ﮔﺮﻓﺘﻦ ﻧﻈﺮ ﺩﺭ ﺑﺎ ﺳﻤﺖ ﺯﺍﻭﻳﻪ ﺑﺎ ﺗﻨﻬﺎ ﻳﺎﺑﻲ ﻣﻮﻗﻌﻴﺖ ﺩﺭ ﮔ

C E

ISSN 2008-8345 ﺪﻠﺟ 8 ﻩﺭﺎﻤﺷ ، 1 ﺭﺎﻬﺑ ، 1393 ﻪﺤﻔﺻ ، 71 - 55

ﻦﻴﻴﻌﺗ ﺮﻴﺴﻣ

ﺖﻳﻭﺭ ﺮﮔ

ﺭﺩ ﺖﻴﻌﻗﻮﻣ ﻲﺑﺎﻳ

ﺎﻬﻨﺗ ﺎﺑ ﻪﻳﻭﺍﺯ ﺖﻤﺳ ﺎﺑ ﺭﺩ ﺮﻈﻧ ﻦﺘﻓﺮﮔ

ﺖﻳﺩﻭﺪﺤﻣ ﻥﺍﺪﻴﻣ

ﺪﻳﺩ

ﻪﻧﺎﺘﺳﺁ ﻲﺒﻳﺎﻧ ﻦﻴﺴﺣﺮﻴﻣﺍ ،

1

ﺰﻳﺮﭘ ﺮﺻﺎﻧ ﻲﻧﺎﺘﺴﻴﺳ ﻲﺒﻴﻘﻧ ﺮﻗﺎﺑﺪﻤﺤﻣ ،

2

3

،ﻕﺮﺑ ﻲﺳﺪﻨﻬﻣ ﻱﺮﺘﻛﺩ ﻱﻮﺠﺸﻧﺍﺩ1

ﻩﻭﺮﮔ ﻝﺮﺘﻨﻛ ﻩﺎﮕﺸﻧﺍﺩ ، ﺮﻓ ﺩ ﺪﻬﺸﻣ ﻲﺳﻭ

، am_nayebi@yahoo.com

ﺩﺎﺘﺳﺍ2

، ﻩﺪﻜﺸﻧﺍﺩ ﻲﺳﺪﻨﻬﻣ ﻩﻭﺮﮔ ، ﻝﺮﺘﻨﻛ ﻩﺎﮕﺸﻧﺍﺩ ، ﺪﻬﺸﻣ ﻲﺳﻭﺩﺮﻓ

، n-pariz@um.ac.ir

،ﺭﺎﻳﺩﺎﺘﺳﺍ3

ﻩﺪﻜﺸﻧﺍﺩ ﻲﺳﺪﻨﻬﻣ ﻩﻭﺮﮔ ، ﻝﺮﺘﻨﻛ ﻩﺎﮕﺸﻧﺍﺩ ، ﺪﻬﺸﻣ ﻲﺳﻭﺩﺮﻓ

، naghib@yahoo.com

ﺭﺎﺗ) ﻳ ﺭﺩ ﺦ ﻳ ﻪﻟﺎﻘﻣ ﺖﻓﺎ 16 / 02 / 1393 ﺭﺎﺗ ، ﻳ ﺬﭘ ﺦ ﻳ ﻪﻟﺎﻘﻣ ﺵﺮ 31 / 03 / 1393 (

ﻜﭼ ﻴ ﻩﺪ : ﻝﺮﺘﻨﻛ ﻪﻨﻴﻬﺑ ﺖﻳﻭﺭ ﻱﺮﮔ ﻪﻛ ﺎﻬﻨﺗ ﺎﺑ ﻪﻳﻭﺍﺯ ﺖﻤﺳ ﺭﺩ ﻝﺎﺣ ﻥﺎﻜﻣ ﻲﺑﺎﻳ ﻲﻓﺪﻫ ﻦﻛﺎﺳ

،ﺖﺳﺍ ﺮﻈﻧﺪﻣ ﺖﺳﺍ . ﻦﻳﺪﺑ ﺭﻮﻈﻨﻣ ﻝﺎﻨﮕﻴﺳ ﻝﺮﺘﻨﻛ

ﻪﺑ ﻪﻧﻮﮔ ﻱﺍ ﺪﻴﻟﻮﺗ ﻲﻣ ﺩﻮﺷ ﺎﺗ ﻱﺎﻄﺧ ﻦﻴﻤﺨﺗ ﻥﺎﻜﻣ ﻑﺪﻫ ﺶﻫﺎﻛ ﺪﺑﺎﻳ . ﺭﺎﻴﻌﻣ

،ﻲﮕﻨﻴﻬﺑ ﺮﺛﺍ ﺲﻳﺮﺗﺎﻣ ﺲﻧﺎﻳﺭﺍﻭﻮﻛ ﻱﺎﻄﺧ

ﻦﻴﻤﺨﺗ ﺭﺩ ﻪﻈﺤﻟ ﻲﻳﺎﻬﻧ

ﺏﺎﺨﺘﻧﺍ ﻩﺪﺷ ﺖﺳﺍ . ﻦﻳﺍ ﻪﻠﺌﺴﻣ ﺎﺑ ﻪﺋﺍﺭﺍ ﻥﻮﻧﺎﻗ ﻲﻟﺮﺘﻨﻛ ﻪﻛ ﺖﻬﺟ ﺖﻛﺮﺣ ﺖﻳﻭﺭ ﺮﮔ ﺍﺭ ﻪﺑ ﻪﻳﻭﺍﺯ ﺖﻤﺳ ﻑﺪﻫ ﻂﺒﺗﺮﻣ ﻲﻣ

،ﺩﺯﺎﺳ ﻞﺣ ﻩﺪﺷ ﺖﺳﺍ .

ﻲﮔﮋﻳﻭ ﺵﻭﺭ ﻪﺋﺍﺭﺍ ﻩﺪﺷ ﻩﻭﻼﻋ ﺮﺑ ﺪﻴﻟﻮﺗ ﮓﻧﺭﺩﻼﺑ ﻲﻳﺎﻫﺮﻴﺴﻣ ﻪﻛ ﺭﺎﻴﺴﺑ ﻚﻳﺩﺰﻧ ﻪﺑ ﺮﻴﺴﻣ ﻪﻨﻴﻬﺑ ﻲﻣ

،ﺪﻨﺷﺎﺑ ﺭﺩ ﺮﻈﻧ ﻦﺘﻓﺮﮔ ﺖﻳﺩﻭﺪﺤﻣ ﻥﺍﺪﻴﻣ

ﺪﻳﺩ

ﺖﻳﻭﺭ ﺮﮔ ﺖﺳﺍ . ﻲﻳﺍﺭﺎﻛ ﺵﻭﺭ ﻪﺋﺍﺭﺍ ﻩﺪﺷ ﻂﺳﻮﺗ ﻪﻴﺒﺷ ﻱﺯﺎﺳ ﺭﺩ ﻂﻳﺍﺮﺷ ﻒﻠﺘﺨﻣ ﻭ ﺭﺩ ﻪﺴﻳﺎﻘﻣ ﺎﺑ ﻲﺷﻭﺭ ﻪﺑﺎﺸﻣ ﻥﺎﺸﻧ ﻩﺩﺍﺩ ﻩﺪﺷ ﺖﺳﺍ . ﻦﻴﻨﭽﻤﻫ ﻦﻳﺍ

ﺵﻭﺭ ﻪﺑ ﺕﺭﻮﺻ ﻲﻠﻤﻋ ﺭﺩ ﻝﺮﺘﻨﻛ ﻚﻳ ﺕﺎﺑﺭ ﻙﺮﺤﺘﻣ ﻪﺑ ﺭﺎﻛ ﻪﺘﻓﺭ ﺖﺳﺍ .

ﻠﻛ ﺕﺎﻤﻠﻛ ﻴ

:ﻱﺪ ﺮﻴﺴﻣ ﻪﻨﻴﻬﺑ ﺖﻳﻭﺭ

،ﺮﮔ ﺪﻴﻟﻮﺗ ﮓﻧﺭﺩﻼﺑ

،ﺮﻴﺴﻣ ﻥﺎﻜﻣ ﻲﺑﺎﻳ ﻑﺪﻫ ﺎﻬﻨﺗ ﺎﺑ ﻪﻳﻭﺍﺯ

،ﺖﻤﺳ ﺮﺘﻠﻴﻓ ﻦﻤﻟﺎﻛ ﻪﻌﺳﻮﺗ

،ﻪﺘﻓﺎﻳ ﻥﺍﺪﻴﻣ ﺪﻳﺩ

ﺩﻭﺪﺤﻣ .

Observer Path Planning for Bearings-Only Localization Considering Limited Field of View

Amirhossein Nayebi-Astaneh, Naser Pariz, Mohammad-Bagher Naghibi- Sistani

Abstract: Optimal control of an observer trying to localize a stationary target is presented. The objective is to generate the control signal in order to reduce the position estimate error. The trace of estimation error covariance matrix at final time is selected as the optimality criterion. This problem is solved by presenting a control policy which relates the observer course to the target bearing. In addition to generating paths in real-time which are very close to the optimal path, the advantage of the proposed method is its ability to consider the observer’s field of view. In comparison to a similar method, the performance of the proposed method is shown using various simulations. This method is also applied to the control of a mobile robot.

Keywords: Optimal Observer Path, Real-Time Path Planning, Bearings-only Target Localization, Extended Kalman Filter, Limited Field of View.

0B

1 - ﻪﻣﺪﻘﻣ

ﻥﺎﻜﻣ ﺯﺍ ﻩﺩﺎﻔﺘﺳﺍ ﺎﺑ ﻑﺪﻫ ﻲﺑﺎﻳ ﺲﺣ

ﺎﻫﺮﮔ ﻱ ﻝﺎﻌﻓﺮﻴﻏ ﺭﺩ ﻱﺩﺎﻳﺯ ﻱﺎﻫﺩﺮﺑﺭﺎﻛ

ﻲﻣ ﻥﺎﻴﻣ ﻦﻳﺍ ﺭﺩ .ﺩﺭﺍﺩ ﻲﻋﺎﻓﺩ ﺮﻴﻏ ﻭ ﻲﻋﺎﻓﺩ ﻊﻳﺎﻨﺻ ﻥﺎﻜﻣ ﻪﺑ ﻥﺍﻮﺗ

ﻲﺑﺎﻳ

ﻝﺎﻌﻓﺮﻴﻏ ﻥﺎﻜﻣ ﻭ ﻑﺍﺪﻫﺍ ﻲﺳﺮﺘﺳﺩ ﻪﻄﻘﻧ ﻲﺑﺎﻳ

P0F

1

Pﻪﻜﺒﺷ ﺭﺩ ﻲﺑ ﻱﺎﻫ ﻢﻴﺳ

.ﺩﻮﻤﻧ ﻩﺭﺎﺷﺍ ﻲﺗﺍﺮﺑﺎﺨﻣ ﻪﻠﻤﺟﺯﺍ

ﻝﻮﻤﻌﻣ ﻦﻳﺮﺗ ﺲﺣ ﺎﻫﺮﮔ ﻱ ﻝﺎﻌﻓﺮﻴﻏ ،

ﺲﺣ ﺎﻫﺮﮔ ﻲﻳ ﻩﺯﺍﺪﻧﺍ ﻲﻳﺎﻧﺍﻮﺗ ﺎﻬﻨﺗ ﻪﻛ ﺪﻨﺘﺴﻫ ﺍﺭ ﻑﺪﻫ ﺖﻤﺳ ﻪﻳﻭﺍﺯ ﻱﺮﻴﮔ

ﻥﺎﻜﻣ ﻪﻟﺎﻘﻣ ﻦﻳﺍ ﺭﺩ .ﺪﻧﺭﺍﺩ ﺖﻳﻭﺭ ﻚﻳ ﻂﺳﻮﺗ ﻦﻛﺎﺳ ﻑﺪﻫ ﻚﻳ ﻲﺑﺎﻳ

ﺮﮔ

ﻪﺑ ﺰﻬﺠﻣ ﻙﺮﺤﺘﻣ ﺲﺣ

ﺮﮔ ﺨﺸﺗ ﻴ ﺺ ﻩﺪﻨﻫﺩ ﺖﻤﺳ ﺮﻈﻧﺪﻣ .ﺖﺳﺍ

ﺖﻳﻭﺭ ﻱﺮﻳﺬﭘ ﻪﻧﺎﻣﺎﺳ ﺎﻫ ﻱ ﻥﺎﻜﻣ ﺖﻤﺳ ﻪﻳﻭﺍﺯ ﺮﺑ ﻲﻨﺘﺒﻣ ﺏﺎﻳ

ًﻼﻣﺎﻛ ﻪﺑ ﻪﺘﺴﺑﺍﻭ

ﺖﻳﻭﺭ ﻂﺳﻮﺗ ﻩﺪﺷ ﻩﺩﻮﻤﻴﭘ ﺮﻴﺴﻣ ﺮﮔ

ﺖﺳﺍ ﻲﻄﺧﺮﻴﻏ ﻞﻴﻟﺩ ﻪﺑ ﺮﮕﻳﺩ ﻑﺮﻃ ﺯﺍ .

ﻥﺍﻮﺘﺑ ﻥﺁ ﻂﺳﻮﺗ ﻪﻛ ﻱﺭﺎﻴﻌﻣ ﻦﻴﻴﻌﺗ ،ﻢﺘﺴﻴﺳ ﻝﺪﻣ ﻥﺩﻮﺑ ﻪﺑ

ﺭﻮﻃ ﻖﻴﻗﺩ

ﺖﻳﻭﺭ ﺐﻠﻏﺍ ﺪﻴﺠﻨﺳ ﺍﺭ ﻢﺘﺴﻴﺳ ﻱﺮﻳﺬﭘ ﻏﻴ

ﻦﻜﻤﻣﺮ ﺯﺍ ﻩﺩﺎﻔﺘﺳﺍ ،ﺍﺬﻟ ؛ﺖﺳﺍ

ﻦﻴﻨﭼ ﺭﺎﻛﺩﻮﺧ ﻝﺮﺘﻨﻛ.ﺖﺳﺍ ﻱﺭﻭﺮﺿ ﺭﺎﻴﻌﻣ ﻦﻳﺍ ﻦﻴﻴﻌﺗ ﺭﺩ ﺐﻳﺮﻘﺗ ﺖﻳﻭﺭ ﺮﺘﺸﻴﺑ ﻪﭼﺮﻫ ﺶﻫﺎﻛ ﺚﻋﺎﺑ ﻪﻛ ﻱﺮﻴﺴﻣ ﺭﺩ ﻱﺮﮔ ﺭﺍﻭﻮﻛ

ﻳ ﺲﻧﺎ ﻱﺎﻄﺧ

ﻑﺪﻫ ﻥﺎﻜﻣ ﻦﻴﻤﺨﺗ ﻪﺑ

ﻥﺍﻮﻨﻋ ﺖﻳﻭﺭ ﻱﺍﺮﺑ ﻲﺒﻳﺮﻘﺗ ﻱﺭﺎﻴﻌﻣ ﺰﺋﺎﺣ ،ﺩﻮﺷ ﻱﺮﻳﺬﭘ

ﺪﻳﺩ ﻥﺍﺪﻴﻣ ﻦﻴﻨﭽﻤﻫ .ﺖﺳﺍ ﺖﻴﻤﻫﺍ

P1F

2

Pﺖﻳﻭﺭ ﺩﻭﺪﺤﻣ ﺍﺭ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻪﻛ ﺮﮔ

ﺖﺤﺗ ﺛﺄﺗ ﻴﺮ ﻲﻣ ﺭﺍﺮﻗ ﺰﻴﻧ ﺪﻫﺩ ﻪﻠﺌﺴﻣ ﺍ ﻱ .ﺩﻮﺷ ﻪﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ ﺪﻳﺎﺑ ﻪﻛ ﺖﺳﺍ

ﻱﺎﻫﺭﺎﻛ ﺮﺜﻛﺍ ﻡﺎﺠﻧﺍ

ﻩﺪﺷ ﻥﺎﻜﻣ ﻱﺍﺮﺑ ﺯﻭﺮﻣﺍ ﻪﺑ ﺎﺗ ﺭﺎﻬﭼ ﺱﺎﺳﺍ ﺮﺑ ﻑﺪﻫ ﻲﺑﺎﻳ

ﻩﺯﺍﺪﻧﺍ ﻉﻮﻧ ﻱﺮﻴﮔ AOA^P2F3P ] 1[

، TOA^P3F4P ] 2[

، TDOA^P4F5P ] 3[

ﻭ RSS^P5F6P ] 4[

ﻲﻣ ﻥﺎﻜﻣ ﺭﺩ .ﺪﻨﺷﺎﺑ ﻩﺯﺍﺪﻧﺍ ،ﺖﻤﺳ ﻪﻳﻭﺍﺯ ﺎﺑ ﺎﻬﻨﺗ ﻲﺑﺎﻳ

ﻱﺮﻴﮔ ﺯﺍ ﺎﻫ ﻉﻮﻧ AOA

ﻪﻛ ﺖﺳﺍ ﻦﻳﺍ ﺮﺑ ﺽﺮﻓ .ﺪﻨﺘﺴﻫ ﺲﺣ

ﺮﮔ ﺪﻧﺭﺍﺩ ﺭﺍﺮﻗ ﻪﺤﻔﺻ ﻚﻳ ﺭﺩ ﻑﺪﻫ ﻭ

ﻲﻣ ﻩﺪﻴﺠﻨﺳ ﻲﻳﺎﻴﻓﺍﺮﻐﺟ ﻝﺎﻤﺷ ﻪﺑ ﺖﺒﺴﻧ ﺖﻤﺳ ﻪﻳﻭﺍﺯ ﻭ .ﺩﻮﺷ

ﻪﻠﻤﺟﺯﺍ

ﺲﺣ ﻱﺎﻫﺮﮔ ﺨﺸﺗ ﻴ ﺺ ﻩﺪﻨﻫﺩ ﻲﻣ ﺖﻤﺳ ﻪﻳﻭﺍﺯ ﻦﻴﺑﺭﻭﺩ ﻪﺑ ﻥﺍﻮﺗ

]5 [ ﻭ

ﻦﺘﻧﺁ ﻲﻳﻮﻳﺩﺍﺭ ﻱﺎﻫ ﺨﺸﺗ

ﻴ ﺺ ﻩﺪﻨﻫﺩ ﺖﻬﺟ ]6 [ .ﺩﻮﻤﻧ ﻩﺭﺎﺷﺍ

ﺖﻳﻭﺭ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻦﻴﻴﻌﺗ ﻥﺎﻜﻣ ﺭﺩ ﺮﮔ

ﻪﻛ ﺖﺳﺍ ﻲﻋﻮﺿﻮﻣ ﺖﻤﺳ ﻪﻳﻭﺍﺯ ﺎﺑ ﻲﺑﺎﻳ

ﺭﺎﻴﺴﺑ ﻪﺟﻮﺗﺩﺭﻮﻣ ﻱﺎﻫﺭﺎﻛ ﺐﻠﻏﺍ ﺭﺩ .ﺖﺴﻫ ﻭ ﻩﺩﻮﺑ ﻥﺍﺮﮕﺸﻫﻭﮋﭘ ﻡﺎﺠﻧﺍ

ﻩﺪﺷ

ﺮﺸﻴﻓ ﺕﺎﻋﻼﻃﺍ ﺲﻳﺮﺗﺎﻣ ﺯﺍ ﺮﻟﺎﻜﺳﺍ ﻲﻌﺑﺎﺗ

P6F

7

P ﻪﺑ

ﻥﺍﻮﻨﻋ ﻲﮕﻨﻴﻬﺑ ﺭﺎﻴﻌﻣ

ﻩﺩﺎﻔﺘﺳﺍﺩﺭﻮﻣ ﻪﺘﻓﺮﮔﺭﺍﺮﻗ

.ﺖﺳﺍ ﻪﺑ ﻥﺍﻮﻨﻋ ﻝﺎﺜﻣ ] 7[

ﻥﺎﻨﻴﻣﺮﺗﺩ ﺯﺍ ﺲﻳﺮﺗﺎﻣ

ﺮﺸﻴﻓ ﺕﺎﻋﻼﻃﺍ ﺭﺎﻴﻌﻣ ﺎﺑ ﻲﻜﻳﺩﺰﻧ ﻁﺎﺒﺗﺭﺍ ﻪﻛ ﺖﺳﺍ ﻩﺩﻮﻤﻧ ﻩﺩﺎﻔﺘﺳﺍ

ﻲﮕﻨﻴﻬﺑ D

]8 [ ﺭﺩ .ﺩﺭﺍﺩ ﺭﺎﻣﺁ ﻢﻠﻋ ﺶﻳﺎﻣﺯﺁ ﺡﺮﻃ ﻱﺭﻮﺌﺗ ﺭﺩ ]9

[ ﻭ ] 10 [ ﻩﺪﺷ ﻩﺩﺍﺩ ﻥﺎﺸﻧ

ﺱﻮﻜﻌﻣ ﺮﺛﺍ ﺯﺍ ﻩﺩﺎﻔﺘﺳﺍ ﻪﻛ ﺖﺳﺍ ﺮﺸﻴﻓ ﺕﺎﻋﻼﻃﺍ ﺲﻳﺮﺗﺎﻣ

ﺭﺎﻴﻌﻣ ﻪﺑ ﻪﻛ)

ﻲﮕﻨﻴﻬﺑ ﻥﺎﻜﻣ ﺭﺩ (ﺖﺳﺍ ﺭﻮﻬﺸﻣA ﺭﺎﻴﻌﻣ ﺖﻤﺳ ﻪﻳﻭﺍﺯ ﺎﺑ ﻲﺑﺎﻳ

ﺐﺳﺎﻨﻣ ﺮﺗ ﻱ

ﺭﺎﻴﻌﻣ ﻪﺑ ﺖﺒﺴﻧ ﻲﮕﻨﻴﻬﺑ

ﺖﺳﺍD .

ﺏﺎﺨﺘﻧﺍ ﻪﺑ ﻁﻮﺑﺮﻣ ﺩﺭﺍﺩ ﺩﻮﺟﻭ ﻲﮕﻨﻴﻬﺑ ﺭﺎﻴﻌﻣ ﺏﺎﺨﺘﻧﺍ ﺭﺩ ﻪﻛ ﻱﺮﮕﻳﺩ ﻪﻠﺌﺴﻣ ﺭﺎﻴﻌﻣ ﻪﻛ ﺖﺳﺍ ﻲﻧﺎﻣﺯ ﺮﻈﻧﺩﺭﻮﻣ

ﻲﻣ ﻪﻨﻴﻬﺑ ﻥﺎﻣﺯ ﻥﺁ ﺭﺩ .ﺩﻮﺷ

ﻪﺑ ﻥﺍﻮﻨﻋ ﺭﺩ ﻝﺎﺜﻣ

]7 [ ﻥﺎﻨﻴﻣﺮﺗﺩ ﻥﺩﺮﻛ ﻪﻨﻴﺸﻴﺑ ﺮﺸﻴﻓ ﺕﺎﻋﻼﻃﺍ ﺲﻳﺮﺗﺎﻣ

،ﺮﺗﻮﻠﺟ ﻡﺎﮔ ﻚﻳ ﺭﺩ

1Access Point

2Field Of View

3Angle of Arrival

4Time of Arrival

5Time Delay of Arrival

6Receive Signal Strength

7Fisher Information Matrix ﺖﻳﻭﺭ ﺮﻴﺴﻣ ﻦﻴﻴﻌﺗ ﺭﺎﻴﻌﻣ

ﺮﮔ ﺖﺳﺍ ؛ ﺗﺭﻮﺻﺭﺩ ﻲ ﻪﻛ ﺭﺩ ] 11 [ ﺩﺮﻛ ﻪﻨﻴﺸﻴﺑ ﻥ

ﻥﺎﻨﻴﻣﺮﺗﺩ ﺮﺸﻴﻓ ﺕﺎﻋﻼﻃﺍ ﺲﻳﺮﺗﺎﻣ .ﺖﺳﺍ ﻩﺪﺷ ﻪﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ ﻲﻳﺎﻬﻧ ﻪﻈﺤﻟ ﺭﺩ

ﻱﺎﻫﺮﻴﺴﻣ ﻟﻮﺗ ﻴ ﻩﺪﺷﺪ ﺵﻭﺭ ﺎﺑ ﺮﻈﻧ ﺭﺩ ﺍﺭ ﻮﻠﺟ ﻪﺑ ﻡﺎﮔ ﻚﻳ ﺎﻬﻨﺗ ﻪﻛ ﻲﻳﺎﻫ

ﻲﻣ ﺪﻧﺮﻴﮔ ﻪﺑ ﺕﺭﻮﺻ ﻲﻣ ﻑﺪﻫ ﻝﻮﺣ ﭻﻴﭘﺭﺎﻣ ﺪﻨﺷﺎﺑ

] 12 [ ﺭﺩ ﺮﮕﻳﺩ ﻑﺮﻃ ﺯﺍ .

ﺵﻭﺭ ﻪﻨﻴﻬﺑ ﻪﻛ ﻲﻳﺎﻫ ﻪﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ ﺍﺭ ﻲﻳﺎﻬﻧ ﻥﺎﻣﺯ ﺭﺩ ﻱﺯﺎﺳ

ﻴﺴﻣ ﺪﻧﺍ ﻪﻨﻴﻬﺑ ﺮ

ﻪﺑ ﻪﻧﻮﮔ ﺍ ﻱ ﺖﻳﻭﺭ ﺍﺪﺘﺑﺍ ﺭﺩ ﻪﻛ ﺩﻮﺑ ﺪﻫﺍﻮﺧ ﻩﺩﺮﻛ ﻚﻳﺩﺰﻧ ﻑﺪﻫ ﻪﺑ ﺍﺭ ﺩﻮﺧ ﺮﮔ

ﻲﻣ ﻥﺁ ﻥﺩﺯ ﺭﻭﺩ ﻪﺑ ﻉﻭﺮﺷ ﺲﭙﺳ ﻭ ﺪﻨﻛ

] 13 [.

ﺮﺜﻛﺍ ﺲﺣ ﺎﻫﺮﮔ ﻲﻳ ﻩﺯﺍﺪﻧﺍ ﻱﺍﺮﺑ ﻪﻛ ﻲﻣ ﻩﺩﺎﻔﺘﺳﺍ ﺖﻤﺳ ﻪﻳﻭﺍﺯ ﻱﺮﻴﮔ

،ﺪﻧﻮﺷ

ﺖﻳﻭﺭ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻦﻴﻴﻌﺗ ﺭﺩ ﻪﻛ ﺪﻧﺭﺍﺩ ﻱﺩﻭﺪﺤﻣ ﺪﻳﺩ ﻥﺍﺪﻴﻣ ﻅﺎﺤﻟ ﺪﻳﺎﺑ ﺮﮔ

ﺭﺩ .ﺩﻮﺷ ] 11 [ ﺪﻴﻗ ﺩﻮﺟﻭ ﻪﺑ ﺕﺭﻮﺻ ﺮﻈﻧ ﺭﺩ ﻲﻠﻛ ﻪﺘﻓﺮﮔ

ﻩﺪﺷ ﻪﻛ ﺖﺳﺍ

ﻲﻣ ﺪﻴﻗ ﻞﻣﺎﺷ ﺪﻧﺍﻮﺗ ﺪﻳﺩ ﻥﺍﺪﻴﻣ

ﺵﻭﺭ ﻲﻟﻭ ﺪﺷﺎﺑ ﺰﻴﻧ ﻪﺋﺍﺭﺍ

ﻩﺪﺷ ﻥﻭﺮﺑ ﻂﺧ

P7F

8

P

ﻊﺟﺮﻣ .ﺖﺳﺍ ]7

[ ﻲﺷﻭﺭ ﻭ ﺖﺳﺍ ﻪﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ ﺍﺭ ﻲﻠﻛ ﺖﻟﺎﺣ ﺭﺩ ﺪﻴﻗ ﺰﻴﻧ

ﻪﻨﻴﻬﺑ ﺮﺑ ﻲﻨﺘﺒﻣ ﺯﺎﺳ

ﻥﺎﻨﻴﻣﺮﺗﺩ ﻱ ﺮﺸﻴﻓ ﺕﺎﻋﻼﻃﺍ ﺲﻳﺮﺗﺎﻣ

ﻮﻠﺟ ﻪﺑ ﻡﺎﮔ ﻚﻳ ﺭﺩ

ﺭﺩ ﻪﻛ ﺖﺳﺍ ﻩﺩﺍﺩ ﻪﺋﺍﺭﺍ ﻪﻈﺤﻟﺮﻫ

ﻪﻨﻴﻬﺑ ﻪﻠﺌﺴﻣ ﻚﻳ ﻦﻴﻴﻌﺗ ﻱﺍﺮﺑ ﻲﻄﺧﺮﻴﻏ ﻱﺯﺎﺳ

ﺖﻳﻭﺭ ﺖﻛﺮﺣ ﺖﻬﺟ ﻲﻣ ﻞﺣ ﺮﮔ

ﺵﺯﺍﺩﺮﭘ ﻭ ﺩﻮﺷ

ًﺎﺘﺒﺴﻧ ﻲﻣ ﺍﺭ ﻱﺩﺎﻳﺯ .ﺪﺒﻠﻃ

ﺭﺩ ] 14 [ ﺪﻴﻗ ﺪﻳﺩ ﻥﺍﺪﻴﻣ ﻱﺍﺮﺑ ﻮﺠﺘﺴﺟ ﺮﺑ ﻲﻨﺘﺒﻣ ﻲﺷﻭﺭ ﻭ ﻩﺪﺷ ﻪﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ

ﺖﻳﻭﺭ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻦﻴﻴﻌﺗ ﻥﺎﻣﺯ ﺶﻫﺎﻛ ﻱﺍﺮﺑ ﻥﺁ ﺭﺩ ﻪﻛ ﺖﺳﺍ ﻩﺪﺷ ﻪﺋﺍﺭﺍ ﺮﮔ

ﺍﺭ ﻲﻳﺎﻫﺮﻴﺴﻣ ﺍﺪﺘﺑﺍ ﻮﺠﺘﺴﺟ ﻪﺑ

ﺕﺭﻮﺻ ﻪﻌﻄﻗ ﻪﻌﻄﻗ ﻲﻄﺧ ﻪﺑ ﻥﺍﻮﻨﻋ ﻱﺎﻫﺮﻴﺴﻣ

ﻲﻣ ﺪﻴﻟﻮﺗ ﺪﻳﺪﻧﺎﻛ ﻦﻴﺑ ﺭﺩ ﺲﭙﺳ ﺪﻨﻛ

ﺍﺭ ﺮﻴﺴﻣ ﻦﻳﺮﺘﻬﺑ ،ﺪﻳﺪﻧﺎﻛ ﻱﺎﻫﺮﻴﺴﻣ

ﻲﻣ ﻮﺠﺘﺴﺟ ﺎﺑ ﺵﻭﺭ ﻦﻳﺍ ﺭﺩ .ﺪﻨﻛ ﺯﻳ

ﻥﺪﺷﺩﺎ ﺖﻳﻭﺭ ﻪﻠﺻﺎﻓ ﺩﺍﺪﻌﺗ ﻑﺪﻫ ﺯﺍ ﺮﮔ

ﺰﻴﻧ ﺪﻳﺪﻧﺎﻛ ﻱﺎﻫﺮﻴﺴﻣ ﻪﺑ

ﺕﺪﺷ ﻲﻣ ﺶﻳﺍﺰﻓﺍ ﺵﻭﺭ ﻥﺪﺷ ﺪﻨﻛ ﺚﻋﺎﺑ ﻭ ﺪﺑﺎﻳ

ﻪﺋﺍﺭﺍ ﻩﺪﺷ ﻲﻣ .ﺩﻮﺷ

ﺵﻼﺗ .ﺖﺳﺍ ﻪﺘﻓﺮﮔ ﺕﺭﻮﺻ ﻉﻮﺿﻮﻣ ﻦﻳﺍ ﻲﻠﻴﻠﺤﺗ ﻞﺣ ﻱﺍﺮﺑ ﺰﻴﻧ ﻲﻳﺎﻫ

ﻪﺑ ﻥﺍﻮﻨﻋ ﻝﺎﺜﻣ ﺭﺩ ] 13 [ ﻥﺎﻨﻴﻣﺮﺗﺩ ﻱﺍﺮﺑ ﻦﻴﻳﺎﭘ ﺪﺣ ﻚﻳ ﻦﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ ﺎﺑ

ﺮﺸﻴﻓ ﺕﺎﻋﻼﻃﺍ ﺲﻳﺮﺗﺎﻣ ﻲﻳﺎﻬﻧ ﻪﻈﺤﻟ ﺭﺩ

] 15 [ ﺏﺎﺴﺣ ﻱﺭﻮﺌﺗ ﺯﺍ ﻩﺩﺎﻔﺘﺳﺍ ﺎﺑ ﻭ

ﻪﻄﺑﺍﺭ ،ﺕﺍﺮﻴﻴﻐﺗ ﺖﻳﻭﺭ (ﺱﺭﻮﻛ) ﺖﻛﺮﺣ ﺖﻬﺟ ﻦﻴﺑ ﻱﺍ

ﺖﻤﺳ ﻪﻳﻭﺍﺯ ﻭ ﺮﮔ

.ﺖﺳﺍ ﻩﺪﺷ ﻪﺋﺍﺭﺍ ﺪﻳﺩ ﻥﺍﺪﻴﻣ ﺪﻴﻗ ﻦﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ ﻥﻭﺪﺑ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﺭﺩ ﻑﺪﻫ ﻊﺟﺮﻣ ﺭﺩ ] 16 [ ﺭﺎﻴﻌﻣ ﻭﺩ ﻦﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ ﺎﺑ ﺰﻴﻧ ﻲﮕﻨﻴﻬﺑ

ﺩﺮﺑ ﻦﻴﻤﺨﺗ ﺖﻗﺩ ﻭD

ﻩﺪﺷ ﻲﻌﺳ ،ﺪﻳﺩ ﻥﺍﺪﻴﻣ ﺪﻴﻗ ﻦﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ ﻥﻭﺪﺑ ﻭ ﻲﻳﺎﻬﻧ ﻪﻈﺤﻟ ﺭﺩ ﻑﺪﻫ ﺮﺑ ﻲﻠﻴﻠﺤﺗ ﻲﺷﻭﺭ ﺎﺗ ﺖﺳﺍ ﺎﻬﻨﺗ ﻥﺎﻳﺎﭘ ﺭﺩ ﻲﻟﻭ ﺩﻮﺷ ﻪﺋﺍﺭﺍ ﻪﻠﺌﺴﻣ ﻦﻳﺍ ﻞﺣ ﻱﺍ

ﻞﺣ ﻪﺑ ﻖﻓﻮﻣ ﻪﻠﺌﺴﻣ

ﻪﺑ ﺕﺭﻮﺻ ﻲﻠﻴﻠﺤﺗ - ﺭﺩ .ﺖﺳﺍ ﻩﺪﺷ ﻱﺩﺪﻋ ]

17 [ ﺎﺑ

ﻩﺩﺎﺳ ﺖﻳﻭﺭ ﻲﻳﺎﻬﻧ ﺖﻟﺎﺣ ﻦﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ ﺖﺑﺎﺛ ﻭ ﻱﺯﺎﺳ ﻥﻭﺪﺑ ﻦﻴﻨﭽﻤﻫ ﻭ ﺮﮔ

ﺪﻴﻣ ﺪﻴﻗ ﻪﺑ ﻪﺟﻮﺗ .ﺖﺳﺍ ﻩﺪﺷ ﻪﺋﺍﺭﺍ ﻱﺯﺎﺑ ﻪﻘﻠﺣ ﻪﻨﻴﻬﺑ ﻝﺮﺘﻨﻛ ،ﺪﻳﺩ ﻥﺍ

ﺖﻳﻭﺭ ﻚﻳ ﻝﺮﺘﻨﻛ ﻱﺍﺮﺑ ﮓﻧﺭﺩﻼﺑ ﻲﺷﻭﺭ ﻪﻟﺎﻘﻣ ﻦﻳﺍ ﺭﺩ ﺭﺩ ﻙﺮﺤﺘﻣ ﺮﮔ

ﺖﻳﻭﺭ ﻪﻛ ﺖﺳﺍ ﻩﺪﺷ ﺽﺮﻓ .ﺖﺳﺍ ﻩﺪﺷ ﻪﺋﺍﺭﺍ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﺩﻮﺧ ﻥﺎﻜﻣ ﺯﺍ ﺮﮔ

ﻦﻤﻟﺎﻛ ﺮﺘﻠﻴﻓ ﻝﺎﻤﻋﺍ ﺎﺑ ﻭ ﺖﺳﺍ ﻩﺎﮔﺁ ﻪﻌﺳﻮﺗ

ﻳ ﻪﺘﻓﺎ (EKF)^P8F9P ﻱﻭﺭ ﺮﺑ

ﻩﺯﺍﺪﻧﺍ ﻱﺮﻴﮔ ﺖﻤﺳ ﻪﻳﻭﺍﺯ ﻱﺎﻫ ﻪﺑ

ﺖﺳﺩ ﻣﺁ ﻩﺪ ﺖﻴﻌﻗﻮﻣ ﺎﺑ) ﻦﻛﺎﺳ ﻲﻓﺪﻫ ﺯﺍ

ﻲﻣ ﻦﻴﻤﺨﺗ ﺍﺭ ﻥﺁ ﻥﺎﻜﻣ ،(ﻡﻮﻠﻌﻣﺎﻧ ،ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﺕﺎﻴﺻﻮﺼﺧ ﻲﺳﺭﺮﺑ ﺎﺑ .ﺪﻧﺯ

ﻲﻣ ﻩﺩﺍﺩ ﻥﺎﺸﻧ ﻪﻄﺑﺍﺭ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﺭﺩ ﻪﻛ ﺩﻮﺷ

ﻦﻴﺑ ﻱﺍ ﺖﻳﻭﺭ ﺱﺭﻮﻛ ﻭ ﺮﮔ

8Offline

9Extended Kalman Filter

ﻪﻧﺎﺘﺳﺁ ﻲﺒﻳﺎﻧ ﻦﻴﺴﺣﺮﻴﻣﺍ ،

ﻲﻧﺎﺘﺴﻴﺳ ﻲﺒﻴﻘﻧ ﺮﻗﺎﺑﺪﻤﺤﻣ ،ﺰﻳﺮﭘ ﺮﺻﺎﻧ

ﻪﻴﻟﻭﺍ ﺖﻴﻌﻗﻮﻣ ﺯﺍ ﻞﻘﺘﺴﻣ ﻪﻄﺑﺍﺭ ﻦﻳﺍ ﻭ ﺩﺭﺍﺩ ﺩﻮﺟﻭ ﻑﺪﻫ ﺖﻤﺳ ﻪﻳﻭﺍﺯ ﺖﻳﻭﺭ ﻑﺪﻫ ﺖﻴﻌﻗﻮﻣ ﻭ ﺮﮔ ﺖﺳﺍ

ﻄﺧ ﻊﺑﺎﺗ ﻚﻳ ﺵﺯﺍﺮﺑ ﺎﺑ . ﻱﻭﺭ ﺮﺑ ﻱﺮﺴﻛ ﻲ

ﻩﺩﺍﺩ ﻱﺎﻫ ﻪﺑ ﺖﺳﺩ ﻩﺪﻣﺁ ﻪﻴﺒﺷ ﺯﺍ ﻲﺑﻮﺧ ﺭﺎﻴﺴﺑ ﺐﻳﺮﻘﺗ ﺎﺑ ﻪﻄﺑﺍﺭ ﻦﻳﺍ ،ﻱﺯﺎﺳ ﻪﺑ

ﺖﺳﺩ ﻲﻣ ﻭ ﺪﻳﺁ ﻪﺑ ﺭﻮﻈﻨﻣ ﺖﻳﻭﺭ ﻪﺘﺴﺑ ﻪﻘﻠﺣ ﺖﻳﺍﺪﻫ ﻥﻮﻧﺎﻗ ،ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﺭﺩ ﺮﮔ

ﻲﻣ ﻪﺋﺍﺭﺍ ﻥﺁ ﺱﺎﺳﺍ ﺮﺑ ﻲﻟﺮﺘﻨﻛ ﻥﻮﻧﺎﻗ ﺲﭙﺳ .ﺩﻮﺷ

ﻪﺋﺍﺭﺍ ﻩﺪﺷ ﻪﺑ ﻪﻧﻮﮔ ﺍ ﻱ ﺡﻼﺻﺍ

ﻲﻣ ﺖﻳﺩﻭﺪﺤﻣ ﺎﺗ ﺩﻮﺷ ﺪﻳﺩ ﻥﺍﺪﻴﻣ

ﺲﺣ ﺮﮔ ﺮﻴﺴﻣ ﻦﻴﻴﻌﺗ ﻱﺍﺮﺑ .ﺩﻮﺷ ﻅﺎﺤﻟ ﺰﻴﻧ

ﻲﮕﻨﻴﻬﺑ ﺭﺎﻴﻌﻣ ﺯﺍ ﻪﻨﻴﻬﺑ ﻩﺩﺎﻔﺘﺳﺍ (ﺮﺸﻴﻓ ﺕﺎﻋﻼﻃﺍ ﺲﻳﺮﺗﺎﻣ ﺱﻮﻜﻌﻣ ﺮﺛﺍ)A

.ﺖﺳﺍ ﻩﺪﺷ ﻪﻛﺎﺠﻧﺁﺯﺍ

ﺮﺸﻴﻓ ﺕﺎﻋﻼﻃﺍ ﺲﻳﺮﺗﺎﻣ ﺖﻳﻭﺭ ﺮﻴﺴﻣ ﺮﺑ ﻩﻭﻼﻋ

ﻪﺑ ﺮﮔ

ﻑﺪﻫ ﻥﺎﻜﻣ ﻲﻌﻗﺍﻭ ﺭﺍﺪﻘﻣ ﻭ ﺖﺳﺍ ﻪﺘﺴﺑﺍﻭ ﺰﻴﻧ ﻑﺪﻫ ﻥﺎﻜﻣ ﻲﻌﻗﺍﻭ ﺭﺍﺪﻘﻣ ﻃﺍ ﺲﻳﺮﺗﺎﻣ ﺯﺍ ﻩﺩﺎﻔﺘﺳﺍ ﻞﻤﻋ ﺭﺩ ،ﺖﺴﻴﻧ ﻡﻮﻠﻌﻣ ﻥﺎﻜﻣﺍ ﺮﺸﻴﻓ ﺕﺎﻋﻼ

ﺮﻳﺬﭘ

ﻧﻴ ﺖﺴ ﺯﺍ ﺍﺬﻟ ، ﺭﺍﻭﻮﻛ ﻳ ﺲﻧﺎ ﻦﻴﻤﺨﺗ ﻱﺎﻄﺧ ﻪﺑ

ﻥﺍﻮﻨﻋ ﺱﻮﻜﻌﻣ ﺯﺍ ﻲﺒﻳﺮﻘﺗ

ﺮﺸﻴﻓ ﺕﺎﻋﻼﻃﺍ ﺲﻳﺮﺗﺎﻣ .ﺖﺳﺍ ﻩﺪﺷ ﻩﺩﺎﻔﺘﺳﺍ

ﻊﻗﺍﻭﺭﺩ ﺮﺛﺍ ،ﻲﮕﻨﻴﻬﺑ ﺭﺎﻴﻌﻣ

ﺭﺍﻭﻮﻛ ﻳ ﺲﻧﺎ ﺖﺳﺍ ﻩﺪﺷ ﻪﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ ﻲﻳﺎﻬﻧ ﻪﻈﺤﻟ ﺭﺩ ﻥﺎﻜﻣ ﻦﻴﻤﺨﺗ ﻱﺎﻄﺧ

ﻲﻣ ﻩﺩﺍﺩ ﻥﺎﺸﻧ ﻭ ﺮﺘﺸﻴﺑ ﺶﻫﺎﻛ ﺚﻋﺎﺑ ﺭﺎﻴﻌﻣ ﻦﻳﺍ ﻪﻛ ﺩﻮﺷ

ﺍﻭﻮﻛ ﺭﻳ ﺲﻧﺎ ﻱﺎﻄﺧ

ﺭﺩ ﻦﻴﻤﺨﺗ ﺕﺪﻣﺯﺍﺭﺩ ﺵﻭﺭ .ﺪﺷ ﺪﻫﺍﻮﺧ ﻮﻠﺟ ﻪﺑ ﻡﺎﮔ ﻚﻳ ﺵﻭﺭ ﻪﺑ ﺖﺒﺴﻧ

ﻪﺋﺍﺭﺍ ﻩﺪﺷ ﺵﻭﺭ ﺪﻨﻧﺎﻣ ﻪﻟﺎﻘﻣ ﻦﻳﺍ ﺭﺩ Hammel

] 13 [ ﻪﻄﺑﺍﺭ ﺱﺭﻮﻛ ﻦﻴﺑ ﻱﺍ

ﺖﻳﻭﺭ ﻲﻣ ﻪﺋﺍﺭﺍ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﺭﺩ ﻑﺪﻫ ﺖﻤﺳ ﻭ ﺮﮔ ﻪﻛ ﺕﻭﺎﻔﺗ ﻦﻳﺍ ﺎﺑ ﺪﻫﺩ

ﻪﻄﺑﺍﺭ Hammel ﻪﻄﺑﺍﺭ

ﻪﻄﺑﺍﺭ ﻭ ﺖﺳﺍ ﻲﻄﺧ ﻱﺍ ﻪﺋﺍﺭﺍ

ﻩﺪﺷ ﻪﻟﺎﻘﻣ ﻦﻳﺍ ﺭﺩ

ﻪﺑ ﺕﺭﻮﺻ ﻱﺮﺴﻛ ﻲﻄﺧ ﺖﺳﺍ

ﺭﺎﻴﺴﺑ ﻱﺎﻫﺮﻴﺴﻣ ﺪﻴﻟﻮﺗ ﺚﻋﺎﺑ ﻪﻛ ﺩﺰﻧ

ﻳ ﻚ ﺮﺗ ﻪﺑ

ﻲﻣ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ .ﺩﻮﺷ

ﻦﻳﺍ ﺵﻭﺭ ﻪﺑ ﺕﺭﻮﺻ ﻲﻠﻤﻋ ﺰﻴﻧ ﺮﺑ ﻱﻭﺭ ﻚﻳ ﺕﺎﺑﺭ ﺎﺑ ﻭﺩ

ﺥﺮﭼ ﻙﺮﺤﻣ ﻭ ﻚﻳ ﻦﻴﺑﺭﻭﺩ ﻞﺼﺘﻣ ﻪﺑ ﻥﺁ ﻪﺑ ﻥﺍﻮﻨﻋ ﺲﺣ ﺮﮔ

ﺨﺸﺗ ﻴ ﺺ ﻩﺪﻨﻫﺩ

،ﺖﻤﺳ ﻩﺩﺎﻴﭘ ﻩﺪﺷ ﺖﺳﺍ .

ﻪﻟﺎﻘﻣ ﻦﻳﺍ ﺭﺎﺘﺧﺎﺳ ﻪﺑ

ﺕﺭﻮﺻ ﺮﻳﺯ ﺖﺳﺍ ﺶﺨﺑ ﺭﺩ . 2

ﺭﺩ ﻪﻠﺌﺴﻣ ﻦﻳﺍ

ﻲﻣ ﻝﺪﻣ ﻪﻨﻴﻬﺑ ﻝﺮﺘﻨﻛ ﻱﺭﻮﺌﺗ ﺏﻮﭼﺭﺎﻬﭼ ﺶﺨﺑ ﺭﺩ ﺲﭙﺳ .ﺩﻮﺷ

3 ﺛﺄﺗ ﻴﺮ ﺮﻴﺴﻣ

ﺖﻳﻭﺭ ﺮﺑ ﺮﮔ ﺭﺍﻭﻮﻛ ﻳ ﺲﻧﺎ ﻲﺳﺭﺮﺑ ﻦﻴﻤﺨﺗ ﻱﺎﻄﺧ ﻲﻣ

ﻩﺩﺍﺩ ﻥﺎﺸﻧ ﻭ ﺩﻮﺷ

ﻲﻣ ﻩﺮﻳﺍﺩ ﺮﺘﺸﻴﺑ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ،ﻲﻳﺎﻬﻧ ﻥﺎﻣﺯ ﺶﻫﺎﻛ ﺎﺑ ﻪﻛ ﺩﻮﺷ ﺪﻫﺍﻮﺧ ﻞﻜﺷ ﻱﺍ

ﺶﺨﺑ ﺭﺩ .ﺩﻮﺑ 4

ﺖﻴﻌﻗﻮﻣ ﻱﺍﺯﺍ ﻪﺑ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﺖﻳﻭﺭ ﻒﻠﺘﺨﻣ ﻱﺎﻫ

ﻭ ﺮﮔ

ﻑﺪﻫ ﻪﺑ ﺕﺭﻮﺻ ﻱﺩﺪﻋ ﻪﺑ ﺖﺳﺩ ﻲﻣ ﻲﻣ ﻩﺩﺍﺩ ﻥﺎﺸﻧ ﻭ ﺪﻳﺁ ﺮﻴﺴﻣ ﺭﺩ ﻪﻛ ﺩﻮﺷ

ﺖﻳﻭﺭ ﺱﺭﻮﻛ ﻦﻴﺑ ﻪﻄﺑﺍﺭ ﻪﻨﻴﻬﺑ ﺖﻴﻌﻗﻮﻣ ﺯﺍ ﻞﻘﺘﺴﻣ ،ﻑﺪﻫ ﺖﻤﺳ ﻭ ﺮﮔ

ﻱﺎﻫ

ﺖﻳﻭﺭ ﻒﻠﺘﺨﻣ ﻑﺪﻫ ﻭ ﺮﮔ

ﺖﺳﺍ ﺶﺨﺑ ﺭﺩ ﻭ ﻪﻣﺍﺩﺍ ﺭﺩ . 5

ﻊﺑﺎﺗ ﻚﻳ ﺵﺯﺍﺮﺑ ﺎﺑ

ﺱﺭﻮﻛ ﺭﺍﺩﻮﻤﻧ ﺮﺑ ﻱﺮﺴﻛ ﻲﻄﺧ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﺭﺩ ﻝﺮﺘﻨﻛ ﻥﻮﻧﺎﻗ ،ﺖﻤﺳ–

ﻝﺮﺘﻨﻛ ﻥﻮﻧﺎﻗ ﺎﺑ ﻥﺁ ﺩﺮﻜﻠﻤﻋ ﻭ ﻞﺻﺎﺣ ﻪﺋﺍﺭﺍ

ﺷ ﻩﺪ ﻂﺳﻮﺗ Hammel ]

13 [

ﻲﻣ ﻪﺴﻳﺎﻘﻣ ﻝﺮﺘﻨﻛ ﻥﻮﻧﺎﻗ ﺮﻴﻴﻐﺗ .ﺩﻮﺷ ﻪﺑ

ﺭﻮﻈﻨﻣ ﺪﻳﺩ ﻥﺍﺪﻴﻣ ﻦﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ

ﺖﻳﻭﺭ ﺩﻭﺪﺤﻣ ﺰﻴﻧ ﺮﮔ

ﺶﺨﺑ ﺭﺩ 6 ﻲﻣ ﻡﺎﺠﻧﺍ ﺶﺨﺑ ﺭﺩ .ﺩﻮﺷ 7

ﻝﺮﺘﻨﻛ ﻪﻠﺌﺴﻣ

ﺖﻳﻭﺭ ﻥﺎﻜﻣ ﺎﺑ ﻥﺎﻣﺰﻤﻫ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﺭﺩ ﺮﮔ ﻪﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ ﻦﻛﺎﺳ ﻑﺪﻫ ﻲﺑﺎﻳ

ﻲﻣ ﻩﺩﺎﻴﭘ ﺯﺍ ﻞﺻﺎﺣ ﺞﻳﺎﺘﻧ .ﺩﻮﺷ ﻱﻭﺭ ﺵﻭﺭ ﻦﻳﺍ ﻱﺯﺎﺳ

ﺕﺎﺑﺭ ﺭﺩ ﻙﺮﺤﺘﻣ

ﺶﺨﺑ 8 ﻭ ﺖﺳﺍ ﻩﺪﻣﺁ ﺎﻬﻧﺭﺩ

ﻳ ﺖ ﺶﺨﺑ ﺭﺩ 9 ﻊﻤﺟ ﻪﺠﻴﺘﻧ ﻭ ﻱﺪﻨﺑ ﻭ ﻱﺮﻴﮔ

ﺋﺍﺭﺍ ﺭﺎﻛ ﻪﻣﺍﺩﺍ ﻱﺍﺮﺑ ﻲﻳﺎﻫﺩﺎﻬﻨﺸﻴﭘ ﻲﻣ ﻪ

.ﺩﻮﺷ

1B

2

- ﻝﺪﻣ ﻪﻠﺌﺴﻣ ﻱﺯﺎﺳ

ﻱﺎﻫﺮﻴﻐﺘﻣ ﻩﺩﺎﻔﺘﺳﺍ ﻩﺪﺷ ﻲﻣ ﺮﻳﺯ ﺡﺮﺷ ﻪﺑ ﻪﻟﺎﻘﻣ ﻦﺘﻣ ﺭﺩ :ﺪﻨﺷﺎﺑ

𝑥𝑥^𝑡 ﻭ 𝑦𝑦^𝑡 ﻑﺪﻫ ﻱﺪﻌﺑﻭﺩ ﻥﺎﻜﻣ

𝑥𝑥̇^𝑡 ﻭ 𝑦𝑦̇^𝑡 ﺖﻬﺟ ﺭﺩ ﺐﻴﺗﺮﺗ ﻪﺑ ﻑﺪﻫ ﺖﻋﺮﺳ ﻭ𝑥𝑥

𝑦𝑦

𝑥𝑥^𝑜 ﻭ 𝑦𝑦^𝑜 ﺖﻳﻭﺭ ﻱﺪﻌﺑﻭﺩ ﻥﺎﻜﻣ ﺮﮔ

𝑥𝑥̇^𝑜 ﻭ 𝑦𝑦̇^𝑜 ﺖﻳﻭﺭ ﺖﻋﺮﺳ ﺖﻬﺟ ﺭﺩ ﺐﻴﺗﺮﺗ ﻪﺑ ﺮﮔ

ﻭ𝑥𝑥 𝑦𝑦

𝑣𝑣^𝑜 ﻩﺯﺍﺪﻧﺍ

ﺖﻳﻭﺭ ﻲﻄﺧ ﺖﻋﺮﺳ ﺮﮔ

𝑣𝑣𝑚𝑎𝑥𝑜

ﺖﻳﻭﺭ ﻲﻄﺧ ﺖﻋﺮﺳ ﻪﻨﻴﺸﻴﺑ ﺮﮔ

𝜃𝜃^𝑜 ﺖﻳﻭﺭ ﺱﺭﻮﻛ ﻥﺎﻤﻫ ﺎﻳ ﺖﻛﺮﺣ ﺖﻬﺟ

ﺮﮔ

𝜔𝑥

ﻭ 𝜔𝑦

ﺖﻬﺟ ﺭﺩ ﻑﺪﻫ ﺖﻋﺮﺳ ﺖﻴﻌﻄﻗ ﻡﺪﻋ ﻭ𝑥𝑥

ﻱﺎﻫﺮﻴﻐﺘﻣ ،𝑦𝑦

ﻭ ﺮﻔﺻ ﻦﻴﮕﻧﺎﻴﻣ ﺎﺑ ﻞﻘﺘﺴﻣ ﻲﺳﻮﮔ ﻲﻓﺩﺎﺼﺗ ﺭﺍﻭ

ﻳ ﺲﻧﺎ ﺎﻫ ﻱ ﻪﺑ

ﺐﻴﺗﺮﺗ 𝜎𝑥2

ﻭ 𝜎𝑦2

𝐐 ﺲﻳﺮﺗﺎﻣ

ﺭﺍﻭﻮﻛ ﻳ ﺲﻧﺎ ﻱﺭﺍﺩﺮﺑ ﻲﻓﺩﺎﺼﺗ ﺮﻴﻐﺘﻣ [𝜔𝑥𝑥 𝜔_𝑦]

ﺎﺑ ﺖﺳﺍ ﺮﺑﺍﺮﺑ ﻪﻛ

�𝜎𝑥2 0 0 𝜎𝑦2�

𝜈 ﻩﺯﺍﺪﻧﺍ ﺰﻳﻮﻧ

ﺲﻧﺎﻳﺭﺍﻭ ﻭ ﺮﻔﺻ ﻦﻴﮕﻧﺎﻴﻣ ﺎﺑ ﻲﺳﻮﮔ ،ﻱﺮﻴﮔ 𝜎𝜈2

𝑡𝑡𝑓

ﻲﻳﺎﻬﻧ ﻥﺎﻣﺯ

ﻭ𝛽𝛽 ﻩﺯﺍﺪﻧﺍ ﻭ ﻲﻌﻗﺍﻭ ﺭﺍﺪﻘﻣ ﺐﻴﺗﺮﺗ ﻪﺑ 𝑧

ﻩﺪﺷ ﻱﺮﻴﮔ ﺖﻤﺳ ﻪﻳﻭﺍﺯ

ﻑﺪﻫ

𝛽𝛽0

ﻭ 𝛽𝛽𝑓

ﻑﺪﻫ ﺖﻤﺳ ﻪﻳﻭﺍﺯ ﻲﻳﺎﻬﻧ ﻭ ﻪﻴﻟﻭﺍ ﻪﻈﺤﻟ ﺭﺩ ﺐﻴﺗﺮﺗ ﻪﺑ

𝑥𝑥�^𝑡 ﻭ 𝑦𝑦�^𝑡 ﻑﺪﻫ ﻥﺎﻜﻣ ﻦﻴﻤﺨﺗ

𝛽𝛽̂

ﻦﻴﻤﺨﺗ 𝛽𝛽

𝑟̂

ﺖﻳﻭﺭ ﻲﻨﻴﻤﺨﺗ ﻪﻠﺻﺎﻓ ﻑﺪﻫ ﺎﺗ ﺮﮔ

ﻭ𝐏 ﺲﻳﺮﺗﺎﻣ ﺐﻴﺗﺮﺗ ﻪﺑ 𝐏̇

ﺭﺍﻭﻮﻛ ﻳ ﺲﻧﺎ ﻭ ﻑﺪﻫ ﻥﺎﻜﻣ ﻦﻴﻤﺨﺗ ﻱﺎﻄﺧ

ﻥﺁ ﻖﺘﺸﻣ ﺐﺴﺣﺮﺑ ﻥﺎﻣﺯ

𝐏_𝑓 ﺭﺍﻭﻮﻛ

ﻳ ﺲﻧﺎ ﻲﻳﺎﻬﻧ ﻥﺎﻣﺯ ﺭﺩ ﻥﺎﻜﻣ ﻦﻴﻤﺨﺗ ﻱﺎﻄﺧ

𝑝𝑖𝑗

ﺮﻄﺳ ﻪﺑ ﻁﻮﺑﺮﻣ ﺮﺼﻨﻋ ﻥﻮﺘﺳ ﻭ ﻡﺍ𝑖

ﺲﻳﺮﺗﺎﻣ ﻡﺍ𝑗 𝐏

𝐇 ﻥﺎﻳﺩﺍﺮﮔ

ﻪﺑ ﺖﺒﺴﻧ𝛽𝛽 [𝑥𝑥^𝑡 𝑦𝑦^𝑡] ﻪﻄﻘﻧ ﺭﺩ

[𝑥𝑥�^𝑡 𝑦𝑦�^𝑡]

𝐅𝐈𝐌 ﺮﺸﻴﻓ ﺕﺎﻋﻼﻃﺍ ﺲﻳﺮﺗﺎﻣ

𝐱 ﻚﻳ ﺭﺩ ﺞﻨﭘ ﺭﺍﺩﺮﺑ

[𝑥𝑥^𝑜 𝑦𝑦^𝑜 𝑝11 𝑝21 𝑝22]^𝑇

ﻖﺘﺸﻣ 𝐱̇

ﻥﺎﻣﺯ ﺐﺴﺣ ﺮﺑ𝐱

𝐱_𝑓 ﺭﺍﺪﻘﻣ

ﻲﻳﺎﻬﻧ ﻪﻈﺤﻟ ﺭﺩ𝐱

𝐮 ﻚﻳ ﺭﺩ ﻭﺩ ﺭﺍﺩﺮﺑ

[𝑣𝑣^𝑜 𝜃𝜃^𝑜]^𝑇

ﺖﻳﻭﺭ ﺪﻳﺩ ﻥﺍﺪﻴﻣ 𝛼 ﺮﮔ

ﻥﺎﻣﺯ ﺖﻟﺎﺣ ﻱﺎﻀﻓ ﺕﻻﺩﺎﻌﻣ ﻩﺭﺍﺪﻧﺍ ﺎﺑ ﻦﻛﺎﺳ ﻑﺪﻫ ﻚﻳ ﻪﺘﺳﻮﻴﭘ

ﺎﻬﻨﺗ ﻱﺮﻴﮔ

ﻲﻣ ﺮﻳﺯ ﺕﺭﻮﺻ ﻪﺑ ﺖﻤﺳ ﻪﻳﻭﺍﺯ :ﺪﻨﺷﺎﺑ

ﻥﺁ ﺭﺩ ﻪﻛ )𝛽𝛽 ﻞﻜﺷ 1 ﻲﻣ ﻒﻳﺮﻌﺗ ﺮﻳﺯ ﺕﺭﻮﺻ ﻪﺑ ( :ﺩﻮﺷ

𝑥𝑥̇^𝑡=𝜔𝑥 ( )1

𝑦𝑦̇^𝑡=𝜔𝑦 ( )2

𝑧=𝛽𝛽+𝜈 ( )3

𝛽𝛽(𝑥𝑥^𝑡,𝑦𝑦^𝑡) = tan⁻¹𝑥𝑥^𝑡− 𝑥𝑥^𝑜

𝑦𝑦^𝑡− 𝑦𝑦^𝑜 ( )4

T arget



y

t x x yt

xo

yo

r

Observer

o

ﻞﻜﺷ 1 : ﻱﻮﻳﺭﺎﻨﺳ ﺖﻤﺳ ﻪﻳﻭﺍﺯ ﺎﺑ ﺎﻬﻨﺗ ﻲﺑﺎﻳﺩﺭ

ﻪﺘﺳﻮﻴﭘ ﻥﺎﻣﺯ ﺕﻻﺩﺎﻌﻣ ﻪﺑ ﻕﻮﻓ ﻢﺘﺴﻴﺳ ﺭﺩ ﻑﺪﻫ ﻥﺎﻜﻣ ﻦﻴﻤﺨﺗ ﻱﺍﺮﺑEKF

ﻲﻣ ﺮﻳﺯ ﺕﺭﻮﺻ ﺪﺷﺎﺑ

] 18 [:

ﻥﺁ ﺭﺩ ﻪﻛ ﻲﻣ ﻪﺒﺳﺎﺤﻣ ﺮﻳﺯ ﺕﺭﻮﺻ ﻪﺑ𝐇

:ﺩﻮﺷ

ﻲﻣ ﻕﺪﺻ ﺮﻳﺯ ﻪﻄﺑﺍﺭ ﺭﺩ ﺰﻴﻧ𝑟̂

:ﺪﻨﻛ

ﺖﻳﻭﺭ ﻲﻜﻴﻣﺎﻨﻳﺩ ﺕﻻﺩﺎﻌﻣ ﻦﻴﻨﭽﻤﻫ ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ ﺮﮔ

ﻞﻜﺷ 1 ﺮﻳﺯ ﺕﺭﻮﺻ ﻪﺑ

ﻲﻣ :ﺪﻨﺷﺎﺑ

ﺖﻳﻭﺭ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻦﻴﻴﻌﺗ ﺭﻮﻈﻨﻣ ﻪﺑ ﺭﺎﻴﻌﻣ ﺱﺎﺳﺍ ﺮﺑ ﺮﮔ

ﻲﮕﻨﻴﻬﺑ ﻪﻛA

ﺱﻮﻜﻌﻣ (ﻱﺮﻄﻗ ﺮﺻﺎﻨﻋ ﻉﻮﻤﺠﻣ) ﺮﺛﺍ ﺮﺑﺍﺮﺑ ﺮﺸﻴﻓ ﺕﺎﻋﻼﻃﺍ ﺲﻳﺮﺗﺎﻣ

ﻲﻣ ﺪﺷﺎﺑ

ﺐﻳﺮﻘﺗ ﺯﺍ ﻩﺩﺎﻔﺘﺳﺍ ﺎﺑ ﻭ 𝐏 ≅ 𝐅𝐈𝐌⁻¹

ﺕﺭﻮﺻ ﻪﺑ ﻪﻨﻳﺰﻫ ﻊﺑﺎﺗ ،

ﻲﻣ ﻪﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ ﺯﺍ ﺭﻮﻈﻨﻣ ﻥﺁ ﺭﺩ ﻪﻛ ﺩﻮﺷ

𝑡𝑡𝑟(. ) ﻲﻣ ﺲﻳﺮﺗﺎﻣ ﺮﺛﺍ ﺎﺑ .ﺪﺷﺎﺑ

ﻪﻨﻴﻬﺑ ﻪﻠﺌﺴﻣ ﺪﺷﺎﺑ ﻡﻮﻠﻌﻣ ﻑﺪﻫ ﻥﺎﻜﻣ ﻪﻜﻨﻳﺍ ﺽﺮﻓ ﻲﻣ ﺍﺭ ﻕﻮﻓ ﻱﺯﺎﺳ

ﻪﺑ ﻥﺍﻮﺗ

:ﺖﺷﻮﻧ ﺮﻳﺯ ﻪﻨﻴﻬﺑ ﻝﺮﺘﻨﻛ ﻪﻠﺌﺴﻣ ﻡﺮﻓ

ﺪﻴﻗ ﺎﺑ ﻥﺁ ﺭﺩ ﻪﻛ

ﻊﺑﺎﺗ ﻱﻭﺭ ﺯﺍ ﺰﻴﻧ𝐟 )6

،(

)9 ﻭ ( ) 10 ﻲﻣ ﻪﺘﺧﺎﺳ ( .ﺩﻮﺷ

ﻪﻛ ﺖﺳﺍ ﺮﻛﺫ ﻪﺑ ﻡﺯﻻ

ﺮﮔﺍ 𝐏0

) ﻪﻴﻟﻭﺍ ﻪﻈﺤﻟ ﺭﺩ𝐏 𝑡𝑡0

ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ ﺪﺷﺎﺑ ﻥﺭﺎﻘﺘﻣ ( )6

،(

ﻪﻴﻘﺑ ﺭﺩ𝐏

ﻥﺎﻣﺯ ﻩﺭﺍﻮﻤﻫ ﺍﺬﻟ .ﺪﻧﺎﻣ ﺪﻫﺍﻮﺧ ﻥﺭﺎﻘﺘﻣ ﺰﻴﻧ ﺎﻫ 𝑝12

ﺎﺑ 𝑝21

.ﺩﻮﺑ ﺪﻫﺍﻮﺧ ﺮﺑﺍﺮﺑ

ﻪﺑ ﺖﻟﺎﺣ ﺭﺍﺩﺮﺑ ﺭﺩ ﻞﻴﻟﺩ ﻦﻴﻤﻫ ،𝐱

𝑝12

.ﺖﺳﺍ ﻩﺪﺸﻧ ﺝﺭﺩ

2B

3

- ﺖﻳﻭﺭ ﺮﻴﺴﻣ ﺮﻴﺛﺎﺗ ﻲﺳﺭﺮﺑ ﺮﺑ ﺮﮔ

ﻮﻛ ﺲﻧﺎﻳﺭﺍ

ﻦﻴﻤﺨﺗ ﻱﺎﻄﺧ

ﺖﻳﻭﺭ ﺮﻴﺴﻣ ﺮﻴﺛﺎﺗ ﻲﺳﺭﺮﺑ ﺭﻮﻈﻨﻣ ﻪﺑ ﻪﻨﻳﺰﻫ ﻊﺑﺎﺗ ﺮﺑ ﺮﮔ

) 12 ﻪﻴﺒﺷ ( ﻱﺯﺎﺳ

ﻪﻴﺒﺷ ﻦﻳﺍ ﺭﺩ .ﺖﺳﺍ ﻩﺪﺷ ﻡﺎﺠﻧﺍ ﺮﻳﺯ ﻲﻣ ﺽﺮﻓ ﻱﺯﺎﺳ

ﺩﻮﺷ 𝜎𝑥2=𝜎𝑦2=

،0.01 𝜎𝜈= 5^∘ ﺖﻳﻭﺭ ﺖﻋﺮﺳ ﻭ ، ﺕﺎﻈﺤﻟ ﻡﺎﻤﺗ ﺭﺩ ﺮﮔ

𝑣𝑣^𝑜= 0.5^𝑚_𝑠

ﺪﻳﺎﻤﻧ ﺖﻛﺮﺣ ﻪﺑ ﻉﻭﺮﺷ ﺍﺪﺒﻣ ﺯﺍ ﻭ ﻩﺩﻮﺑ ([𝑥𝑥^𝑜(𝑡𝑡₀) 𝑦𝑦^𝑜(𝑡𝑡₀)] =

[0 0]) ﻥﺁ ﺖﻬﺟ ﻭ (𝜃𝜃^𝑜)

ﻥﺎﻜﻣ .ﺪﺷﺎﺑ ﺖﺑﺎﺛ ﻩﺭﺍﻮﻤﻫ ﺮﻴﺴﻣ ﻝﻮﻃ ﺭﺩ

ﺰﻴﻧ ﻑﺪﻫ [0 5]

ﻪﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ ﻩﺪﺷ

ﻲﻳﺎﻬﻧ ﻥﺎﻣﺯ ﻦﻴﻨﭽﻤﻫ .ﺖﺳﺍ 𝑡𝑡𝑓

، 𝜌

ﺖﻳﻭﺭ ﻥﺪﻴﺳﺭ ﻱﺍﺮﺑ ﻡﺯﻻ ﻥﺎﻣﺯ ﺕﺪﻣ ﺮﺑﺍﺮﺑ ،ﻢﻴﻘﺘﺴﻣ ﺖﻛﺮﺣ ﺭﺩ ﻑﺪﻫ ﻪﺑ ﺮﮔ

ﻲﻣ ﻪﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ ﻲﻨﻌﻳ ﺩﻮﺷ

) 15 𝑡𝑡𝑓=𝜌‖[𝑥𝑥^𝑡− 𝑥𝑥^𝑜(𝑡𝑡₀) 𝑦𝑦^𝑡− 𝑦𝑦^𝑜(𝑡𝑡₀)]‖ (

𝑣𝑣^𝑜

ﺖﻳﻭﺭ ﺮﻴﺴﻣ ﻭ ﺮﮔ 𝑡𝑡𝑟(𝐏) ﻱﺍﺯﺍ ﻪﺑ 𝜌= 0.5 ﻒﻠﺘﺨﻣ ﺭﺍﺪﻘﻣ ﻪﺳ ﻭ 𝜃𝜃^𝑜

ﺭﺩ

ﻞﻜﺷ 2 .ﺖﺳﺍ ﻩﺪﺷ ﻩﺩﺍﺩ ﻥﺎﺸﻧ ﺭﻮﻄﻧﺎﻤﻫ

ﻪﻛ ﻲﻣ ﺭﺎﻈﺘﻧﺍ ﺖﻳﻭﺭ ﺮﮔﺍ ﺖﻓﺭ ﻪﺑ ﺮﮔ

ﺪﻨﻛ ﺖﻛﺮﺣ ﻑﺪﻫ ﻑﺮﻃ ﻪﺑ ﻢﻴﻘﺘﺴﻣ ﺭﻮﻃ (𝜃𝜃^𝑜= 0^∘)

، 𝑡𝑡𝑟(𝐏) ﺩﺎﻳﺯ

ﺖﻳﻭﺭ ﻪﻠﺌﺴﻣ ﺖﻟﺎﺣ ﻦﻳﺍ ﺭﺩ ﻊﻗﺍﻭ ﺭﺩ .ﺩﻮﺑ ﺪﻫﺍﻮﺧ ﻥﺎﻨﻴﻣﺮﺗﺩ ﻭ ﺖﺳﺍ ﺮﻳﺬﭘﺎﻧ

𝐏

ﻲﻣ ﺮﻔﺻ ﺮﺛﺍ ﺶﻫﺎﻛ ﺚﻋﺎﺑ ﺮﻴﺴﻣ ﻦﻳﺍ ﺭﺩ ﺖﻛﺮﺣ ﻭ ﺩﻮﺷ ﺲﻧﺎﻳﺭﺍﻮﻛ

ﻱﺎﻄﺧ

ﻲﻤﻧ ﻦﻴﻤﺨﺗ ﻪﻳﻭﺍﺯ ﺎﺑ ﺖﻛﺮﺣ ﻪﻜﻨﻳﺍ ﺎﺑ ﻪﻛ ﺖﺳﺍ ﻦﻳﺍ ﺮﮕﻳﺩ ﻢﻬﻣ ﻪﺘﻜﻧ .ﺩﻮﺷ

90^∘ ﺮﺘﺸﻴﺑ ﺶﻫﺎﻛ ﺚﻋﺎﺑ ﺍﺪﺘﺑﺍ ﺭﺩ ﻑﺪﻫ ﻪﺑ ﺖﺒﺴﻧ 𝑡𝑡𝑟(𝐏)

ﻲﻣ ﻲﻟﻭ ﺩﻮﺷ

،ﺪﻌﺑ ﻪﺑ ﺭﺎﻬﭼ ﻪﻴﻧﺎﺛ ﺯﺍ ﺍﺩﻭﺪﺣ 𝑡𝑡𝑟(𝐏)

ﻪﻳﻭﺍﺯ ﺎﺑ ﺮﻴﺴﻣ ﻱﺍﺮﺑ 30^∘

ﻩﺪﺷ ﺮﺘﻤﻛ

ﺭﺩ .ﺖﺳﺍ ﻞﻜﺷ 3 𝑡𝑡𝑟�𝐏_𝑓� ﺐﺴﺣ ﺮﺑ 𝜃𝜃^𝑜 ﻪﻈﺣﻼﻣ .ﺖﺳﺍ ﻩﺪﺷ ﻢﺳﺭ

ﻲﻣ ﻱﺍﺯﺍ ﻪﺑ ﻪﻛ ﺩﻮﺷ 𝜃𝜃^𝑜= 48^∘

، 𝑡𝑡𝑟�𝐏𝑓� ﻲﻨﻌﻳ ﻦﻳﺍ ﻭ ﺖﺳﺍ ﻩﺪﺷ ﻪﻨﻴﻤﻛ

ﺖﻳﻭﺭ ﺮﮔﺍ ﻧ ﻥﺎﻣﺯ ﻭ ﺪﺷﺎﺑ ﻢﻴﻘﺘﺴﻣ ﺮﻴﺴﻣ ﺭﺩ ﺖﻛﺮﺣ ﻪﺑ ﺭﺩﺎﻗ ﺎﻬﻨﺗ ﺮﮔ ﻲﻳﺎﻬ

ﺖﻳﻭﺭ ﻢﻴﻘﺘﺴﻣ ﻥﺪﻴﺳﺭ ﻱﺍﺮﺑ ﺯﺎﻴﻧ ﺩﺭﻮﻣ ﻥﺎﻣﺯ ﻒﺼﻧ ﺪﺷﺎﺑ ﻑﺪﻫ ﻪﺑ ﺮﮔ

(𝜌= 0.5) ﺖﻳﻭﺭ ﺮﮔﺍ ﻩﺎﮕﻧﺁ ،

ﺱﺭﻮﻛ ﺎﺑ ﺮﮔ 𝜃𝜃^𝑜= 48^∘

ﻂﺧ ﻪﺑ ﺖﺒﺴﻧ

ﺖﻳﻭﺭ ﻪﻴﻟﻭﺍ ﻥﺎﻜﻣ ﻞﺻﺍﻭ ،ﺪﻨﻛ ﺖﻛﺮﺣ ﻑﺪﻫ ﻭ ﺮﮔ

𝑡𝑡𝑟�𝐏𝑓� ﻦﻳﺮﺘﻤﻛ

ﻱﺍﺮﺑ ﻻﺎﺑ ﺭﺩ ﻩﺪﺷ ﺮﻛﺫ ﺮﻳﺩﺎﻘﻣ ﺎﺑ ﻪﺘﺒﻟﺍ) ﺖﺷﺍﺩ ﺪﻫﺍﻮﺧ ﺍﺭ ﻦﻜﻤﻣ ﺭﺍﺪﻘﻣ 𝜎𝑥2

،

𝜎_𝑦² ﻭ 𝜎_𝜈 .(

ﻒﻠﺘﺨﻣ ﺮﻳﺩﺎﻘﻣ ﻱﺍﺯﺍ ﻪﺑ ﻪﻨﻴﻬﺑ ﺱﺭﻮﻛ ﺭﺩ𝜌

ﻞﻜﺷ 4 .ﺖﺳﺍ ﻩﺪﺷ ﻢﺳﺭ

ﺶﻫﺎﻛ ﺎﺑ ﻪﻛ ﺖﺳﺍ ﻦﻳﺍ ﻪﺟﻮﺗ ﻞﺑﺎﻗ ﻪﺘﻜﻧ ﻲﻳﺎﻬﻧ ﻥﺎﻣﺯ ﺶﻫﺎﻛ ﻪﺑ ﺮﺠﻨﻣ ﻪﻛ𝜌

ﻲﻣ ﻪﺑ ﻪﻨﻴﻬﺑ ﺱﺭﻮﻛ ،ﺩﻮﺷ 90^∘

ﻲﻣ ﻚﻳﺩﺰﻧ ﻦﻳﺍ ﻭ ﺩﻮﺷ

ﻑﺪﻫ ﺮﮔﺍ ﻲﻨﻌﻳ

ﻥﺩﺮﻛ ﻪﻨﻴﻤﻛ 𝑡𝑡𝑟(𝐏)

ﻪﺑ ﻡﺎﮔ ﻚﻳ ﺵﻭﺭ ﻞﺜﻣ) ﺪﺷﺎﺑ ﺮﺘﻜﻳﺩﺰﻧ ﻩﺪﻨﻳﺁ ﺭﺩ

ﻩﺮﻳﺍﺩ ﺮﺘﺸﻴﺑ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ،(ﻮﻠﺟ ﻪﺑ ﻪﻨﻳﺰﻫ ﻊﺑﺎﺗ ﻪﻨﻴﻤﻛ .ﺩﻮﺑ ﺪﻫﺍﻮﺧ ﻞﻜﺷ ﻱﺍ

�𝑥𝑥�̇^𝑡 𝑦𝑦�̇^𝑡�=𝐏𝐇^𝑇

𝜎𝜈2 �𝑧 − 𝛽𝛽̂� ( )5 𝐏̇=𝐐 − 1

𝜎_𝜈²𝐏𝐇^𝑇𝐇𝐏 ( )6

𝐇=�𝜕𝛽𝛽

𝜕𝑥𝑥^𝑡

𝜕𝛽𝛽

𝜕𝑦𝑦^𝑡�_{𝑥𝑡=𝑥�𝑡}

𝑦^𝑡=𝑦�^𝑡

=[cos𝛽𝛽̂ −sin𝛽𝛽̂]

𝑟̂ ( )7

𝑟̂²= (𝑥𝑥�^𝑡− 𝑥𝑥^𝑜)²+ (𝑦𝑦�^𝑡− 𝑦𝑦^𝑜)² ( )8

𝑥𝑥̇^𝑜=𝑣𝑣^𝑜sin𝜃𝜃^𝑜 ( )9 𝑦𝑦̇^𝑜=𝑣𝑣^𝑜cos𝜃𝜃^𝑜 ( 10)

𝐽=𝑡𝑡𝑟�𝐏𝑓� ( 11)

minℎ�𝐱𝑓� ( 12)

𝐱̇=𝐟(𝐱,𝐮) ( 13)

ℎ�𝐱_𝑓�=𝑡𝑡𝑟�𝐏_𝑓�=𝑝₁₁�𝑡𝑡_𝑓�+𝑝₂₂�𝑡𝑡_𝑓� ( 14)

ﻪﻧﺎﺘﺳﺁ ﻲﺒﻳﺎﻧ ﻦﻴﺴﺣﺮﻴﻣﺍ ،

ﻲﻧﺎﺘﺴﻴﺳ ﻲﺒﻴﻘﻧ ﺮﻗﺎﺑﺪﻤﺤﻣ ،ﺰﻳﺮﭘ ﺮﺻﺎﻧ

ﻒﻠﺘﺨﻣ ﺮﻳﺩﺎﻘﻣ ﻱﺍﺯﺍ ﺭﺩ𝜌

ﻞﻜﺷ 5 ﻦﻳﺍ ﺯﺍ ﻪﻛ ﻪﭽﻧﺁ .ﺖﺳﺍ ﻩﺪﺷ ﻩﺩﺍﺩ ﻥﺎﺸﻧ

ﻲﻣ ﻪﺠﻴﺘﻧ ﺭﺍﺩﻮﻤﻧ ﺮﺛﺍ ،ﺪﺷﺎﺑ ﺮﺘﺸﻴﺑ ﻲﻳﺎﻬﻧ ﻥﺎﻣﺯ ﻪﭼ ﺮﻫ ﻪﻛ ﺖﺳﺍ ﻦﻳﺍ ﺩﻮﺷ

ﺲﻧﺎﻳﺭﺍﻮﻛ .ﺩﻮﺑ ﺪﻫﺍﻮﺧ ﺮﺘﻤﻛ ﺰﻴﻧ ﻪﻨﻴﻬﺑ ﺱﺭﻮﻛ ﻱﺍﺯﺍ ﻪﺑ ﻲﻳﺎﻬﻧ ﻦﻴﻤﺨﺗ ﻱﺎﻄﺧ

ﻪﺤﻟﺎﺼﻣ ﻪﻛ ﺖﺳﺍ ﺺﺨﺸﻣ ﻭ ﻲﻳﺎﻬﻧ ﻥﺎﻣﺯ ﻦﻴﺑ ﻱﺍ

ﺲﻧﺎﻳﺭﺍﻮﻛ ﻲﻳﺎﻬﻧ ﻱﺎﻄﺧ

ﺖﻳﻭﺭ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻦﻴﻴﻌﺗ ﺭﻮﻈﻨﻣ ﻪﺑ ﺍﺬﻟ .ﺩﺭﺍﺩ ﺩﻮﺟﻭ ﻲﻣ ﺕﺭﻮﺻ ﻭﺩ ﻪﺑ ﺮﮔ

ﻥﺍﻮﺗ

:ﺩﻮﻤﻧ ﻞﻤﻋ 1.

،ﺺﺨﺸﻣ ﻲﻳﺎﻬﻧ ﻥﺎﻣﺯ ﺎﺑ ﺲﻧﺎﻳﺭﺍﻮﻛ

.ﺩﻮﺷ ﻪﻨﻴﻤﻛ ﻲﻳﺎﻬﻧ ﻱﺎﻄﺧ

2.

ﺎﺑ ﺲﻧﺎﻳﺭﺍﻮﻛ .ﺩﻮﺷ ﻪﻨﻴﻤﻛ ﻲﻳﺎﻬﻧ ﻥﺎﻣﺯ ،ﻡﻮﻠﻌﻣ ﻲﻳﺎﻬﻧ ﻱﺎﻄﺧ

(ﻒﻟﺍ)

(ﺏ)

ﻞﻜﺷ 2 ﺖﻳﻭﺭ ﺮﻴﺴﻣ ﺮﻴﺛﺎﺗ : ﺮﺑ ﺮﮔ

𝒕𝒓(𝐏) ﺖﻳﻭﺭ ﺮﻴﺴﻣ (ﻒﻟﺍ) . ﻒﻠﺘﺨﻣ ﺭﺍﺪﻘﻣ ﺪﻨﭼ ﻱﺍﺯﺍ ﻪﺑ ﺮﮔ

𝜽^𝒐 ﺕﺍﺮﻴﻴﻐﺗ (ﺏ) . 𝒕𝒓(𝐏)

.ﻥﺎﻣﺯ ﻝﻮﻃ ﺭﺩ ﻞﻜﺷ

3 : 𝒕𝒓(𝐏) ﺖﻬﺟ ﻱﺍﺯﺍ ﻪﺑ ﻲﻳﺎﻬﻧ ﻪﻈﺤﻟ ﺭﺩ ﺖﻳﻭﺭ ﺖﻛﺮﺣ ﻒﻠﺘﺨﻣ ﻱﺎﻫ

ﻪﻨﻴﻤﻛ .ﺮﮔ

𝒕𝒓�𝐏_𝒇� ، 𝟏.𝟑𝟖 ﻲﻣ ﺱﺭﻮﻛ ﻱﺍﺯﺍ ﻪﺑ ﻪﻛ ﺪﺷﺎﺑ 𝜽^𝒐=𝟒𝟖^∘

.ﺖﺳﺍ ﻩﺩﺎﺘﻓﺍ ﻕﺎﻔﺗﺍ

ﻞﻜﺷ 4 : ﻒﻠﺘﺨﻣ ﺮﻳﺩﺎﻘﻣ ﻱﺍﺯﺍ ﻪﺑ ﻪﻨﻴﻬﺑ ﺱﺭﻮﻛ . 𝝆

ﻞﻜﺷ 5 : ﻒﻠﺘﺨﻣ ﺮﻳﺩﺎﻘﻣ ﺐﺴﺣ ﺮﺑ ﻪﻨﻴﻬﺑ ﺱﺭﻮﻛ ﻱﺍﺯﺍ ﻪﺑ ﻪﻨﻳﺰﻫ ﻊﺑﺎﺗ . 𝝆

ﺯﺍ ﺎﺠﻧﺁ ﻪﻛ ﺲﻧﺎﻳﺭﺍﻮﻛ ﻩﺯﺍﺪﻧﺍ ﺖﻗﺩ ﻪﺑ ﻪﺘﺴﺑﺍﻭ ﻲﻳﺎﻬﻧ ﻱﺎﻄﺧ ﻝﺪﻣ ﻭ ﻱﺮﻴﮔ

ﻲﻣ ﻢﺘﺴﻴﺳ ﻲﻟﻭ ﻲﻧﺪﺸﻧ ﻢﻴﻳﻮﮕﻧ ﺮﮔﺍ ﻻﻮﻤﻌﻣ ﻥﺁ ﺐﺳﺎﻨﻣ ﺭﺍﺪﻘﻣ ﻦﻴﻴﻌﺗ ،ﺪﺷﺎﺑ ﻪﺘﺷﺍﺪﻧ ﻢﻫ ﻪﻨﻴﻬﺑ ﺏﺍﻮﺟ ﻪﻠﺌﺴﻣ ﻉﻮﻧ ﻦﻳﺍ ﻲﺘﺣ ﺖﺳﺍ ﻦﻜﻤﻣ ﻭ ﺖﺳﺍ ﻞﻜﺸﻣ

ﺖﻳﻭﺭ ﺮﮔﺍ ﻲﻨﻌﻳ) ﺩﻮﺷ ﺮﻔﺻ ﻪﻨﻴﻬﺑ ﻲﻳﺎﻬﻧ ﻥﺎﻣﺯ ﺎﻳ ﺪﺷﺎﺑ ﺮﺘﻬﺑ ﺪﻨﻜﻧ ﺖﻛﺮﺣ ﺮﮔ

(!ﺖﺳﺍ ] 19 [ .ﺖﺳﺍ ﻪﺘﻓﺮﮔ ﺭﺍﺮﻗ ﺮﻈﻧ ﺪﻣ ﻝﻭﺍ ﻉﻮﻧ ﻲﮕﻨﻴﻬﺑ ﺶﻫﻭﮋﭘ ﻦﻳﺍ ﺭﺩ ﺍﺬﻟ .

ﻪﻨﻴﻤﻛ ﻪﺑ ﻥﺪﻴﺳﺭ ﻑﺪﻫ ﺮﮕﻳﺩ ﺕﺭﺎﺒﻋ ﻪﺑ ﺲﻧﺎﻳﺭﺍﻮﻛ

ﺭﺩ ﻦﻜﻤﻣ ﻲﻳﺎﻬﻧ ﻱﺎﻄﺧ

ﺺﺨﺸﻣ ﻲﻳﺎﻬﻧ ﻥﺎﻣﺯ .ﺖﺳﺍ

3B

4 - ﻦﻴﻴﻌﺗ ﺮﻴﺴﻣ ﻪﻨﻴﻬﺑ ﻡﺮﻧ ﻪﺘﺴﺑ ﺯﺍ ﻩﺩﺎﻔﺘﺳﺍ ﺎﺑ ﻱﺭﺍﺰﻓﺍ

GPOPS

ﺖﻳﻭﺭ ﺖﻋﺮﺳ ﺪﺷ ﺽﺮﻓ ﻼﺒﻗ ﺖﺑﺎﺛ ﺰﻴﻧ ﻥﺁ ﺱﺭﻮﻛ ﻭ ﻡﻮﻠﻌﻣ ﻭ ﺖﺑﺎﺛ ﺮﮔ

ﻥﺩﺮﻛ ﻪﻨﻴﻤﻛ ﺎﺑ ﻪﻨﻴﻬﺑ ﺱﺭﻮﻛ ﻭ ﺖﺳﺍ ﻡﻮﻠﻌﻣﺎﻧ ﻲﻟﻭ 𝑡𝑡𝑟�𝐏𝑓�

.ﺪﺷ ﻞﺻﺎﺣ

ﻪﻨﻴﻬﺑ ﺱﺭﻮﻛ ﻢﻫ ﻭ ﻪﻨﻴﻬﺑ ﺖﻋﺮﺳ ﻢﻫ ،ﺖﻳﺩﻭﺪﺤﻣ ﻭﺩ ﻦﻳﺍ ﻑﺬﺣ ﺎﺑ ﻥﻮﻨﻛﺍ ﺖﻳﻭﺭ

ﻥﺩﺮﻛ ﻪﻨﻴﻤﻛ ﺭﻮﻈﻨﻣ ﻪﺑ ﺮﮔ 𝑡𝑡𝑟�𝐏𝑓�

ﻲﻣ ﻦﻴﻴﻌﺗ ﻪﻜﻨﻳﺍ ﻱﺍﺮﺑ ﻪﺘﺒﻟﺍ .ﺩﻮﺷ

ﺖﻳﻭﺭ ﺖﻋﺮﺳ ﻱﻻﺎﺑ ﻥﺍﺮﻛ ﺪﺷﺎﺑ ﻪﺘﺷﺍﺩ ﺏﺍﻮﺟ ﻪﻠﺌﺴﻣ ﺮﮔ

𝑣𝑣𝑚𝑎𝑥𝑜 = 0.5^𝑚_𝑠 ،

ﻪﻨﻴﻬﺑ ﻝﺮﺘﻨﻛ ﻪﻠﺌﺴﻣ ﻞﺣ ﻲﭘ ﺭﺩ ﻊﻗﺍﻭ ﺭﺩ .ﺖﺳﺍ ﻩﺪﺷ ﻪﺘﻓﺮﮔ ﺮﻄﻧ ﺭﺩ )

12 ( ﻭ

) 13 ( .ﻢﻴﺘﺴﻫ ﻪﺘﺴﺑ ﺎﺑ ﻪﻠﺌﺴﻣ ﻦﻳﺍ ﺍﺪﺘﺑﺍ ،ﻝﺮﺘﻨﻛ ﻥﻮﻧﺎﻗ ﻚﻳ ﻪﺋﺍﺭﺍ ﺯﺍ ﻞﺒﻗ

ﻡﺮﻧ ﻱﺭﺍﺰﻓﺍ GPOPS ] 20 - 23 [ ﻲﻣ ﻞﺣ .ﺩﻮﺷ

ﻞﻜﺷ 6 : (ﺏ) ،ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ (ﻒﻟﺍ) 𝒕𝒓(𝐏)

ﻒﻠﺘﺨﻣ ﺮﻳﺩﺎﻘﻣ ﻱﺍﺯﺍ ﻪﺑ ﻪﻨﻴﻬﺑ ﺖﻋﺮﺳ (ﺩ) ،ﻪﻨﻴﻬﺑ ﺱﺭﻮﻛ (ﺝ) ،ﻪﻨﻴﻬﺑ . 𝝆

ﻡﺮﻧ ﺭﺍﺰﻓﺍ GPOPS ﻲﻔﻴﻃ ﻪﺒﺷ ﺵﻭﺭ ﺯﺍ

P9F

1

Pﺵﻭﺭ ءﺰﺟ ﻪﻛ ﻢﻴﻘﺘﺴﻣ ﻱﺎﻫ

P10F

2

P

ﻲﻣ ﻪﻨﻴﻬﺑ ﻝﺮﺘﻨﻛ ﻞﺋﺎﺴﻣ ﻱﺩﺪﻋ ﻞﺣ ﻱﺍﺮﺑ ﻲﻣ ﻩﺩﺎﻔﺘﺳﺍ ،ﺪﺷﺎﺑ

ﺭﺩ .ﺪﻨﻛ ﻞﻜﺷ 6

ﺮﺘﻣﺍﺭﺎﭘ ﻒﻠﺘﺨﻣ ﺭﺍﺪﻘﻣ ﻪﺳ ﻱﺍﺯﺍ ﻪﺑ ﻩﺪﺷ ﻪﺋﺍﺭﺍ ﻩﺪﻣﺁ ﺖﺳﺪﺑ ﻪﻨﻴﻬﺑ ﺏﺍﻮﺟ𝜌

ﻪﻴﺒﺷ ﺞﻳﺎﺘﻧ ﺎﺑ ﻩﺪﻣﺁ ﺖﺳﺪﺑ ﺞﻳﺎﺘﻧ .ﺖﺳﺍ ﺖﻳﻭﺭ) ﻞﺒﻗ ﻱﺯﺎﺳ

ﺱﺭﻮﻛ ﺎﺑ ﺮﮔ

ﺭﺍﺩﻮﻤﻧ ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ .ﺩﺭﺍﺩ ﻲﻧﺍﻮﺨﻤﻫ (ﺖﺑﺎﺛ ﻞﻜﺷ

6 - ﺭﺎﻈﺘﻧﺍ ﻪﻛ ﺭﻮﻄﻧﺎﻤﻫ ،ﻒﻟﺍ

ﻲﻣ ) ﺪﺷﺎﺑ ﺮﺘﻤﻛ ﻲﻳﺎﻬﻧ ﻥﺎﻣﺯ ﻪﭼ ﺮﻫ ﺖﻓﺭ ﺮﺘﺸﻴﺑ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ،(ﺪﺷﺎﺑ ﺮﺘﻤﻛ𝜌

ﺖﻳﻭﺭ ﺮﮔﺍ ﺖﻟﺎﺣ ﻦﻳﺍ ﺭﺩ ﻭ ﺩﻮﺑ ﺪﻫﺍﻮﺧ ﻩﺮﻳﺍﺩ ﻪﻴﺒﺷ ﺍﺭ ﺩﻮﺧ ﻪﻜﻨﻳﺍ ﻱﺎﺟ ﻪﺑ ﺮﮔ

ﻧﺰﺑ ﺭﻭﺩ ﺍﺭ ﻥﺁ ﺪﻨﻛ ﻚﻳﺩﺰﻧ ﻑﺪﻫ ﻪﺑ ) ﺖﺳﺍ ﺮﺘﻬﺑ ﺪ

ﻞﻜﺷ 6 - .(ﺏ ﻑﺮﻃ ﺯﺍ

ﺖﻳﻭﺭ ،ﻲﻳﺎﻬﻧ ﻥﺎﻣﺯ ﺶﻳﺍﺰﻓﺍ ﺎﺑ ﺮﮕﻳﺩ ﻩﺩﺮﻛ ﻚﻳﺩﺰﻧ ﻑﺪﻫ ﻪﺑ ﺍﺭ ﺩﻮﺧ ﺍﺪﺘﺑﺍ ﺮﮔ

ﻲﻣ ﺭﻭﺩ ﺍﺭ ﻥﺁ ﺲﭙﺳ ﺐﻴﺗﺮﺗ ﻦﻳﺍ ﻪﺑ ﺪﻧﺯ

ﺲﻧﺎﻳﺭﺍﻮﻛ ﻱﺮﺘﻤﻛ ﻲﻳﺎﻬﻧ ﻱﺎﻄﺧ

ﻲﻣ ﻞﺻﺎﺣ .ﺩﻮﺷ ﺖﻳﻭﺭ ﻪﻨﻴﻬﺑ ﺖﻋﺮﺳ ﻩﺯﺍﺪﻧﺍ ﺮﮕﻳﺩ ﻪﺟﻮﺗ ﻞﺑﺎﻗ ﻪﺘﻜﻧ ﺖﺳﺍ ﺮﮔ

1Pseudospectral

2Direct Methods ﻲﻣ ﺩﻮﺧ ﺭﺍﺪﻘﻣ ﻪﻨﻴﺸﻴﺑ ﺮﺑﺍﺮﺑ ﻩﺭﺍﻮﻤﻫ ﻪﻛ

) ﺪﺷﺎﺑ ﻞﻜﺷ 6 - ﻪﻠﺌﺴﻣ ﻞﺣ ﺭﺩ ﺍﺬﻟ .(ﺩ

ﻪﻨﻴﻬﺑ ﻝﺮﺘﻨﻛ )

12 ( ﻭ ) 13 ( ﻪﻨﻴﺸﻴﺑ ﺭﺍﺪﻘﻣ ﺭﺩ ﺖﻋﺮﺳ ﻦﺘﺷﺍﺩ ﻪﮕﻧ ﺖﺑﺎﺛ ﺎﺑ ،

ﺖﻳﻭﺭ ﻪﻨﻴﻬﺑ ﺱﺭﻮﻛ ﻪﻛ ﺖﺳﺍ ﻲﻓﺎﻛ ﺎﻬﻨﺗ ،ﺩﻮﺧ .ﺪﻳﺁ ﺖﺳﺪﺑ ﻪﻈﺤﻟ ﺮﻫ ﺭﺩ ﺮﮔ

ﻱﺍﺯﺍ ﻪﺑ ﻪﻨﻴﻬﺑ ﻱﺎﻫﺮﻴﺴﻣ 𝜌= 0.5

ﻪﻴﻟﻭﺍ ﺩﺮﺑ ﻒﻠﺘﺨﻣ ﺮﻳﺩﺎﻘﻣ ﻭ (𝑟₀)

ﻭ

ﻪﻴﻟﻭﺍ ﺖﻤﺳ (𝛽𝛽₀)

ﺭﺩ ﻞﻜﺷ 7 ﻩﺪﺷ ﻢﺳﺭ ﻱﺯﺍﻮﻣ ﺖﺳﺍ ﺢﺿﺍﻭ ﻪﻛ ﻪﭽﻧﺁ .ﺪﻧﺍ

ﻦﻳﺍ .ﺖﺳﺍ ﺺﺨﺸﻣ ﻪﻴﻟﻭﺍ ﺖﻤﺳ ﻱﺍﺯﺍ ﻪﺑ ﺮﮕﻳﺪﻜﻳ ﻪﺑ ﺖﺒﺴﻧ ﺎﻫﺮﻴﺴﻣ ﻦﻳﺍ ﻥﺩﻮﺑ ﻲﻣ ﺮﻈﻧ ﻪﺑ ﺭﻮﻃ ﺮﮔﺍ ﻪﻛ ﺪﺳﺭ

𝛽𝛽0

ﺖﻳﻭﺭ ،ﺪﺷﺎﺑ ﺖﺑﺎﺛ ﻪﻠﺻﺎﻓ ﺮﻫ ﺎﺑ ﺮﮔ

ﺯﺍ ﻱﺍ

ﺍﺭ ﺪﻨﻛ ﺖﻛﺮﺣ ﻪﺑ ﻉﻭﺮﺷ ﻪﻛ ﻑﺪﻫ ﺖﻤﺳ ﻪﻳﻭﺍﺯ ﻭ ﻥﺁ ﺱﺭﻮﻛ ﻦﻴﺑ ﻪﻄﺑ

ﺭﺍﺩﻮﻤﻧ .ﺩﻮﺑ ﺪﻫﺍﻮﺧ ﻥﺎﺴﻜﻳ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﺭﺩ ﻑﺪﻫ ﻞﻜﺷ

8 ﺍﺭ ﻉﻮﺿﻮﻣ ﻦﻳﺍ

ﻲﻣ ﺖﺑﺎﺛ .ﺪﻨﻛ ﻪﻴﻟﻭﺍ ﻥﺎﻜﻣ ﻞﺻﺍﻭ ﻂﺧ ﻪﺑ ﺖﺒﺴﻧ ﻪﻨﻴﻬﺑ ﻱﺎﻫﺮﻴﺴﻣ ﺮﮔﺍ ﻩﻭﻼﻋ ﻪﺑ

ﺖﻳﻭﺭ ﻫ ﻭ ﺮﮔ ﺖﻳﻭﺭ ﺱﺭﻮﻛ ﻦﻴﺑ ﻪﻄﺑﺍﺭ ﻩﺎﮕﻧﺁ ﺪﻧﻮﺷ ﻪﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ ﻑﺪ ﻭ ﺮﮔ

ﺖﻳﻭﺭ ﻪﻴﻟﻭﺍ ﺖﻴﻌﻗﻮﻣ ﺯﺍ ﻞﻘﺘﺴﻣ ﻼﻣﺎﻛ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﺭﺩ ﻑﺪﻫ ﺖﻤﺳ ﻭ ﺮﮔ

(ﺏ) (ﻒﻟﺍ)

(ﺩ) (ﺝ)

ﻪﻧﺎﺘﺳﺁ ﻲﺒﻳﺎﻧ ﻦﻴﺴﺣﺮﻴﻣﺍ ،

ﻲﻧﺎﺘﺴﻴﺳ ﻲﺒﻴﻘﻧ ﺮﻗﺎﺑﺪﻤﺤﻣ ،ﺰﻳﺮﭘ ﺮﺻﺎﻧ

.ﺩﻮﺑ ﺪﻫﺍﻮﺧ ﻑﺪﻫ ﺖﻴﻌﻗﻮﻣ ﻞﻜﺷ

8 ﻪﻄﺑﺍﺭ ﻦﻴﺑ 𝜃𝜃^𝑜− 𝛽𝛽0

ﻭ 𝛽𝛽 − 𝛽𝛽0

ﻪﺑ ﺍﺭ

ﺭﺩ ﻩﺪﺷ ﻢﺳﺭ ﻱﺎﻫﺮﻴﺴﻣ ﻡﺎﻤﺗ ﻱﺍﺯﺍ ﻞﻜﺷ

7 ﻲﻣ ﻥﺎﺸﻧ ﺖﺳﺍ ﺺﺨﺸﻣ .ﺪﻫﺩ

ﺯﺍ ﻩﺩﺎﻔﺘﺳﺍ ﺎﺑ .ﺖﺳﺍ ﻩﺪﺷ ﺪﻴﻟﻮﺗ ﻲﻧﺎﺴﻜﻳ ﺭﺍﺩﻮﻤﻧ ﺎﻫﺮﻴﺴﻣ ﻦﻳﺍ ﻡﺎﻤﺗ ﻱﺍﺯﺍ ﻪﺑ ﻪﻛ ﻲﻣ ﺖﻴﻌﻗﺍﻭ ﻦﻳﺍ ﺑ ﻲﻟﺮﺘﻨﻛ ﻥﻮﻧﺎﻗ ﻥﺍﻮﺗ

ﺖﻳﻭﺭ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﺪﻴﻟﻮﺗ ﻱﺍﺮ ﺖﺳﺪﺑ ﺮﮔ

.ﺩﺭﻭﺁ

4B

5

- ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﺪﻴﻟﻮﺗ ﻱﺍﺮﺑ ﻝﺮﺘﻨﻛ ﻥﻮﻧﺎﻗ

ﺖﻳﻭﺭ ﺮﮔ

ﻪﻴﺒﺷ ﺞﻳﺎﺘﻧ ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ ﺱﺭﻮﻛ ﻦﻴﺑ ﻪﻄﺑﺍﺭ ﻪﻛ ﺪﺷ ﺺﺨﺸﻣ ﻞﺒﻗ ﻱﺯﺎﺳ

ﺖﻳﻭﺭ ﻦﻳﺍ ﺭﺩ .ﺖﺳﺍ ﺖﺑﺎﺛ ﻪﻄﺑﺍﺭ ﻚﻳ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﺭﺩ ﻑﺪﻫ ﺖﻤﺳ ﻭ ﺮﮔ

ﺯﺍ .ﻢﻴﺘﺴﻫ ﻪﻄﺑﺍﺭ ﻦﻳﺍ ﻥﺩﺮﻛ ﺍﺪﻴﭘ ﻝﺎﺒﻧﺩ ﻪﺑ ﺖﻤﺴﻗ ﻞﻜﺷ

8 ﻪﻛ ﺖﺳﺍ ﺺﺨﺸﻣ ﺭﺍﺩﻮﻤﻧ

𝜃𝜃^𝑜− 𝛽𝛽0

ﺐﺴﺣ ﺮﺑ 𝛽𝛽 − 𝛽𝛽0

ﺏﺭﻮﻣ ﻭ ﻱﺩﻮﻤﻋ ﺐﻧﺎﺠﻣ ﻭﺩ ﻱﺍﺭﺍﺩ

ﻲﻣ ﺪﺷﺎﺑ ﻪﺘﺷﺍﺩ ﺍﺭ ﺖﻴﺻﺎﺧ ﻦﻳﺍ ﻪﻛ ﻱﺮﺴﻛ ﻲﻄﺧ ﻊﺑﺎﺗ ﻚﻳ ﻲﻠﻛ ﻡﺮﻓ .ﺪﺷﺎﺑ

:ﺖﺳﺍ ﺮﻳﺯ ﺕﺭﻮﺻ ﻪﺑ

ﻊﺑﺎﺗ ﻦﻳﺍ ﻱﺩﻮﻤﻋ ﺐﻧﺎﺠﻣ 𝛽𝛽 − 𝛽𝛽0=−𝑑

ﻥﺁ ﺏﺭﻮﻣ ﺐﻧﺎﺠﻣ ﻭ

𝜃𝜃^𝑜− 𝛽𝛽0=𝑚𝑚(𝛽𝛽 − 𝛽𝛽₀) +𝑏 ﻲﻣ

ﻩﺩﺍﺩ ﺯﺍ ﻩﺩﺎﻔﺘﺳﺍ ﺎﺑ .ﺪﺷﺎﺑ ﻱﺎﻫ

ﺭﺍﺩﻮﻤﻧ ﻞﻜﺷ 8 ﺕﺎﻌﺑﺮﻣ ﻪﻨﻴﻤﻛ ﺵﻭﺭ ﺯﺍ ﻩﺩﺎﻔﺘﺳﺍ ﻭ (ﻥﺎﻳﺩﺍﺭ ﺐﺴﺣ ﺮﺑ)

ﻲﻄﺧﺮﻴﻏ

، ﻱﺎﻫﺮﺘﻣﺍﺭﺎﭘ ،𝑚𝑚

،𝑏 ﻭ𝑐 ﺖﺳﺪﺑ ﺮﻳﺩﺎﻘﻣ .ﺪﻧﺪﺷ ﻩﺩﺯ ﻦﻴﻤﺨﺗ𝑑

ﺭﺩ ﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﻦﻳﺍ ﻱﺍﺮﺑ ﻩﺪﻣﺁ ﻝﻭﺪﺟ

1 .ﺖﺳﺍ ﻩﺪﺷ ﻩﺩﺭﻭﺁ

ﻞﻜﺷ 7 : ﻱﺍﺯﺍ ﻪﺑ ﻪﻨﻴﻬﺑ ﻱﺎﻫﺮﻴﺴﻣ 𝝆=𝟎.𝟓

ﻭ ﻒﻠﺘﺨﻣ ﺮﻳﺩﺎﻘﻣ 𝒓_𝟎

ﻭ 𝜷_𝟎 .

ﻞﻜﺷ 8 : 𝜽^𝒐− 𝜷_𝟎 ﺐﺴﺣ ﺮﺑ 𝜷 − 𝜷_𝟎 ﻱﺍﺯﺍ ﻪﺑ 𝝆=𝟎.𝟓 ﻒﻠﺘﺨﻣ ﺮﻳﺩﺎﻘﻣ ﻭ 𝒓_𝟎

ﻭ 𝜷_𝟎 . ﺮﺘﻣﺍﺭﺎﭘ 𝑚𝑚

𝑏 𝑐

𝑑

ﺭﺍﺪﻘﻣ 1.045

1.47 0.06794

−0.04875

ﺭﺩ ﻞﻜﺷ 9 ﻲﻌﻗﺍﻭ ﺭﺍﺩﻮﻤﻧ ﺎﺑ ﺖﻤﺳ ﺐﺴﺣ ﺮﺑ ﺱﺭﻮﻛ ﻲﻨﻴﻤﺨﺗ ﺭﺍﺩﻮﻤﻧ

ﻲﻣ ﻪﻈﺣﻼﻣ .ﺖﺳﺍ ﻩﺪﺷ ﻪﺴﻳﺎﻘﻣ ﻥﺁ ﻲﺑﻮﺧ ﻪﺑ ﻲﻨﻴﻤﺨﺗ ﺭﺍﺩﻮﻤﻧ ﻪﻛ ﺩﻮﺷ

ﻲﻣ ﻝﺎﺒﻧﺩ ﺍﺭ ﻲﻌﻗﺍﻭ ﺭﺍﺩﻮﻤﻧ ﻲﻣ ﺍﺬﻟ .ﺪﻨﻛ

ﺯﺍ ﻥﺍﻮﺗ ) 16 ( ﻝﺮﺘﻨﻛ ﻥﻮﻧﺎﻗ ﻥﺍﻮﻨﻋ ﻪﺑ

ﺕﺪﻣ ﻒﺼﻧ ﻲﻳﺎﻬﻧ ﻥﺎﻣﺯ ﺮﮔﺍ ﻊﻗﺍﻭ ﺭﺩ .ﺩﻮﻤﻧ ﻩﺩﺎﻔﺘﺳﺍ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﺪﻴﻟﻮﺗ ﺖﻬﺟ ﺖﻳﻭﺭ ﻥﺪﻴﺳﺭ ﻱﺍﺮﺑ ﻡﺯﻻ ﻥﺎﻣﺯ ﺪﺷﺎﺑ ﻢﻴﻘﺘﺴﻣ ﺖﻛﺮﺣ ﺭﺩ ﻑﺪﻫ ﻪﺑ ﺮﮔ

(𝜌= 0.5) ﻝﺮﺘﻨﻛ ﻥﻮﻧﺎﻗ ،

) 16 ( .ﺩﻮﺑ ﺪﻫﺍﻮﺧ ﺭﺍﺮﻗﺮﺑ

𝜃𝜃^𝑜− 𝛽𝛽0=𝑚𝑚(𝛽𝛽 − 𝛽𝛽₀) +𝑏+ 𝑐

𝛽𝛽 − 𝛽𝛽0+𝑑 ( 16)

ﻝﻭﺪﺟ 1 ﻱﺎﻫﺮﺘﻣﺍﺭﺎﭘ : .ﺖﻤﺳ ﻭ ﺱﺭﻮﻛ ﻦﻴﺑ ﻪﻄﺑﺍﺭ ﻱﺍﺮﺑ ﻩﺪﺷ ﻩﺩﺯ ﻦﻴﻤﺨﺗ

ﺵﻭﺭ ﻦﻴﺑ ﺯﺍ ﻂﺳﻮﺗ ﻩﺪﺷ ﻪﺋﺍﺭﺍ ﺵﻭﺭ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻦﻴﻴﻌﺗ ﺭﺩ ﺩﻮﺟﻮﻣ ﻱﺎﻫ

Hammel ] 13 [ ﺍﺬﻟ .ﺩﺭﺍﺩ ﻪﻟﺎﻘﻣ ﻦﻳﺍ ﺭﺩ ﻩﺪﺷ ﻪﺋﺍﺭﺍ ﺵﻭﺭ ﺎﺑ ﺍﺭ ﻪﺑﺎﺸﺗ ﻦﻳﺮﺘﺸﻴﺑ

ﻂﺳﻮﺗ ﻩﺪﺷ ﺪﻴﻟﻮﺗ ﺮﻴﺴﻣ ،ﻩﺪﺷ ﻪﺋﺍﺭﺍ ﺵﻭﺭ ﺩﺮﻜﻠﻤﻋ ﺮﺘﺸﻴﺑ ﻲﺳﺭﺮﺑ ﺭﻮﻈﻨﻣ ﻪﺑ ﺵﻭﺭ ﻂﺳﻮﺗ ﻩﺪﻣﺁ ﺖﺳﺪﺑ ﺮﻴﺴﻣ ﺎﺑ ﺵﻭﺭ ﻦﻳﺍ Hammel

ﺭﺩ ، ﻞﻜﺷ 10

.ﺖﺳﺍ ﻩﺪﺷ ﻪﺴﻳﺎﻘﻣ

ﻞﻜﺷ 9 : .ﺖﻤﺳ ﺐﺴﺣ ﺮﺑ ﺱﺭﻮﻛ ﻲﻨﻴﻤﺨﺗ ﻭ ﻲﻌﻗﺍﻭ ﺭﺍﺩﻮﻤﻧ ﺵﻭﺭ ﺭﺩ

Hammel ﺖﻳﻭﺭ ﺱﺭﻮﻛ ﻦﻴﺑ ﻪﻄﺑﺍﺭ ﺭﺩ ﻑﺪﻫ ﺖﻤﺳ ﻭ ﺮﮔ

ﻲﻣ ﺮﻳﺯ ﺕﺭﻮﺻ ﻪﺑ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ :ﺪﺷﺎﺑ

ﻥﺁ ﺭﺩ ﻪﻛ 𝛽𝛽_𝑓 ﺎﺑ ﺮﻳﺯ ﺢﻳﺮﺻﺎﻧ ﻲﻄﺧﺮﻴﻏ ﻪﻄﺑﺍﺭ ﻖﺒﻃ 𝛽𝛽₀

:ﺖﺳﺍ ﻂﺒﺗﺮﻣ

ﻩﺯﺍﺪﻧﺍ ﺍﺪﺒﻣ ﺕﻭﺎﻔﺗ ﻞﻴﻟﺪﺑ ﻪﻛ ﺖﺳﺍ ﺮﻛﺫ ﻪﺑ ﻡﺯﻻ ﺎﺑ ﻪﻟﺎﻘﻣ ﻦﻳﺍ ﺭﺩ ﺎﻳﺍﻭﺯ ﻱﺮﻴﮔ

ﻪﻟﺎﻘﻣ Hammel ﻩﺪﺷ ﺎﺠﺑﺎﺟ ﻕﻮﻓ ﻪﻄﺑﺍﺭ ﺭﺩ ﻝﺍﺮﮕﺘﻧﺍ ﺩﻭﺪﺣ ، ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ .ﺪﻧﺍ

ﺭﺍﺩﻮﻤﻧ ﻞﻜﺷ 11 ﺵﻭﺭ ﺯﺍ ﺮﺘﻬﺑ ﻩﺪﺷ ﻪﺋﺍﺭﺍ ﺵﻭﺭ ﻪﻛ ﺖﺳﺍ ﺺﺨﺸﻣ

Hammel ﻭ ﺖﺳﺍ ﻩﺩﻮﻤﻧ ﻞﻤﻋ 𝑡𝑡𝑟(𝐏)

.ﺖﺳﺍ ﻩﺩﻮﺑ ﺮﺘﻤﻛ ﻩﺭﺍﻮﻤﻫ ﻥﺁ ﺭﺩ

ﺵﻭﺭ ﻲﮕﻨﻴﻬﺑ ﺭﺎﻴﻌﻣ ﻥﻮﭼ ﻪﻛ ﺪﺳﺮﺑ ﺮﻈﻧ ﻪﺑ ﻪﻧﻮﮕﻨﻳﺍ ﺪﻳﺎﺷ ﺍﺪﺘﺑﺍ Hammel

ﺮﺑ

ﻲﮕﻨﻴﻬﺑ ﺭﺎﻴﻌﻣ ﺱﺎﺳﺍ ،ﺖﺳﺍ ﻩﺩﻮﺑD

𝑡𝑡𝑟(𝐏) ﺭﺩ ﻥﺁ ﺑﻴ ﺮﺘﺸ ﻩﺪﺷ ﺖﺳﺍ ﻲﻟﻭ ؛

ﺭﺍﺩﻮﻤﻧ ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ ﻞﻜﺷ

13 ﻲﻣ ﻪﻈﺣﻼﻣ ﺭﺩ ﻩﺪﺷ ﻪﺋﺍﺭﺍ ﺵﻭﺭ ﻢﻫ ﺯﺎﺑ ﺩﻮﺷ

ﻥﺎﻨﻴﻣﺮﺗﺩ ﻭ ﺖﺳﺍ ﻩﺩﻮﻤﺗ ﻞﻤﻋ ﺮﺘﻬﺑ ﻪﻟﺎﻘﻣ ﻦﻳﺍ 𝐏⁻¹

.ﺖﺳﺍ ﻩﺪﺷ ﺮﺘﺸﻴﺑ ﻥﺁ ﺭﺩ

𝑡𝑡𝑟�𝐏_𝑓� ﻭ

�𝐏_𝑓⁻¹� ﺭﺩ ﺰﻴﻧ ﺵﻭﺭ ﻭﺩ ﻦﻳﺍ ﻞﻜﺷ

13 ﻩﺪﺷ ﻪﺴﻳﺎﻘﻣ ﻢﻫ ﺎﺑ .ﺪﻧﺍ

ﻞﻜﺷ 10 : ﻪﺴﻳﺎﻘﻣ ﺮﻴﺴﻣ ﺪﻴﻟﻮﺗ ﻩﺪﺷ ﻂﺳﻮﺗ ﻥﻮﻧﺎﻗ ﻝﺮﺘﻨﻛ ﺖﺳﺪﺑ ﻩﺪﻣﺁ ﺎﺑ ﺮﻴﺴﻣ ﻪﻨﻴﻬﺑ ﻭ ﺮﮕﻳﺩ ﺵﻭﺭ ﺎﻫ .

ﺭﺩ ﻞﻜﺷ 10 ﻢﻴﻘﺘﺴﻣ ﺮﻴﺴﻣ ، ﻪﻨﻴﻬﺑ ﺱﺭﻮﻛ ﺎﺑ ﻂﺨﻟﺍ

ﺮﻴﺴﻣ ﻚﻳ ﻭ48°

ﻑﺪﻫ ﻑﺮﻃ ﻪﺑ ﭻﻴﭘﺭﺎﻣ (Spiral1)

ﺱﺭﻮﻛ ﺖﻬﺟ ﺭﺩ ﺮﮕﻳﺩ ﭻﻴﭘﺭﺎﻣ ﺮﻴﺴﻣ ﻭ

ﻪﻨﻴﻬﺑ (Spiral2) ﻩﺪﺷ ﻢﺳﺭ ﺰﻴﻧ ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ .ﺪﻧﺍ

ﻞﻜﺷ 11 ، 𝑡𝑡𝑟(𝐏) ﻱﺍﺮﺑ ﺮﻫ

ﻲﻣ ﺮﮕﻳﺩ ﺮﻴﺴﻣ ﺭﺎﻬﭼ ﺯﺍ ﺮﺘﺸﻴﺑ ﭻﻴﭘﺭﺎﻣ ﺮﻴﺴﻣ ﻭﺩ ﺮﻴﺴﻣ ﻪﺘﺒﻟﺍ .ﺪﺷﺎﺑ

Spiral2 ﻪﻛ ﻲﻣ ﻪﻨﻴﻬﺑ ﺱﺭﻮﻛ ﺖﻬﺟ ﺭﺩ

ﺮﻴﺴﻣ ﻪﺑ ﺖﺒﺴﻧ ﻱﺮﺘﻬﺑ ﺖﻴﻌﺿﻭ ،ﺪﺷﺎﺑ Spiral1

ﺩﺭﺍﺩ ،ﺮﮕﻳﺩ ﻑﺮﻃ ﺯﺍ . ﻢﻴﻘﺘﺴﻣ ﺮﻴﺴﻣ

(ﻪﻴﻧﺎﺛ ﻪﺳ ﺩﻭﺪﺣ ﺯﺍ ﻞﺒﻗ ﺎﺗ) ﺍﺪﺘﺑﺍ ﺭﺩ ﻂﺨﻟﺍ

ﻲﻣ ﻞﻤﻋ ﺎﻫﺮﻴﺴﻣ ﺮﻳﺎﺳ ﺯﺍ ﺮﺘﻬﺑ ﺮﻴﺴﻣ ﻭﺩ ﻊﻔﻧ ﻪﺑ ﻉﻮﺿﻮﻣ ﻦﻳﺍ ،ﺎﻬﺘﻧﺍ ﺭﺩ ﻲﻟﻭ ﺪﻨﻛ

ﻝﺮﺘﻨﻛ ﻥﻮﻧﺎﻗ ﺎﺑ ﻩﺪﺷ ﺪﻴﻟﻮﺗ ﺮﻴﺴﻣ ﻭ ﻪﻨﻴﻬﺑ )

16 ( ﻲﻣ ﺮﻴﻴﻐﺗ ﻪﺟﻮﺗ ﻞﺑﺎﻗ ﻪﺘﻜﻧ .ﺪﻨﻛ

𝜃𝜃^𝑜= 3𝛽𝛽_𝑓−2𝛽𝛽+𝜋

2 ( 17)

𝜌= cos¹³�3�𝛽𝛽𝑓− 𝛽𝛽0�� � 𝑑𝛽𝛽 cos⁴³�3�𝛽𝛽_𝑓− 𝛽𝛽��

𝛽0 𝛽𝑓

) 18 (

ﻪﻧﺎﺘﺳﺁ ﻲﺒﻳﺎﻧ ﻦﻴﺴﺣﺮﻴﻣﺍ ،

ﻲﻧﺎﺘﺴﻴﺳ ﻲﺒﻴﻘﻧ ﺮﻗﺎﺑﺪﻤﺤﻣ ،ﺰﻳﺮﭘ ﺮﺻﺎﻧ

ﺩﺎﻳﺯ ﺭﺎﻴﺴﺑ ﻖﺑﺎﻄﺗ ﺮﮕﻳﺩ 𝑡𝑡𝑟(𝐏)

ﻂﺳﻮﺗ ﻩﺪﺷ ﺪﻴﻟﻮﺗ ﺮﻴﺴﻣ ﻱﺍﺮﺑ ﻝﺮﺘﻨﻛ ﻥﻮﻧﺎﻗ

) 16 ( ﺎﺑ 𝑡𝑡𝑟(𝐏) ﻲﻣ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻱﺍﺮﺑ ﺩﺎﻳﺯ ﺭﺎﻴﺴﺑ ﻲﮕﻨﻴﻬﺑ ﻩﺪﻨﻫﺩ ﻥﺎﺸﻧ ﻪﻛ ﺪﺷﺎﺑ

ﻲﻣ ﻩﺪﺷ ﻪﺋﺍﺭﺍ ﺵﻭﺭ ﻦﻴﻨﭽﻤﻫ .ﺪﺷﺎﺑ

ﻪﻨﻴﻬﺑ ﺱﺭﻮﻛ 𝜃𝜃𝑜𝑝𝑡𝑜

ﺪﻴﻟﻮﺗ ﺱﺭﻮﻛ ﺎﺑ ﺰﻴﻧ ﺭﺩ ﻩﺪﺷ

ﻞﻜﺷ 14 ﻲﻣ ﻪﻈﺣﻼﻣ .ﺖﺳﺍ ﻩﺪﺷ ﻪﺴﻳﺎﻘﻣ ﺪﻴﻟﻮﺗ ﺱﺭﻮﻛ ﻪﻛ ﺩﻮﺷ

ﻲﻣ ﻝﺎﺒﻧﺩ ﺍﺭ ﻪﻨﻴﻬﺑ ﺱﺭﻮﻛ ﻲﺑﻮﺧ ﻪﺑ ﻩﺪﺷ ﻨﻛ

ﺰﻴﻧ ﻢﺘﺴﻴﺳ ﻦﻳﺍ ﻲﻛﻮﻠﺑ ﻡﺍﺮﮔﺎﻳﺩ .ﺪ

ﺭﺩ ﻞﻜﺷ 15 .ﺖﺳﺍ ﻩﺪﺷ ﻢﻴﺳﺮﺗ

ﻞﻜﺷ 11 : 𝒕𝒓(𝐏) ﺮﺑ ﺐﺴﺣ

،ﻥﺎﻣﺯ ﻁﻮﺑﺮﻣ ﻪﺑ ﺶﺷ ﺮﻴﺴﻣ ﻞﻜﺷ 10 .

ﻞﻜﺷ 12 :

|𝐏^−𝟏| ﺮﻴﺴﻣ ﺶﺷ ﻪﺑ ﻁﻮﺑﺮﻣ ،ﻥﺎﻣﺯ ﺐﺴﺣ ﺮﺑ ﻞﻜﺷ

10 .

(ﻒﻟﺍ)

(ﺏ)

ﻞﻜﺷ 13 : ﻪﺴﻳﺎﻘﻣ 𝒕𝒓(𝐏) ﻭ (ﻒﻟﺍ)

|𝐏^−𝟏| ﺮﻴﺴﻣ ﺶﺷ ﻱﺍﺮﺑ ،ﻲﻳﺎﻬﻧ ﻪﻈﺤﻟ ﺭﺩ (ﺏ) ﻞﻜﺷ

10 .

ﻞﻜﺷ 14 .ﻝﺮﺘﻨﻛ ﻥﻮﻧﺎﻗ ﻂﺳﻮﺗ ﻩﺪﺷ ﺪﻴﻟﻮﺗ ﺱﺭﻮﻛ ﺎﺑ ﻪﻨﻴﻬﺑ ﺱﺭﻮﻛ ﻪﺴﻳﺎﻘﻣ :

5B

6

- ﺪﻴﻗ ﻦﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ ﺪﻳﺩ ﻥﺍﺪﻴﻣ

ﻪﻨﻴﻤﻛ ﺍﺪﺘﺑﺍ ﺖﻤﺴﻗ ﻦﻳﺍ ﺭﺩ ﺪﻳﺩ ﻥﺍﺪﻴﻣ

ﻲﻣ ﻦﻴﻴﻌﺗ ﻱﺭﻮﻃ ﺎﺑ ﻪﻛ ،ﺩﻮﺷ

ﻝﺮﺘﻨﻛ ﻥﻮﻧﺎﻗ ﺯﺍ ﻩﺪﻣﺁ ﺖﺳﺪﺑ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﺭﺩ ﺖﻛﺮﺣ )

16 ( ﻩﺭﺍﻮﻤﻫ ﻑﺪﻫ ،

ﺖﻳﻭﺭ ﺪﻳﺩ ﺭﺩ ﺪﻴﻗ ﺐﻴﺗﺮﺗ ﻦﻳﺪﺑ .ﺪﺷﺎﺑ ﻪﺘﺷﺍﺩ ﺭﺍﺮﻗ ﺮﮔ

ﺪﻳﺩ ﻥﺍﺪﻴﻣ ﺮﺑ ﻱﺮﻴﺛﺎﺗ

ﻧ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ .ﺩﻮﺑ ﺪﻫﺍﻮﺧ ﺎﺟ ﺮﺑ ﺎﭘ ﻥﺎﻨﭽﻤﻫ ﻞﺒﻗ ﻝﺮﺘﻨﻛ ﻥﻮﻧﺎﻗ ﻭ ﺖﺷﺍﺩ ﺪﻫﺍﻮﺨ

ﻪﻛ ﻲﺘﻟﺎﺣ ﻱﺍﺮﺑ ﻝﺮﺘﻨﻛ ﻥﻮﻧﺎﻗ ﻥﺁ ﺯﺍ ﺲﭘ ﺪﻳﺩ ﻥﺍﺪﻴﻣ

ﺭﻮﻛﺬﻣ ﻪﻨﻴﻤﻛ ﺭﺍﺪﻘﻣ ﺯﺍ ﻲﻣ ﻩﺩﺍﺩ ﺮﻴﻴﻐﺗ ﻱﺭﻮﻃ ﺪﺷﺎﺑ ﺮﺘﻤﻛ

ﺪﻴﻗ ﻪﻛ ﺩﻮﺷ ﺪﻳﺩ ﻥﺍﺪﻴﻣ

ﻪﺘﻓﺮﮔ ﺮﻈﻧ ﺭﺩ

.ﺩﻮﺷ

ﻚ ﻴﻣ ﺎﻨ ﻳﺩ ﺭ ﺖ ﻳﻭ ﺮﮔ

ﻝ ﺮﺘ ﻨ ﻛ ﻥ ﻮﻧ ﺎ ﻗ

𝑥𝑥^𝑡𝑡

tan⁻¹𝑥𝑥^𝑡𝑡− 𝑥𝑥^𝑜𝑜 𝑦𝑦^𝑡𝑡− 𝑦𝑦^𝑜𝑜 𝑦𝑦^𝑡𝑡

𝛽𝛽 𝑥𝑥^𝑜𝑜

𝑦𝑦^𝑜𝑜 𝑣𝑣_{𝑚𝑚𝑚𝑚𝑥𝑥}^𝑜𝑜

𝜃𝜃^𝑜𝑜

𝛽𝛽₀

ﻞﻜﺷ 15 ﻡﺍﺮﮔﺎﻳﺩ : ﺖﻳﻭﺭ ﻝﺮﺘﻨﻛ ﻢﺘﺴﻴﺳ ﻲﻛﻮﻠﺑ ﻥﺎﻜﻣ ﻥﺩﻮﺑ ﻡﻮﻠﻌﻣ ﺽﺮﻓ ﺎﺑ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﺭﺩ ﺮﮔ

.ﻦﻛﺎﺳ ﻑﺪﻫ

T arget



y

t x x yt

xo

yo

r

Observer

o

/ 2

/ 2

ﻞﻜﺷ 16 ﺖﻳﻭﺭ : ﺪﻳﺩ ﻥﺍﺪﻴﻣ ﺎﺑ ﺮﮔ . 𝜶

ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ ﻞﻜﺷ 16 ﺖﻳﻭﺭ ﺪﻳﺩ ﻥﺍﺪﻴﻣ ﺮﮔﺍ ، ﺮﮔ

ﻪﻜﻨﻳﺍ ﻱﺍﺮﺑ ،ﺪﺷﺎﺑα

ﺖﻳﻭﺭ ﺪﻳﺩ ﺭﺩ ﻩﺭﺍﻮﻤﻫ ﻑﺪﻫ :ﻢﻴﺷﺎﺑ ﻪﺘﺷﺍﺩ ﺪﻳﺎﺑ ﺩﺮﻴﮔ ﺭﺍﺮﻗ ﺮﮔ

ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ ) 16 ( :ﺖﺷﺍﺩ ﻢﻴﻫﺍﻮﺧ

ﻊﺑﺎﺗ ﺭﺩ𝑓

ﺍﺭ ﺩﻮﺧ ﻪﻨﻴﺸﻴﺑ ﺭﺍﺪﻘﻣ ﺎﺑ ﺖﺳﺍ ﺮﺑﺍﺮﺑ ﻪﻛ ﺖﺷﺍﺩ ﺪﻫﺍﻮﺧ

ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ ) 19 ( ﺮﻳﺩﺎﻘﻣ ﻭ ﻝﻭﺪﺟ 1 ﺮﮔﺍ ،

−𝛼

2≤ 𝜃𝜃^𝑜− 𝛽𝛽 ≤𝛼

2 ( 19)

𝜃𝜃^𝑜− 𝛽𝛽 ≜ 𝑓(𝛽𝛽 − 𝛽𝛽₀) = (𝑚𝑚 −1)(𝛽𝛽 − 𝛽𝛽0) +𝑏+ 𝑐

𝛽𝛽 − 𝛽𝛽0+𝑑 ( 20)

𝛽𝛽 − 𝛽𝛽0=− �� 𝑐

𝑚𝑚 −1 +𝑑� ( 21)

max(𝜃𝜃^𝑜− 𝛽𝛽) =

−(𝑚𝑚 −1)�� 𝑐

𝑚𝑚 −1 +𝑑�+ 𝑏 − �𝑐(𝑚𝑚 −1) = 𝑏 −2�𝑐(𝑚𝑚 −1)− 𝑑(𝑚𝑚 −1)

) 22 (

𝛼 ≥2 max(𝜃𝜃^𝑜− 𝛽𝛽)≅156^∘ ( 23)