♥ ♦♥ t❤❡ ♣r♦❝❡ss ❛♥❞✴♦r ♦❜s❡r✈❛t✐♦♥ ♠♦❞❡❧ ❛❝❝✉r❛❝②✳ ✶✻✵ ❬✸❪ ▼♦✉r✐❦✐s✱ ❆✳■✳✱ ✫ ❘♦✉♠❡❧✐♦t✐s✱ ❙✳■✳ ✭✷✵✵✻✮✳ P❡r❢♦r♠❛♥❝❡ ❆♥❛❧②s✐s ♦❢ ▼✉❧t✐✲r♦❜♦t ❈♦♦♣✲ ❡r❛t✐✈❡ ▲♦❝❛❧✐③❛t✐♦♥✳ ■❊❊❊ ❚r❛♥s❛❝t✐♦♥s ♦♥ ❘♦❜♦t✐❝s✱ ✷✷✭✹✮✱ ✻✻✻✲✻✽✶✳ ❬✹❪ ❘♦✉♠❡❧✐♦t✐s✱ ❙✳■✳✱ ✫ ❘❡❦❧❡✐t✐s✱ ■✳▼✳ ✭✷✵✵✹✮✳ Pr♦♣❛❣❛t✐♦♥ ♦❢ ❯♥❝❡rt❛✐♥t② ✐♥ ❈♦♦♣❡r❛t✐✈❡ ▼✉❧t✐✲r♦❜♦t ▲♦❝❛❧✐③❛t✐♦♥✿ ❆♥❛❧②s✐s ❛♥❞ ❊①✲ ♣❡r✐♠❡♥t❛❧ ❘❡s✉❧ts✳ ❆✉t♦♥♦♠♦✉s ❘♦❜♦ts✱ ✶✼✭✶✮✱ ✹✶✲✺✹✳ ❬✺❪ ❇✉r❣❛r❞✱ ❲✳✱ ❋♦①✱ ❉✳✱ ✫ ❚❤r✉♥✱ ❙✳ ✭✶✾✾✼✮✳ ❆❝t✐✈❡ ♠♦❜✐❧❡ r♦❜♦t ❧♦❝❛❧✐③❛t✐♦♥ ❜② ❡♥tr♦♣② ♠✐♥✐♠✐③❛t✐♦♥✳ ■♥ ❆❞✈❛♥❝❡❞ ▼♦❜✐❧❡ ❘♦❜♦ts✱ ✶✾✾✼✳ Pr♦❝❡❡❞✐♥❣s✳✱ ❙❡❝♦♥❞ ❊❯❘❖▼■❈❘❖ ✇♦r❦s❤♦♣ ♦♥✳ ■❊❊❊✱ ✶✺✺✲✶✻✷✳ ❬✻❪ ❘♦❝❤❛❛❜✱ ❘✳✱ ❉✐❛s❛✱ ❏✳✱ ✫ ❈❛r✈❛❧❤♦❜✱ ❆✳ ✭✷✵✵✺✮✳ ❈♦♦♣❡r❛t✐✈❡ ♠✉❧t✐✲r♦❜♦t s②st❡♠s✿ ❆ st✉❞② ♦❢ ✈✐s✐♦♥ ❜❛s❡❞ ✸❉ ♠❛♣♣✐♥❣ ✉s✐♥❣ ✐♥❢♦r♠❛t✐♦♥ t❤❡♦r②✳ ❏♦✉r♥❛❧ ♦❢ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♥♦♠♦✉s ❙②st❡♠s✱ ✺✸✭✸✲✹✮✱ ✷✽✷✲✸✶✶✳ ❬✼❪ ▼❛rt✐♥❡❧❧✐✱ ❆✳✱ P♦♥t✱ ❋✳✱ ✫ ❙✐❡❣✇❛rt✱ ❘✳ ✭✷✵✵✺✮✳ ▼✉❧t✐✲r♦❜♦t ❧♦❝❛❧✐③❛t✐♦♥ ✉s✐♥❣ r❡❧✲ ❛t✐✈❡ ♦❜s❡r✈❛t✐♦♥s ✭◆♦✳ ❈❖◆❋✮✳ ❬✽❪ ❚r❛✇♥②✱ ◆✳✱ ✫ ❇❛r❢♦♦t✱ ❚✳ ✭✷✵✵✹✮✳ ❖♣t✐✲ ♠✐③❡❞ ♠♦t✐♦♥ str❛t❡❣✐❡s ❢♦r ❝♦♦♣❡r❛t✐✈❡ ❧♦✲ ❝❛❧✐③❛t✐♦♥ ♦❢ ♠♦❜✐❧❡ r♦❜♦ts✳ ■❊❊❊ ■♥t❡r♥❛✲ t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♠❛✲ t✐♦♥✱ ✶✱ ✶✵✷✼✲✶✵✸✷✳ ❬✾❪ ❖③❦✉❝✉r✱ ◆✳❊✳✱ ✫ ❆❦✐♥✱ ❍✳▲✳ ✭✷✵✵✾✮✳ ❈♦✲ ♦♣❡r❛t✐✈❡ ▼✉❧t✐✲r♦❜♦t ▼❛♣ ▼❡r❣✐♥❣ ❯s✲ ✐♥❣ ❋❛st✲❙▲❆▼✳ ❘♦❜♦t ❙♦❝❝❡r ❲♦r❧❞ ❈✉♣ ❳■■■✱ ▲❡❝t✉r❡ ◆♦t❡s ✐♥ ❈♦♠♣✉t❡r ❙❝✐❡♥❝❡ ❙♣r✐♥❣❡r ❇❡r❧✐♥✱ ❍❡✐❞❡❧❜❡r❣✱ ✺✾✹✾✴✷✵✶✵✱ ✹✹✾✲✹✻✵✳ ❝ ✷✵✶✼ ❏♦✉r♥❛❧ ♦❢ ❆❞✈❛♥❝❡❞ ❊♥❣✐♥❡❡r✐♥❣ ❛♥❞ ❈♦♠♣✉t❛t✐♦♥ ✭❏❆❊❈✮ ❱❖▲❯▼❊✿ ✷ | ■❙❙❯❊✿ ✸ | ✷✵✶✽ | ❙❡♣t❡♠❜❡r ❬✶✵❪ ❉✐ss❛♥❛②❛❦❡✱ ▼✳●✳✱ ◆❡✇♠❛♥✱ P✳✱ ❈❧❛r❦✱ ❬✶✽❪ ❍❛❜✐❜✐✱ ❙✳❘✳ ✭✷✵✵✼✮✳ ❚❤❡ ❙♠♦♦t❤ ❱❛r✐❛❜❧❡ ❙✳✱ ✫ ❉✉rr❛♥t✲❲❤②t❡✱ ❍✳❋✳ ✭✷✵✵✶✮✳ ❆ s♦✲ ❙tr✉❝t✉r❡ ❋✐❧t❡r✳ ■❊❊❊ ♣r♦❝❡❡❞✐♥❣✱ ✾✺✭✺✮✱ ❧✉t✐♦♥ t♦ t❤❡ s✐♠✉❧t❛♥❡♦✉s ❧♦❝❛❧✐③❛t✐♦♥ ❛♥❞ ✶✵✷✻✲✶✵✺✾✳ ♠❛♣ ❜✉✐❧❞✐♥❣ ✭❙▲❆▼✮ ♣r♦❜❧❡♠✳ ■❊❊❊ ❚r❛♥✳ ❬✶✾❪ ●❛❞s❞❡♥✱ ❙✳ ❆✳✱ ✫ ❍❛❜✐❜✐✱ ❙✳ ❘✳ ✭✷✵✶✵✮✳ ❆ ❘♦❜♦t✳ ❆✉t♦♠❛t✱ ✶✼✭✸✮✱ ✷✷✾✲✷✹✶✳ ♥❡✇ ❢♦r♠ ♦❢ t❤❡ s♠♦♦t❤ ✈❛r✐❛❜❧❡ str✉❝t✉r❡ ✜❧t❡r ✇✐t❤ ❛ ❝♦✈❛r✐❛♥❝❡ ❞❡r✐✈❛t✐♦♥✳ ■♥ ❉❡❝✐✲ ❬✶✶❪ ●✐❧✱ ❆✳✱ ❘❡✐♥♦s♦✱ ■✳✱ ❇❛❧❧❡st❛✱ ▼✳✱ ✫ ❏✉❧✐❛✱ s✐♦♥ ❛♥❞ ❈♦♥tr♦❧ ✭❈❉❈✮✱ ✷✵✶✵ ✹✾t❤ ■❊❊❊ ▼✳ ✭✷✵✶✵✮✳ ▼✉❧t✐✲r♦❜♦t ✈✐s✉❛❧ ❙▲❆▼ ✉s✐♥❣ ❈♦♥❢❡r❡♥❝❡ ♦♥✳ ■❊❊❊✱ ✼✸✽✾✲✼✸✾✹✳ ❛ ❘❛♦✲❇❧❛❝❦✇❡❧❧✐③❡❞ ♣❛rt✐❝❧❡ ✜❧t❡r✳ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♥♦♠♦✉s ❙②st❡♠s✱ ❘♦❜♦t✐❝s ❛♥❞ ❬✷✵❪ ◆❡♠r❛✱ ❆✳✱ ✫ ❆♦✉❢✱ ◆✳ ✭✷✵✵✾✮✳ ❘♦❜✉st ❛✐r✲ ❆✉t♦♥♦♠♦✉s ❙②st❡♠s✱ ✺✽✭✶✮✱ ✻✽✲✽✵✳ ❜♦r♥❡ ✸❉ ✈✐s✉❛❧ s✐♠✉❧t❛♥❡♦✉s ❧♦❝❛❧✐③❛t✐♦♥ ❬✶✷❪ ❆♥❞❡rss♦♥✱ ▲✳ ❆✳✱ ✫ ◆②❣❛r❞s✱ ❏✳ ✭✷✵✵✽✮✳ ❈✲❙❆▼✿ ▼✉❧t✐✲r♦❜♦t ❙▲❆▼ ✉s✐♥❣ sq✉❛r❡ r♦♦t ✐♥❢♦r♠❛t✐♦♥ s♠♦♦t❤✐♥❣✳ ■♥ ❘♦❜♦t✐❝s ❛♥❞ ❆✉t♦♠❛t✐♦♥✱ ✷✵✵✽✳ ■❈❘❆ ✷✵✵✽✳ ■❊❊❊ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥✳ ■❊❊❊✱ ✷✼✾✽✲ ✷✽✵✺✳ ❬✶✸❪ ●❛❞s❞❡♥✱ ❙✳ ❆✳✱ ❉✉♥♥❡✱ ❉✳✱ ❍❛❜✐❜✐✱ ❙✳ ❘✳✱ ✫ ❑✐r✉❜❛r❛❥❛♥✱ ❚✳ ✭✷✵✵✾✮✳ ❈♦♠♣❛r✐s♦♥ ♦❢ ❡①t❡♥❞❡❞ ❛♥❞ ✉♥s❝❡♥t❡❞ ❑❛❧♠❛♥✱ ♣❛rt✐❝❧❡✱ ❛♥❞ s♠♦♦t❤ ✈❛r✐❛❜❧❡ str✉❝t✉r❡ ✜❧t❡rs ♦♥ ❛ ❜❡❛r✐♥❣✲♦♥❧② t❛r❣❡t tr❛❝❦✐♥❣ ♣r♦❜❧❡♠✳ ■♥ ❙✐❣♥❛❧ ❛♥❞ ❉❛t❛ Pr♦❝❡ss✐♥❣ ♦❢ ❙♠❛❧❧ ❚❛r✲ ❣❡ts ✷✵✵✾ ✭❱♦❧✳ ✼✹✹✺✱ ♣✳ ✼✹✹✺✵❇✮✳ ■♥t❡r♥❛✲ t✐♦♥❛❧ ❙♦❝✐❡t② ❢♦r ❖♣t✐❝s ❛♥❞ P❤♦t♦♥✐❝s✳ ❛♥❞ ♠❛♣♣✐♥❣ ✇✐t❤ ♦❜s❡r✈❛❜✐❧✐t② ❛♥❞ ❝♦♥✲ s✐st❡♥❝② ❛♥❛❧②s✐s✳ ❏♦✉r♥❛❧ ♦❢ ■♥t❡❧❧✐❣❡♥t ❛♥❞ ❘♦❜♦t✐❝ ❙②st❡♠s✱ ✺✺✭✹✲✺✮✱ ✸✹✺✲✸✼✻✳ ❬✷✶❪ ❉❡♠✐♠✱ ❋✳✱ ◆❡♠r❛✱ ❆✳✱ ✫ ▲♦✉❛❞❥✱ ❑✳ ✭✷✵✶✻✮✳ ❘♦❜✉st ❙❱❙❋✲❙▲❆▼ ❢♦r ❯♥♠❛♥♥❡❞ ❱❡❤✐❝❧❡ ✐♥ ❯♥❦♥♦✇♥ ❊♥✈✐r♦♥♠❡♥t✳ ❏♦✉r✲ ♥❛❧ ♦❢ ■❋❆❈✲P❛♣❡rs ❖♥▲✐♥❡ ❙❝✐❡♥❝❡ ❉✐r❡❝t✱ ✹✾✭✷✶✮✱ ✸✽✻✕✸✾✹✳ ❬✷✷❪ ◆❡♠r❛✱ ❆✳✱ ✫ ❆♦✉❢✱ ◆✳ ✭✷✵✶✵✮✳ ❘♦❜✉st ■◆❙✴●P❙ s❡♥s♦r ❢✉s✐♦♥ ❢♦r ❯❆❱ ❧♦❝❛❧✐③❛✲ t✐♦♥ ✉s✐♥❣ ❙❉❘❊ ♥♦♥❧✐♥❡❛r ✜❧t❡r✐♥❣✳ ■❊❊❊ ❙❡♥s♦rs ❏♦✉r♥❛❧✱ ✶✵✭✹✮✱ ✼✽✾✲✼✾✽✳ ❬✷✸❪ ❉❡♠✐♠✱ ❋✳✱ ◆❡♠r❛✱ ❆✳✱ ▲♦✉❛❞❥✱ ❑✳✱ ▼❡❤❛❧✱ ❩✳✱ ❍❛♠❡r❧❛✐♥✱ ▼✳✱ ✫ ❇❛③♦✉❧❛✱ ❆✳ ✭✷✵✶✻✮✳ ❙✐♠✉❧t❛♥❡♦✉s ❧♦❝❛❧✐③❛t✐♦♥ ❛♥❞ ♠❛♣♣✐♥❣ ❛❧✲ ❬✶✹❪ ❆❧✲❙❤❛❜✐✱ ▼✳ ✭✷✵✶✶✮✳ ❚❤❡ ●❡♥❡r❛❧ ❣♦r✐t❤♠ ❢♦r ✉♥♠❛♥♥❡❞ ❣r♦✉♥❞ ✈❡❤✐❝❧❡ ✇✐t❤ ❚♦❡♣❧✐t③✴❖❜s❡r✈❛❜✐❧✐t② ❙❱❙❋✳ ❉❡♣❛rt✲ ❙❱❙❋ ✜❧t❡r✳ ■♥ ▼♦❞❡❧❧✐♥❣✱ ■❞❡♥t✐✜❝❛t✐♦♥ ♠❡♥t ♦❢ ▼❡❝❤❛♥✐❝❛❧ ❊♥❣✐♥❡❡r✐♥❣✱ ▼❝ ❛♥❞ ❈♦♥tr♦❧ ✭■❈▼■❈✮✱ ✷✵✶✻ ✽t❤ ■♥t❡r♥❛✲ ▼❛st❡r ❯♥✐✈❡rs✐t②✱ ❍❛♠✐❧t♦♥✱ ❖♥t❛r✐♦✱ t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥✳ ■❊❊❊✱ ✶✺✺✲✶✻✷✳ P❤✳❉✳ ❬✶✺❪ ❙❢❡✐r✱ ❏✳ ✭✷✵✵✾✮✳ ◆❛✈✐❣❛t✐♦♥ ❞✬✉♥ ❘♦❜♦t ▼♦✲ ❜✐❧❡ ❡♥ ❊♥✈✐r♦♥♥❡♠❡♥t ■♥❝♦♥♥✉ ❯t✐❧✐s❛♥t ❧❡s ❈❤❛♠♣s ❞❡ P♦t❡♥t✐❡❧s ❆rt✐✜❝✐❡❧s✳ ▼❛ïtr✐s❡ ❡♥ ❣é♥✐❡ ❞❡ ❧❛ ♣r♦❞✉❝t✐♦♥ ❛✉t♦♠❛t✐sé❡✱ ❊❝♦❧❡ ❞❡ ❚❡❝❤♥♦❧♦❣✐❡ ❙✉♣❡r✐❡✉r❡✱ ▼♦♥tr✐❛❧❧✱ ❈❛♥❛❞❛✳ ❬✶✻❪ ❆❤♠❡❞✱ ❆✳✱ ❆❜❞❡❧❦r✐♠✱ ◆✳✱ ✫ ▼✉st❛♣❤❛✱ ❍✳ ✭✷✵✶✻✮✳ ❙♠♦♦t❤ ❱❛r✐❛❜❧❡ ❙tr✉❝t✉r❡ ❋✐❧t❡r ❱❙▲❆▼✳ ■❋❆❈✲P❛♣❡rs❖♥▲✐♥❡✱ ✹✾✭✶✺✮✱ ✷✵✺✲ ✷✶✶✳ ❬✷✹❪ ❉❡♠✐♠✱ ❋✳✱ ◆❡♠r❛✱ ❆✳✱ ▲♦✉❛❞❥✱ ❑✳✱ ❍❛♠❡r✲ ❧❛✐♥✱ ▼✳✱ ✫ ❇❛③♦✉❧❛✱ ❆✳ ✭✷✵✶✻✮✳ ❆ ♥❡✇ ❛♣✲ ♣r♦❛❝❤ t♦ ✐♠♣r♦✈❡ t❤❡ s✉❝❝❡ss ❛♥❞ s♦❧✈✐♥❣ t❤❡ ❯●❱s ❈♦♦♣❡r❛t✐♦♥ ❢♦r ❙▲❆▼ Pr♦❜❧❡♠✱ ✉s✐♥❣ ❛ ❙❱❙❋ ❋✐❧t❡r✳ ■♥ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ▼❡❞✐t❡rr❛♥❡❛♥ ❝♦♥❢❡r❡♥❝❡ ♦♥ ♣❛tt❡r♥ r❡❝♦❣✲ ♥✐t✐♦♥ ❛♥❞ ❛rt✐✜❝✐❛❧ ✐♥t❡❧❧✐❣❡♥❝❡✳ ❆❈▼✱ ✺✻✲ ✻✸✳ ❬✷✺❪ ❉❡♠✐♠✱ ❋✳✱ ❇♦✉❝❤❡❧♦✉❦❤✱ ❆✳✱ ◆❡♠r❛✱ ❆✳✱ ▲♦✉❛❞❥✱ ❑✳✱ ❍❛♠❡r❧❛✐♥✱ ▼✳✱ ❇❛③♦✉❧❛✱ ❆✳✱ ✫ ▼❡❤❛❧✱ ❩✳ ✭✷✵✶✼✮✳ ❆ ♥❡✇ ❛❞❛♣t✐✈❡ s♠♦♦t❤ ✈❛r✐❛❜❧❡ str✉❝t✉r❡ ✜❧t❡r ❙▲❆▼ ❛❧❣♦r✐t❤♠ ❬✶✼❪ ❨❛♥✱ ❳✳✱ ❩❤❛♦✱ ❈✳✱ ✫ ❳✐❛♦✱ ❏✳ ✭✷✵✶✶✮✳ ❆ ❢♦r ✉♥♠❛♥♥❡❞ ✈❡❤✐❝❧❡✳ ■♥ ❙②st❡♠s ❛♥❞ ❈♦♥✲ ♥♦✈❡❧ ❋❛st❙▲❆▼ ❛❧❣♦r✐t❤♠ ❜❛s❡❞ ♦♥ ✐t❡r✲ tr♦❧ ✭■❈❙❈✮✱ ✷✵✶✼ ✻t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r✲ ❛t❡❞ ✉♥s❝❡♥t❡❞ ❑❛❧♠❛♥ ✜❧t❡r✳ ■♥ ❘♦❜♦t✐❝s ❡♥❝❡ ♦♥✳ ■❊❊❊✱ ✻✲✶✸✳ ❛♥❞ ❇✐♦♠✐♠❡t✐❝s ✭❘❖❇■❖✮✱ ✷✵✶✶ ■❊❊❊ ■♥✲ t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥✳ ■❊❊❊✱ ✶✾✵✻✲ ❬✷✻❪ ❉❡♠✐♠✱ ❋✳✱ ◆❡♠r❛✱ ❆✳✱ ▲♦✉❛❞❥✱ ❑✳✱ ❍❛♠❡r✲ ✶✾✶✶✳ ❧❛✐♥✱ ▼✳✱ ✫ ❇❛③♦✉❧❛✱ ❆✳ ✭✷✵✶✼✮✳ ❈♦♦♣❡r❛t✐✈❡ ❝ ✷✵✶✼ ❏♦✉r♥❛❧ ♦❢ ❆❞✈❛♥❝❡❞ ❊♥❣✐♥❡❡r✐♥❣ ❛♥❞ ❈♦♠♣✉t❛t✐♦♥ ✭❏❆❊❈✮ ✶✻✶ ❱❖▲❯▼❊✿ ✷ | ■❙❙❯❊✿ ✸ | ✷✵✶✽ | ❙❡♣t❡♠❜❡r ❙▲❆▼ ❢♦r ♠✉❧t✐♣❧❡ ❯●❱s ♥❛✈✐❣❛t✐♦♥ ✉s✐♥❣ ❙❱❙❋ ✜❧t❡r✳ ❆✉t♦♠❛t✐❦❛✱ ✺✽✭✶✮✱ ✶✶✾✲✶✷✾✳ ❆❧❣❡r✐❛✱ ✐♥ ✷✵✶✸✳ ❍❡ ✐s ❝✉rr❡♥t❧② ♣✉rs✉✐♥❣ ❤✐s P❤✳❉✳ ❞❡❣r❡❡ ❛t t❤❡ P♦❧②t❡❝❤♥✐❝ ▼✐❧✐t❛r② ❙❝❤♦♦❧✱ ❆❧❣❡r✐❛✳ ❍✐s ❝✉rr❡♥t r❡s❡❛r❝❤ ✐♥t❡r❡sts ❬✷✼❪ ❉❡♠✐♠✱ ❋✳✱ ◆❡♠r❛✱ ❆✳✱ ▲♦✉❛❞❥✱ ❑✳✱ ❍❛♠❡r✲ ❛r❡ ❛✉t♦♥♦♠♦✉s ♥❛✈✐❣❛t✐♦♥✱ ♦♣t✐♠✐③❛t✐♦♥✱ ♣❛t❤ ❧❛✐♥✱ ▼✳✱ ✫ ❇❛③♦✉❧❛✱ ❆✳ ✭✷✵✶✽✮✳ ❆♥ ❛❞❛♣✲ ♣❧❛♥♥✐♥❣✱ ✉♥♠❛♥♥❡❞ ✈❡❤✐❝❧❡s✱ ❧♦❝❛❧✐③❛t✐♦♥ ♦❢ t✐✈❡ ❙❱❙❋✲❙▲❆▼ ❛❧❣♦r✐t❤♠ t♦ ✐♠♣r♦✈❡ t❤❡ ❣r♦✉♥❞ ✈❡❤✐❝❧❡ ❛♥❞ ♠❛♣ ❜✉✐❧❞✐♥❣✳ s✉❝❝❡ss ❛♥❞ s♦❧✈✐♥❣ t❤❡ ❯●❱s ❝♦♦♣❡r❛t✐♦♥ ♣r♦❜❧❡♠✳ ❏♦✉r♥❛❧ ♦❢ ❊①♣❡r✐♠❡♥t❛❧ ✫ ❚❤❡✲ ❆❜❞❡❧❦r✐♠ ◆❊▼❘❆ r❡❝❡✐✈❡❞ t❤❡ ❊♥✲ ♦r❡t✐❝❛❧ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡✱ ✸✵✭✸✮✱ ✸✽✾✲ ❣✐♥❡❡r ❞❡❣r❡❡ ❛♥❞ ▼✳❙ ❞❡❣r❡❡ ✐♥ ❈♦♥tr♦❧ ✹✶✹✳ s②st❡♠s ❢r♦♠ t❤❡ ❉❡♣❛rt♠❡♥t ♦❢ ❈♦♥tr♦❧✱ P♦❧②✲ t❡❝❤♥✐❝ ▼✐❧✐t❛r② ❙❝❤♦♦❧✱ ❆❧❣❡r✐❛✱ ✐♥ ✷✵✵✹ ❛♥❞ ✷✵✵✻✱ r❡s♣❡❝t✐✈❡❧②✳ ❍❡ r❡❝❡✐✈❡❞ t❤❡ P❤✳❉✳ ❞❡❣r❡❡ ✐♥ ❈♦♥tr♦❧ s②st❡♠s ❢r♦♠ t❤❡ ❉❡♣❛rt♠❡♥t ♦❢ ■♥❢♦r♠❛t✐❝s ❛♥❞ ❙❡♥s♦rs✱ ❈r❛♥✜❡❧❞ ❯♥✐✈❡rs✐t②✱ ❙❤r✐✈❡♥❤❛♠✱ ❯❑ ✐♥ ✷✵✶✵✳ ❍❡ r❡❝❡✐✈❡❞ t❤❡ ❛❝❝r❡❞✐t❛t✐♦♥ t♦ s✉♣❡r✈✐s❡ r❡s❡❛r❝❤ ✭❍❉❘✮ ✐♥ ✷✵✶✻✳ ❍✐s ❝✉rr❡♥t r❡s❡❛r❝❤ ✐♥t❡r❡sts ✐♥❝❧✉❞❡ ❬✷✾❪ ❉❡♠✐♠✱ ❋✳✱ ◆❡♠r❛✱ ❆✳✱ ▲♦✉❛❞❥✱ ❑✳✱ ✉♥♠❛♥♥❡❞ ✈❡❤✐❝❧❡s✱ ❧♦❝❛❧✐③❛t✐♦♥ ♦❢ ❛♥ ❛❡r✐❛❧ ❇♦✉❝❤❡❧♦✉❦❤✱ ❆✳✱ ❑♦❜③✐❧✐✱ ❊✳✱ ❆❧❧❛♠✱ ❆✳✱ ✈❡❤✐❝❧❡ ❛♥❞ ♠❛♣ ❜✉✐❧❞✐♥❣✳ ❍✐s ♣✉❜❧✐❝❛t✐♦♥s ❍❛♠❡r❧❛✐♥✱ ▼✳ ✫ ❇❛③♦✉❧❛✱ ❆✳ ✭✷✵✶✽✮✳ ❱✐✲ ✐♥❝❧✉❞❡ ❛ ♥✉♠❜❡r ♦❢ ❝♦♥❢❡r❡♥❝❡ ❛♥❞ ❥♦✉r♥❛❧ s✉❛❧ ❙❱❙❋✲❙▲❆▼ ❆❧❣♦r✐t❤♠ ❇❛s❡❞ ❖♥ ♣❛♣❡rs ✐♥ ❝♦♠♣✉t❡r ✈✐s✐♦♥ ❛♥❞ ❞❛t❛ ❢✉s✐♦♥ ❛♥❞ ❆❞❛♣t✐✈❡ ❇♦✉♥❞❛r② ▲❛②❡r ❲✐❞t❤✳ ✭❊❞s✳✮✿ ❜♦♦❦ ❝❤❛♣t❡rs ✐♥ r♦❜♦t✐❝s✳ ■❈❊❊❈❆✬✷✵✶✼✱ ❇♦♦❦✿ ❆❞✈❛♥❝❡❞ ❈♦♥tr♦❧ r❡❝❡✐✈❡❞ ❊♥❣✐♥❡❡r✐♥❣ ▼❡t❤♦❞s ✐♥ ❊❧❡❝tr✐❝❛❧ ❊♥✲ ❆❜❞❡❧❣❤❛♥✐ ❇❖❯❈❍❊▲❖❯❑❍ ❣✐♥❡❡r✐♥❣ ❙②st❡♠s✱ ❙P❘■◆●❊❘ ◆❛t✉r❡ t❤❡ ❊♥❣✐♥❡❡r ❞❡❣r❡❡ ❛♥❞ ▼✳❙ ❞❡❣r❡❡ ✐♥ ❝♦♥tr♦❧ s②st❡♠s ❢r♦♠ t❤❡ ❉❡♣❛rt♠❡♥t ♦❢ ❈♦♥tr♦❧✱ ❙✇✐t③❡r❧❛♥❞ ❆●✳ P♦❧②t❡❝❤♥✐❝ ▼✐❧✐t❛r② ❙❝❤♦♦❧✱ ❆❧❣❡r✐❛✱ ✐♥ ✷✵✶✷✳ ❬✸✵❪ ❉❡♠✐♠✱ ❋✳✱ ◆❡♠r❛✱ ❆✳✱ ✫ ▲♦✉❛❞❥✱ ❍❡ ✐s ❝✉rr❡♥t❧② ♣✉rs✉✐♥❣ ❤✐s P❤✳❉✳ ❞❡❣r❡❡ ❛t ❑✳ ✭✷✵✶✽✮✳ P❛t❤ ♣❧❛♥♥✐♥❣ ❢♦r ✉♥♠❛♥♥❡❞ t❤❡ P♦❧②t❡❝❤♥✐❝ ▼✐❧✐t❛r② ❙❝❤♦♦❧✱ ❆❧❣❡r✐❛✳ ❍✐s ❣r♦✉♥❞ ✈❡❤✐❝❧❡✳ ■❊❊❊ ✺t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❝✉rr❡♥t r❡s❡❛r❝❤ ✐♥t❡r❡sts ❛r❡ ❛✉t♦♥♦♠♦✉s ♥❛✈✐✲ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❈♦♥tr♦❧✱ ❉❡❝✐s✐♦♥ ❛♥❞ ■♥❢♦r✲ ❣❛t✐♦♥ ✈❡❤✐❝❧❡✱ ♣❛t❤ ♣❧❛♥♥✐♥❣ ❛♥❞ ❧♦❝❛❧✐③❛t✐♦♥✳ ♠❛t✐♦♥ ❚❡❝❤♥♦❧♦❣✐❡s ✭❈♦❉■❚✬✷✵✶✽✮✱ ❆r✐st♦✲ t❧❡ ❯♥✐✈❡rs✐t② ♦❢ ❚❤❡ss❛❧♦♥✐❦✐✱ ●r❡❡❝❡✱ ✼✹✽✲ ❑❛❤✐♥❛ ▲❖❯❆❉❏ ✐s ❝✉rr❡♥t❧② ❧❡❝t✉r❡r ✼✺✵✳ ❛t t❤❡ ❯♥✐✈❡rs✐t② ♦❢ ❇♦✉✐r❛ ✐♥ t❤❡ ✜❡❧❞ ♦❢ ■♥✲ ❢♦r♠❛t✐❝s✱ ♠❛t❤❡♠❛t✐❝s ❛♥❞ ♣❤②s✐❝s ▲❛❜♦r❛t♦r② ❬✸✶❪ ❉❡♠✐♠✱ ❋✳✱ ◆❡♠r❛✱ ❆✳✱ ❆❜❞❡❧❦❛❞r✐✱ ❍✳✱ ✭▲■▼P❆❋✮✳ ❙❤❡ st✉❞✐❡❞ ❛t t❤❡ ❯♥✐✈❡rs✐t② ♦❢ ▲♦✉❛❞❥✱ ❑✳✱ ❍❛♠❡r❧❛✐♥✱ ▼✳✱ ✫ ❇❛③♦✉❧❛✱ ❆✳ ❚✐③✐ ❖✉③♦✉✳ ❙❤❡ r❡❝❡✐✈❡❞ ❉❊❙ ♦❢ ▼❛t❤❡♠❛t✐❝s ✭✷✵✶✽✮✳ ❙▲❆▼ ♣r♦❜❧❡♠ ❢♦r ❛✉t♦♥♦♠♦✉s ✉♥✲ ✐♥ ✷✵✵✵✱ ❉♦❝t♦r❛t❡ ✐♥ ✷✵✶✷✳ ❍❡r ♠❛✐♥ r❡s❡❛r❝❤ ❞❡r✇❛t❡r ✈❡❤✐❝❧❡ ✉s✐♥❣ ❙❱❙❋ ✜❧t❡r✳ ■❊❊❊ ✐♥t❡r❡sts ❛r❡ ♦♣t✐♠❛❧ ❝♦♥tr♦❧✱ ♦♣t✐♠✐③❛t✐♦♥✱ ✷✺t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❙②s✲ ❛✐r❝r❛❢t ♣r♦❜❧❡♠s✳ t❡♠s✱ ❙✐❣♥❛❧s ❛♥❞ ■♠❛❣❡ Pr♦❝❡ss✐♥❣ ✭■❲❙✲ ❙■P✬✷✵✶✽✮✱ ▼❛r✐❜♦r✱ ❙❧♦✈❡♥✐❛✱ ✶✲✺✳ ▼✉st❛♣❤❛ ❍❆▼❊❘▲❆■◆ r❡❝❡✐✈❡❞ ❤✐s P❤✳❉ ✐♥ ■◆❙❆ ❚♦✉❧♦✉s❡✱ ❋r❛♥❝❡✳ ❈✉rr❡♥t❧②✱ ❤❡ ✐s t❤❡ ❤❡❛❞ ♦❢ ❘♦❜♦t✐❝ ❉✐✈✐s✐♦♥ ❛t t❤❡ ❈❡♥t❡r ❆❜♦✉t ❆✉t❤♦rs ❢♦r ❉❡✈❡❧♦♣♠❡♥t ♦❢ ❆❞✈❛♥❝❡❞ ❚❡❝❤♥♦❧♦❣✐❡s ✭❈❉❚❆✮✱ ❇❛❜❛ ❍❛ss❡♥✱ ❆❧❣✐❡rs✱ ❆❧❣❡r✐❛✳ ❍✐s ❋❡t❤✐ ❉❊▼■▼ r❡❝❡✐✈❡❞ t❤❡ ❊♥❣✐♥❡❡r ❞❡❣r❡❡ ❝✉rr❡♥t r❡s❡❛r❝❤ ✐♥t❡r❡sts ✐♥❝❧✉❞❡ ✉♥♠❛♥♥❡❞ ✐♥ ❊❧❡❝tr♦♥✐❝s ❢r♦♠ t❤❡ ❯♥✐✈❡rs✐t② ♦❢ ❆❜♦✉✲❇❡❦r ✈❡❤✐❝❧❡s✱ ❧♦❝❛❧✐③❛t✐♦♥ ♦❢ ❛♥ ❛❡r✐❛❧ ✈❡❤✐❝❧❡✳ ❍✐s ❇❡❧❦❛ï❞✱ ❚❧❡♠❝❡♥✱ ❆❧❣❡r✐❛✱ ✐♥ ✷✵✵✷ ❛♥❞ ▼✳❙ ♣✉❜❧✐❝❛t✐♦♥s ✐♥❝❧✉❞❡ ❛ ♥✉♠❜❡r ♦❢ ❝♦♥❢❡r❡♥❝❡ ❛♥❞ ❞❡❣r❡❡ ✐♥ ❝♦♥tr♦❧ s②st❡♠s ❢r♦♠ t❤❡ ❉❡♣❛rt✲ ❥♦✉r♥❛❧ ♣❛♣❡rs ❛♥❞ ❜♦♦❦ ❝❤❛♣t❡rs ✐♥ r♦❜♦t✐❝s✳ ♠❡♥t ♦❢ ❈♦♥tr♦❧✱ P♦❧②t❡❝❤♥✐❝ ▼✐❧✐t❛r② ❙❝❤♦♦❧✱ ❬✷✽❪ ❉❡♠✐♠✱ ❋✳✱ ◆❡♠r❛✱ ❆✳✱ ▲♦✉❛❞❥✱ ❑✳✱ ✫ ❍❛♠❡r❧❛✐♥✱ ▼✳ ✭✷✵✶✽✮✳ ❙✐♠✉❧t❛♥❡♦✉s ❧♦❝❛❧✲ ✐③❛t✐♦♥✱ ♠❛♣♣✐♥❣✱ ❛♥❞ ♣❛t❤ ♣❧❛♥♥✐♥❣ ❢♦r ✉♥✲ ♠❛♥♥❡❞ ✈❡❤✐❝❧❡ ✉s✐♥❣ ♦♣t✐♠❛❧ ❝♦♥tr♦❧✳ ❏♦✉r✲ ♥❛❧ ♦❢ ❆❞✈❛♥❝❡s ✐♥ ▼❡❝❤❛♥✐❝❛❧ ❊♥❣✐♥❡❡r✐♥❣✱ ✶✵✭✶✮✱ ✶✲✷✺✳ ✶✻✷ ❝ ✷✵✶✼ ❏♦✉r♥❛❧ ♦❢ ❆❞✈❛♥❝❡❞ ❊♥❣✐♥❡❡r✐♥❣ ❛♥❞ ❈♦♠♣✉t❛t✐♦♥ ✭❏❆❊❈✮ ❱❖▲❯▼❊✿ ✷ | ■❙❙❯❊✿ ✸ | ✷✵✶✽ | ❙❡♣t❡♠❜❡r ❆❜❞❡❧♦✉❛❤❛❜ ❇❆❩❖❯▲❆ r❡❝❡✐✈❡❞ t❤❡ ❊♥❣✐♥❡❡r ❞❡❣r❡❡ ✐♥ ❝♦♥tr♦❧ s②st❡♠s ❢r♦♠ t❤❡ P♦❧②t❡❝❤♥✐❝ ▼✐❧✐t❛r② ■♥st✐t✉t❡✱ ❆❧❣❡r✐❛✱ ✐♥ ✶✾✾✻✱ ❛♥❞ t❤❡ ▼✳❙ ❛♥❞ P❤✳❉ ❞❡❣r❡❡s ❢r♦♠ t❤❡ s❛♠❡ ✐♥st✐t✉t✐♦♥✱ ✐♥ ✷✵✵✷ ❛♥❞ ✷✵✶✶ r❡s♣❡❝t✐✈❡❧②✳ ❈✉r✲ r❡♥t❧②✱ ❤❡ ✐s t❤❡ ❤❡❛❞ ♦❢ t❤❡ r♦❜♦t✐❝s ❧❛❜♦r❛t♦r② ❛t t❤❡ P♦❧②t❡❝❤♥✐❝ ▼✐❧✐t❛r② ■♥st✐t✉t❡✳ ❍✐s ❝✉rr❡♥t r❡s❡❛r❝❤ ✐♥❝❧✉❞❡s✱ ✈✐s✐♦♥ ❛♥❞ r♦❜♦t✐❝s✳ ❍❡ ❤❛s ❛✉t❤♦r❡❞ ❛♥❞ ❝♦✲❛✉t❤♦r❡❞ ♠❛♥② ♣❛♣❡rs ✐♥ t❤❡ ✜❡❧❞ ♦❢ r♦❜♦t✐❝s✳ "This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0)." ❝ ✷✵✶✼ ❏♦✉r♥❛❧ ♦❢ ❆❞✈❛♥❝❡❞ ❊♥❣✐♥❡❡r✐♥❣ ❛♥❞ ❈♦♠♣✉t❛t✐♦♥ ✭❏❆❊❈✮ ✶✻✸ ... article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly... ❡❧❧✐♣s♦✐❞ (ξ i ) ❝❡♥t❡r❡❞ ❛t (µi ) ✇✐t❤ ❛①❡s (σ i )✳ ❚❤❡r❡❢♦r❡ U GVi ❛♥❞ U GVj ✇✐❧❧ ❝♦♦♣❡r❛t❡ (Cooperation(i, j) = 1) ✐❢ ❛♥❞ ♦♥❧② ✐❢✿ ξ i ∩ ξ j = ∅ ❬✷✵❪✳ ❚❤❡ ♣r♦♣♦s❡❞ ❉❈✲❙▲❆▼ str❛t❡❣② ✐s ❞❡✜♥❡❞ ❛s ❢♦❧❧♦✇s✿