طراحی مسیر بهینه ربات متحرک غیرهولونومیک با استفاده از روش کنترل بهینه و صحه گذاری روش با انجام تست های تجربی ربات متحرک اسکات

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شﺮ 23 / 11 / 90

رد ﺎﺳ ﻳ ﺖ 15 / 3 /

91

شور زا هدﺎﻔﺘﺳا ﺎﺑ ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ كﺮﺤﺘﻣ تﺎﺑر ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻲﺣاﺮﻃ تﺎﺑر ﻲﺑﺮﺠﺗ يﺎﻫ

ﻲﻓﺮﻃ

، رﻮﻈﻨﻣ ﻪﺑ

ناﺪﻨﻤﺸﻧاد ﻢﻠﻋ

ﻚﻴﺗﺎﺑر

ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ نآ

ﻢﻴﻘﺘﺴﻣﺮﻴﻏ شور ﻲﮕﻨﻴﻬﺑ جاﺮﺨﺘﺳا هﺪﺷ

ﺖﺤﺻ ﺞﻳﺎﺘﻧ

،يرﻮﺌﺗ

ﻞﻴﻠﺤﺗ ﺞﻳﺎﺘﻧ ﻲﺑﺮﺠﺗ

Optimal

optimal control method

Abstract- nonholonomic mobile robots are widely used in industrial Also, to increase the productivity and efficiency of the mobile robot, their

attracted attention of many of robotic scientists. In this paper, the optimal path planning of the are performed considering their nonlinear dynamic equations and the nonholonomic constraints.

trajectory optimization i equations by means of

numerically, and variant simulations are executed. To v

for the Scout mobile robot and compared to the simulation results. The experimental analysis results, and demonstrates the applicability of the proposed method for the

Keywords: nonholonomic mobile robot, optimal path planning, optimal control method,

رد ﻳ ﺖﻓﺎ ﺬﭘ ﻳ شﺮ ﻪﺋارا رد

شور زا هدﺎﻔﺘﺳا ﺎﺑ ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ كﺮﺤﺘﻣ تﺎﺑر ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻲﺣاﺮﻃ تﺎﺑر ﻲﺑﺮﺠﺗ يﺎﻫ

رﻮﭘرﺎﻔﻏ ﻦﻴﺴﺣ

2

ﻲﻧاواﺮﻓ ﻲﻣ دﻮﺷ . زا ﻲﻓﺮﻃ

يرﺎﻴﺴﺑ زا ناﺪﻨﻤﺸﻧاد

ﻲﻄﺧﺮﻴﻏ و دﻮﻴﻗ ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ

و ﺎﺑ هدﺎﻔﺘﺳا زا ﻢﻴﻘﺘﺴﻣﺮﻴﻏ شور

تﻻدﺎﻌﻣ ﻲﮕﻨﻴﻬﺑ

رﻮﻈﻨﻣ ﻲﺳرﺮﺑ ﺖﺤﺻ

ﻪﺴﻳﺎﻘﻣ ﻲﻣ دﻮﺷ . ﻞﻴﻠﺤﺗ

Optimal path

optimal control method experimental

M. H. Korayem

2- M 3- Instructor,

nonholonomic mobile robots are widely used in industrial to increase the productivity and efficiency of the mobile robot, their

trajectory optimization is formulated, and conditions of the optimality are derived as a set of nonlinear differential equations by means of

nonholonomic mobile robot, optimal path planning, optimal control method,

شور زا هدﺎﻔﺘﺳا ﺎﺑ ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ كﺮﺤﺘﻣ تﺎﺑر ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻲﺣاﺮﻃ ﺖﺴﺗ مﺎﺠﻧا ﺎﺑ شور يراﺬﮔ

تﺎﺑر ﻲﺑﺮﺠﺗ يﺎﻫ

ناﺮﻬﺗ ،ناﺮﻳا ﺖﻌﻨﺻ و ﻢﻠﻋ هﺎﮕﺸﻧ

ﺪﻧوﺎﻣد

mn.nazemizadeh@gmail.com

نآ هدﺎﻔﺘﺳا ﻲﻧاواﺮﻓ

هدﻮﺑ و درﻮﻣ ﻪﺟﻮﺗ يرﺎﻴﺴﺑ

ﻲﻜﻴﻣﺎﻨﻳد ﻲﻄﺧﺮﻴﻏ

هﺪﺷ نﻮﻴﺳﻻﻮﻣﺮﻓ و

جاﺮﺨﺘﺳا ﻲﻣ دﻮﺷ . ﺲﭙﺳ

دﻮﺷ . رد ﻪﻣادا

، ﻪﺑ رﻮﻈﻨﻣ

ﻪﻴﺒﺷ يزﺎﺳ ﻪﺴﻳﺎﻘﻣ

كﺮﺤﺘﻣ ﻲﻣ ﺪﺷﺎﺑ .

،تﺎﻜﺳا كﺮﺤﺘﻣ تﺎﺑر ﻲﺑﺮﺠﺗ ﺖﺴﺗ

path planning optimal control method

xperimental

M. H. Korayem

1- Prof., Mech. Eng., MSc. Student, Mech Instructor, Mech. Eng.,

* P. O. B. 123

s formulated, and conditions of the optimality are derived as a set of nonlinear differential equations by means of indirect method of

87 - 94

شور زا هدﺎﻔﺘﺳا ﺎﺑ ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ كﺮﺤﺘﻣ تﺎﺑر ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻲﺣاﺮﻃ ﺖﺴﺗ مﺎﺠﻧا ﺎﺑ شور يراﺬﮔ

تﺎﻜﺳا كﺮﺤﺘﻣ

ﻲﻤﻇﺎﻧ

2هداز

، 3

، *

ناﺮﻬﺗ ،ناﺮﻳا ﺖﻌﻨﺻ و ﻢﻠﻋ هﺎﮕﺸﻧ ناﺮﻬﺗ ،ناﺮﻳا ﺖﻌﻨﺻ و ﻢﻠﻋ هﺎﮕﺸﻧ

ﻲﻣﻼﺳا ﺪﺣاو

،ﺪﻧوﺎﻣد

يﺎﻀﻓ يرﺎﻛ ﻊﻴﺳو

يا رادرﻮﺧﺮﺑ هدﻮﺑ

ﻦﺘﻓﺮﮔ تﻻدﺎﻌﻣ

ﻪﻨﻴﻬﺑ لﺮﺘﻨﻛ ﻪﻠﺌﺴﻣ ﻚﻳ ناﻮﻨﻋ

، هﺪﺷ نﻮﻴﺳﻻﻮﻣﺮﻓ

ﻲﻄﺧﺮﻴﻏ

، جاﺮﺨﺘﺳا

تﺎﺑر مﺎﺠﻧا ﻲﻣ دﻮﺷ

ﻪﺘﻓﺮﻳﺬﭘ و ﺎﺑ ﺞﻳﺎﺘﻧ

ﻪﻨﻴﻬﺑ تﺎﺑر كﺮﺤﺘﻣ

،تﺎﻜﺳا كﺮﺤﺘﻣ تﺎﺑر

planning of n optimal control method and

xperimental tests

M. H. Korayem¹, M. Nazemizadeh

Mech. Eng., Iran Univ Student, Mech. Eng., Iran Univ

Mech. Eng., Damavand Branch, Islamic Azad Univ B. 1231121142

s formulated, and conditions of the optimality are derived as a set of nonlinear differential indirect method of optimal control method. Then, the optimality equations are solved numerically, and variant simulations are executed. To v

هرﺎﻤﺷ 2 ﺮﻴﺗ 1391 ص ص 87

شور زا هدﺎﻔﺘﺳا ﺎﺑ ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ كﺮﺤﺘﻣ تﺎﺑر ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻲﺣاﺮﻃ ﺖﺴﺗ مﺎﺠﻧا ﺎﺑ شور يراﺬﮔ

تﺎﻜﺳا كﺮﺤﺘﻣ

ﻲﻔﻄﺼﻣ ﻲﻤﻇﺎﻧ

ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ ،

اد ناﺮﻬﺗ ،ناﺮﻳا ﺖﻌﻨﺻ و ﻢﻠﻋ هﺎﮕﺸﻧ

ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ ،

اد ناﺮﻬﺗ ،ناﺮﻳا ﺖﻌﻨﺻ و ﻢﻠﻋ هﺎﮕﺸﻧ

ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ

، هﺎﮕﺸﻧاد دازآ ﻲﻣﻼﺳا

1231121142

، mn.nazemizadeh@gmail.com

خﺮﭼ راد ﻪﺑ ﺖﻠﻋ يﺎﻀﻓ

نآ زا ﺖﻴﻤﻫا هﮋﻳو يا

خﺮﭼ راد ﺎﺑ ﺮﻈﻧرد

ﻪﻨﻴﻬﺑ لﺮﺘﻨﻛ ﻪﻠﺌﺴﻣ ﻚﻳ ناﻮﻨﻋ تﻻدﺎﻌﻣ ﻞﻴﺴﻧاﺮﻔﻳد ﻲﻄﺧﺮﻴﻏ

ياﺮﺑ ﺮﻴﺴﻣ ﻪﻨﻴﻬﺑ تﺎﺑر

ﻲﻫﺎﮕﺸﻳﺎﻣزآ تﺎﻜﺳا

مﺎﺠﻧا ﻪﺘﻓﺮﻳﺬﭘ

ﻲﺣاﺮﻃ ﺮﻴﺴﻣ ﻪﻨﻴﻬﺑ

،ﻪﻨﻴﻬﺑ لﺮﺘﻨﻛ شور ،ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻲﺣاﺮﻃ ،ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ كﺮﺤﺘﻣ تﺎﺑر ،تﺎﻜﺳا كﺮﺤﺘﻣ تﺎﺑر

nonholonomic

and verification of the method ests of the Scout mobile robot

Nazemizadeh

Iran Univ. of Science and Technology, Tehran, Iran Univ. of Science and Technology Damavand Branch, Islamic Azad Univ 1121142 Tehran, mn.nazemizadeh@gmail.com nonholonomic mobile robots are widely used in industrial

to increase the productivity and efficiency of the mobile robot, their

s formulated, and conditions of the optimality are derived as a set of nonlinear differential optimal control method. Then, the optimality equations are solved numerically, and variant simulations are executed. To verify the simulation study, some experimental analysis are done for the Scout mobile robot and compared to the simulation results. The experimental analysis

results, and demonstrates the applicability of the proposed method for the nonholonomic mobile robot, optimal path planning, optimal control method,

هرود 12 هرﺎﻤﺷ

شور زا هدﺎﻔﺘﺳا ﺎﺑ ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ كﺮﺤﺘﻣ تﺎﺑر ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻲﺣاﺮﻃ ﺖﺴﺗ مﺎﺠﻧا ﺎﺑ شور يراﺬﮔ

تﺎﻜﺳا كﺮﺤﺘﻣ

ﻢﻳارﻮﻛ داﮋﻧ ،1

ﻲﻔﻄﺼﻣ

دﺎﺘﺳ ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ

ﺪﺷرا ﻲﺳﺎﻨﺷرﺎﻛ ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ

ﻲﺑﺮﻣ ، ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ

ﻲﺘﺴﭘ قوﺪﻨﺻ 1121142

تﺎﺑر يﺎﻫ كﺮﺤﺘﻣ خﺮﭼ

ﺮﻴﺴﻣ ﺖﻛﺮﺣ نآ

تﺎﺑر كﺮﺤﺘﻣ خﺮﭼ

تﺎﺑر كﺮﺤﺘﻣ

، ﻪﺑ ﻪﻨﻴﻬﺑ لﺮﺘﻨﻛ ﻪﻠﺌﺴﻣ ﻚﻳ ناﻮﻨﻋ

ﻚﻳ ﻪﻋﻮﻤﺠﻣ تﻻدﺎﻌﻣ

يﺎﻫ ﻲﻋﻮﻨﺘﻣ ياﺮﺑ

كﺮﺤﺘﻣ ﻲﻫﺎﮕﺸﻳﺎﻣزآ

يﺎﻫدﺮﺑرﺎﻛ ﻲﻠﻤﻋ

،ﻪﻨﻴﻬﺑ لﺮﺘﻨﻛ شور ،ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻲﺣاﺮﻃ ،ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ كﺮﺤﺘﻣ تﺎﺑر

onholonomic

verification of the method Scout mobile robot

Nazemizadeh^2,3*, H. Ghaffarpour

of Science and Technology, Tehran, of Science and Technology Damavand Branch, Islamic Azad Univ

nonholonomic mobile robots are widely used in industrial environments due to their extended workspace.

to increase the productivity and efficiency of the mobile robot, their path planning is an important task, and attracted attention of many of robotic scientists. In this paper, the optimal path planning of the

are performed considering their nonlinear dynamic equations and the nonholonomic constraints.

s formulated, and conditions of the optimality are derived as a set of nonlinear differential optimal control method. Then, the optimality equations are solved erify the simulation study, some experimental analysis are done for the Scout mobile robot and compared to the simulation results. The experimental analysis

results, and demonstrates the applicability of the proposed method for the optimal path planning of the mobile robots.

شور زا هدﺎﻔﺘﺳا ﺎﺑ ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ كﺮﺤﺘﻣ تﺎﺑر ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻲﺣاﺮﻃ ﻪﺤﺻ و ﻪﻨﻴﻬﺑ لﺮﺘﻨﻛ ﺖﺴﺗ مﺎﺠﻧا ﺎﺑ شور يراﺬﮔ

ﺐﻴﺒﺣ مﺮﺤﻣ ﻢﻳارﻮﻛ داﮋﻧ

1 - ا دﺎﺘﺳ

2 - يﻮﺠﺸﻧاد ﺪﺷرا ﻲﺳﺎﻨﺷرﺎﻛ

3 - ﻲﺑﺮﻣ

* ناﺮﻬﺗ

، ﻲﺘﺴﭘ قوﺪﻨﺻ

ﻲﺘﻌﻨﺻ

، زا تﺎﺑر

،كﺮﺤﺘﻣ يﺎﻫ ﻲﺣاﺮﻃ

ﻲﺣاﺮﻃ ﺮﻴﺴﻣ ﻪﻨﻴﻬﺑ تﺎﺑر

ﺮﻴﺴﻣ ﻪﻨﻴﻬﺑ تﺎﺑر

ﺮﻴﺴﻣ

، ﻪﺑ ترﻮﺻ ﻚﻳ

هﺪﺷ و ﻪﻴﺒﺷ يزﺎﺳ يﺎﻫ

هدﺎﻔﺘﺳا زا تﺎﺑر كﺮﺤﺘﻣ

شور يدﺎﻬﻨﺸﻴﭘ رد

يﺎﻫدﺮﺑرﺎﻛ

onholonomic mobile

verification of the method Scout mobile robot

H. Ghaffarpour

of Science and Technology, Tehran, Iran of Science and Technology, Tehran, Damavand Branch, Islamic Azad Univ., Damavand, Iran

environments due to their extended workspace.

path planning is an important task, and attracted attention of many of robotic scientists. In this paper, the optimal path planning of the

are performed considering their nonlinear dynamic equations and the nonholonomic constraints.

s formulated, and conditions of the optimality are derived as a set of nonlinear differential optimal control method. Then, the optimality equations are solved erify the simulation study, some experimental analysis are done for the Scout mobile robot and compared to the simulation results. The experimental analysis

optimal path planning of the mobile robots.

nonholonomic mobile robot, optimal path planning, optimal control method, the Scout mobile robot

شور زا هدﺎﻔﺘﺳا ﺎﺑ ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ كﺮﺤﺘﻣ تﺎﺑر ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻲﺣاﺮﻃ ﻪﺤﺻ و ﻪﻨﻴﻬﺑ لﺮﺘﻨﻛ

ﺐﻴﺒﺣ مﺮﺤﻣ

ﻂﻴﺤﻣ يﺎﻫ يرﺎﻛ و

تﺎﺑر هدزﺎﺑ و ﻲﻳارﺎﻛ ﺶﻳاﺰﻓا

،كﺮﺤﺘﻣ يﺎﻫ ﻪﻟﺎﻘﻣ

، ﻪﺑ ﻲﺣاﺮﻃ

. ﻪﻠﺌﺴﻣ ﻲﺣاﺮﻃ ﺮﻴﺴﻣ

ﻂﻳاﺮﺷ ﻲﮕﻨﻴﻬﺑ ﺮﻴﺴﻣ

يﺎﻫ يدﺪﻋ ﻞﺣ هﺪﺷ

يدﺪﻌﺘﻣ ﺎﺑ هدﺎﻔﺘﺳا

ﺖﺤﺻ و ﻲﻳارﺎﻛ شور

mobile robot verification of the method

Scout mobile robot

H. Ghaffarpour²

Iran , Damavand, Iran

path planning is an important task, and attracted attention of many of robotic scientists. In this paper, the optimal path planning of the wheeled mobile robots are performed considering their nonlinear dynamic equations and the nonholonomic constraints. Problem of the s formulated, and conditions of the optimality are derived as a set of nonlinear differential optimal control method. Then, the optimality equations are solved erify the simulation study, some experimental analysis are done for the Scout mobile robot and compared to the simulation results. The experimental analysis verifies the simulation

optimal path planning of the mobile robots.

the Scout mobile robot, experimental test.

شور زا هدﺎﻔﺘﺳا ﺎﺑ ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ كﺮﺤﺘﻣ تﺎﺑر ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻲﺣاﺮﻃ ﻪﺤﺻ و ﻪﻨﻴﻬﺑ لﺮﺘﻨﻛ

هﺪﻴﻜﭼ - رد ﻂﻴﺤﻣ

تﺎﺑر هدزﺎﺑ و ﻲﻳارﺎﻛ ﺶﻳاﺰﻓا ﻲﻣ ﺪﺷﺎﺑ . رد ﻦﻳا

ﻪﺘﺧادﺮﭘ ﻲﻣ دﻮﺷ .

ﻪﻨﻴﻬﺑ لﺮﺘﻨﻛ ﻂﻳاﺮﺷ

ﺑ ﻚﻤﻛ ﻪ شور يﺎﻫ

يﺎﻫﺰﻴﻟﺎﻧآ ﻲﺑﺮﺠﺗ

نﺎﺸﻧ هﺪﻨﻫد ﺖﺤﺻ

ﺪﻴﻠﻛ نﺎﮔژاو :

robots using verification of the method via

path planning is an important task, and is mobile robots Problem of the s formulated, and conditions of the optimality are derived as a set of nonlinear differential optimal control method. Then, the optimality equations are solved erify the simulation study, some experimental analysis are done verifies the simulation optimal path planning of the mobile robots.

, experimental test.

هﺪﻴﻜﭼ تﺎﺑر هدزﺎﺑ و ﻲﻳارﺎﻛ ﺶﻳاﺰﻓا ﻲﻣ ﻪﺘﺧادﺮﭘ ﻪﻨﻴﻬﺑ لﺮﺘﻨﻛ ﺑ يﺎﻫﺰﻴﻟﺎﻧآ نﺎﺸﻧ ﺪﻴﻠﻛ

sing

is mobile robots Problem of the s formulated, and conditions of the optimality are derived as a set of nonlinear differential optimal control method. Then, the optimality equations are solved erify the simulation study, some experimental analysis are done verifies the simulation

(2)

1 - ﻪﻣﺪﻘﻣ

تﺎﺑر نآ ﺖﺑﺎﺛ عﻮﻧ ﻪﺑ ﺖﺒﺴﻧ كﺮﺤﺘﻣ يﺎﻫ ﺎﻳاﺰﻣ ياراد

نﻮﭼ ﻲﻳ

ﻊﻴﺳو يرﺎﻛ يﺎﻀﻓ كﺮﺤﺘﻣ ،ﺮﺗ

و هدﻮﺑ ﺮﺗﻻﺎﺑ رﻮﻧﺎﻣ ترﺪﻗ و ندﻮﺑ

ﻮﻣ اﺬﻟ ا ﻲﻧاواﺮﻓ دﺮﺑرﺎﻛ در ﺪﻧراد

. ﻦﻴﻨﭽﻤﻫ

، تﺎﺑر زا كﺮﺤﺘﻣ يﺎﻫ

ﺑﺎﺟ رد ﻪ ﻂﻴﺤﻣ رد مﺎﺴﺟا ﻲﻳﺎﺟ ﻲﺻﺎﺧ يﺎﻫدﺮﺑرﺎﻛ و گرﺰﺑ يﺎﻫ

ﺮﻴﻈﻧ ﻪﺘﺴﻫ و ﻲﻣﺎﻈﻧ ﻊﻳﺎﻨﺻ رد كﺎﻧﺮﻄﺧ داﻮﻣ ﻞﻤﺣ هدﺎﻔﺘﺳا يا

ﻲﻣ دﻮﺷ ] 1

، 2 .[

اﺬﻟ تﺎﺑر ﻣ هراﻮﻤﻫ كﺮﺤﺘﻣ يﺎﻫ نﺎﻘﻘﺤﻣ ﻪﺟﻮﺗ درﻮ

هدﻮﺑ ﻚﻴﺗﺎﺑر ﻢﻠﻋ شور و تﻻﺎﻘﻣ و

ﻪﻨﻴﻣز رد ﻲﻋﻮﻨﺘﻣ يﺎﻫ

نآ لﺮﺘﻨﻛ و ﺮﻴﺴﻣ ﻲﺣاﺮﻃ ﺖﺳا هﺪﺷ ﻪﺋارا ﺎﻫ

] 3 - 6 .[

ﺶﻧارﺎﻜﻤﻫ و ﻮﻠﻴﺘﺳﺎﻛ ]

7 [ رﻮﻈﻨﻣ ﻪﺑ ﻚﻴﺘﻧژ ﻢﺘﻳرﻮﮕﻟا شور زا

ﺮﻴﻏ دﻮﻴﻗ ﻦﺘﻓﺮﮔ ﺮﻈﻧرد ﺎﺑ كﺮﺤﺘﻣ تﺎﺑر ﺮﻴﺴﻣ ﻲﺣاﺮﻃ ﻚﻴﻣﻮﻧﻮﻟﻮﻫ ﻢﺘﺴﻴﺳ

ﺪﻧدﺮﻛ هدﺎﻔﺘﺳا .

و ﺮﻳﺮﭘ نارﺎﻜﻤﻫ ] 8 [ ﻪﺑ

تﺎﺑر ﺮﻴﺴﻣ ﻲﺣاﺮﻃ كﺮﺤﺘﻣ

ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ ﺪﻨﺘﺧادﺮﭘ

. نآ ﺎﻫ رد

شور تﺎﺑر ﻲﻜﻴﺗﺎﻤﻨﻴﺳ يزﺎﺴﻟﺪﻣ ﻪﺑ ﺎﻬﻨﺗ دﻮﺧ يدﺎﻬﻨﺸﻴﭘ

ﺪﻨﺘﺧادﺮﭘ كﺮﺤﺘﻣ .

ﻲﺘﺴﻳﺎﺑ كﺮﺤﺘﻣ تﺎﺑر ﺮﻴﺴﻣ ﻲﺣاﺮﻃ رد ﺎﻣا

ﺖﻳدوﺪﺤﻣ ﻪﺑ كﺮﺤﻣ روﺎﺘﺸﮔ و ﻢﺘﺴﻴﺳ ﻲﺳﺮﻨﻳا يﺎﻫ

ﻪﺟﻮﺗ ﺎﻫ

ﺖﺷاد

، ﻦﻳا ﺮﻴﻏ رد مﺎﺠﻧا رد ﺮﻴﺴﻣ ﻲﺣاﺮﻃ يﺎﻫﺎﻄﺧ ترﻮﺻ

ﺖﺴﺗ ﺖﻓﺎﻳ ﺪﻫاﻮﺧ ﺶﻳاﺰﻓا ﻲﺑﺮﺠﺗ يﺎﻫ .

ﻊﺟﺮﻣ رد ]

9 [ نﺎﻣز ﺎﺑ ﺮﻴﻐﺘﻣ ﺖﻟﺎﺣ ﻚﺑﺪﻴﻓ ﻲﻟﺮﺘﻨﻛ شور زا

،

ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ كﺮﺤﺘﻣ تﺎﺑر ﺮﻴﺴﻣ ﻲﺣاﺮﻃ و لﺮﺘﻨﻛ رﻮﻈﻨﻣ ﻪﺑ

،

هدﺎﻔﺘﺳا ﺖﺳا هﺪﺷ .

ﻲﻓﺮﻃ زا

، هدزﺎﺑ و ﻲﻳارﺎﻛ ﺶﻳاﺰﻓا رﻮﻈﻨﻣ ﻪﺑ

تﺎﺑر ،كﺮﺤﺘﻣ يﺎﻫ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻲﺣاﺮﻃ

نآ ﺎﻫ ﺖﻴﻤﻫا زا هﮋﻳو

يا

رادرﻮﺧﺮﺑ ﺖﺳا

. نﻮﮔﺎﻧﻮﮔ تﻻﺎﻘﻣ رد

، رد ﺎﺑ فﺪﻫ ﻊﺑاﻮﺗ ﻦﺘﻓﺮﮔ ﺮﻈﻧ

ﺖﻛﺮﺣ نﺎﻣز ﻦﻳﺮﺘﻤﻛ نﻮﭼ ﻲﻋﻮﻨﺘﻣ ]

10 [ شﻼﺗ ﻦﻳﺮﺘﻤﻛ ،

يدورو ] 11 [ ﻊﻧﺎﻣ زا يرود ، ]

12 [ و هﺮﻴﻏ

، ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻲﺣاﺮﻃ

ﻲﻣ مﺎﺠﻧا دﻮﺷ .

ﺶﻧارﺎﻜﻤﻫ و ﻢﻳارﻮﻛ ]

13 [ ﻪﻣﺎﻧﺮﺑ شور زا يﺰﻳر

يراﺮﻜﺗ

1ﻲﻄﺧ ﺪﻧدﺮﻛ هدﺎﻔﺘﺳا كﺮﺤﺘﻣ تﺎﺑر ﺮﻴﺴﻣ ﻲﺣاﺮﻃ ياﺮﺑ .

ﻦﻳا

ﻲﻄﺧ نﻮﭼ ﻲﺒﻳﺎﻌﻣ ياراد شور ﻢﻫ مﺪﻋ و تﻻدﺎﻌﻣ يزﺎﺳ

ﻲﻳاﺮﮔ

ﺦﺳﺎﭘ ﺐﺳﺎﻨﻣ دراﺪﻧ ﻲﺒﺳﺎﻨﻣ دﺮﺑرﺎﻛ ﻞﻤﻋ رد اﺬﻟ و هدﻮﺑ

.

ﻊﺟﺮﻣ رد ]

14 [ ﺮﻴﻏ كﺮﺤﺘﻣ تﺎﺑر ﻪﻨﻴﻬﺑ ﻲﺑﺎﻳﺮﻴﺴﻣ

ﻚﻴﻣﻮﻧﻮﻟﻮﻫ

، ﻲﺘﻟﺎﺣ يازا ﻪﺑ ﺪﺷﺎﺑ ﺺﺨﺸﻣ ﻪﺠﻨﭘ ﺮﻴﺴﻣ ﻪﻛ

، ﻣ درﻮ

ﻲﺳرﺮﺑ ﻪﺘﻓﺮﮔ راﺮﻗ ﺖﺳا

. لﺪﻣ اﺪﺘﺑا ﺎﺑ ﻢﺘﺴﻴﺳ ﻲﻜﻴﻣﺎﻨﻳد يزﺎﺳ

ﺮﻴﺴﻣ ﻲﺣاﺮﻃ و هﺪﺷ مﺎﺠﻧا ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ دﻮﻴﻗ ﻦﺘﻓﺮﮔ ﺮﻈﻧرد كﺮﺤﺘﻣ تﺎﺑر ﻪﻨﻴﻬﺑ

، ﻪﺠﻨﭘ ﺺﺨﺸﻣ ﺮﻴﺴﻣ يازا ﻪﺑ ﺪﺷ مﺎﺠﻧا ،

.

ﻲﻤﻇﺎﻧ و ﻢﻳارﻮﻛ

هداز ] 15 [ رد كﺮﺤﺘﻣ تﺎﺑر ﻲﺑﺎﻳﺮﻴﺴﻣ ﻲﺳرﺮﺑ ﻪﺑ

ﻊﺑاﻮﺗ زا و ﻪﺘﺧادﺮﭘ ﻲﻄﻴﺤﻣ ﻊﻧاﻮﻣ رﻮﻀﺣ ﻪﺑ يزﺎﺠﻣ ﻞﻴﺴﻧﺎﺘﭘ

ﺪﻧدﺮﻛ هدﺎﻔﺘﺳا ﻊﻧاﻮﻣ زا كﺮﺤﺘﻣ تﺎﺑر يرود رﻮﻈﻨﻣ .

ﻦﻴﻨﭽﻤﻫ

،

و ﻮﮔﺎﻣارﺎﺳ نارﺎﻜﻤﻫ

] 16 [ ﻪﻨﻴﻬﺑ ﻢﻴﻘﺘﺴﻣ شور زا ياﺮﺑ يزﺎﺳ

دﺮﻛ هدﺎﻔﺘﺳا تﺎﺑر ﺮﻴﺴﻣ ﻲﺣاﺮﻃ ﺪﻧ

. نآ ﻪﺑ شور ﻦﻳا رد ﺎﻫ

ﻪﺘﺴﺴﮔ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻲﺣاﺮﻃ ﻪﺑ و ﻪﺘﺧادﺮﭘ يرﺎﻛ يﺎﻀﻓ يزﺎﺳ

ﻲﻣ ﺶﻳاﺰﻓا ﺚﻋﺎﺑ ﻪﻛ ﺪﻧزادﺮﭘ رﺎﺠﻔﻧا ﺎﺣﻼﻄﺻا و تﺎﺒﺳﺎﺤﻣ

2يدﺪﻋ ﻲﻣ ددﺮﮔ . ﻊﺟﺮﻣ رد ]

17 [ و ] 18 [ ﺮﻴﺴﻣ ﻲﺣاﺮﻃ ﻪﺑ

كﺮﺤﺘﻣ تﺎﺑر ﻪﻨﻴﻬﺑ فﺎﻄﻌﻧا

لﺮﺘﻨﻛ شور زا هدﺎﻔﺘﺳا ﺎﺑ ﺮﻳﺬﭘ

ﺖﺳا هﺪﺷ ﻪﺘﺧادﺮﭘ ﻪﻨﻴﻬﺑ .

كﺮﺤﺘﻣ تﺎﺑر ﺮﻴﺴﻣ ،تﻻﺎﻘﻣ ﻦﻳا رد

و هدﻮﺑ ﺺﺨﺸﻣ هﺪﺸﻧ ﻪﺘﻓﺮﮔ ﺮﻈﻧرد تﺎﺑر ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ دﻮﻴﻗ

ﻪﻨﻴﻬﺑ ﻞﻤﻋ رد و ﺖﺳا يزﺎﺳ

تﺎﺑر ﻪﻄﻘﻧ ﻪﺑ ﻪﻄﻘﻧ ﺖﻛﺮﺣ ﺮﻴﺴﻣ

ﺖﺳا هﺪﺸﻧ مﺎﺠﻧا .

رد ﻦﻳا ﻪﻟﺎﻘﻣ

، تﺎﺑر ﻪﻄﻘﻧ ﻪﺑ ﻪﻄﻘﻧ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻲﺣاﺮﻃ ﻪﺑ

ﺎﺑ نآ ﻪﺴﻳﺎﻘﻣ و كﺮﺤﺘﻣ ﺖﺴﺗ

ﻲﺣاﺮﻃ ﻲﺑﺮﺠﺗ يﺎﻫ ﺮﻴﺴﻣ

ﺮﭘ ﻲﻣ ﻪﺘﺧاد دﻮﺷ

. اﺪﺘﺑا رﻮﻈﻨﻣ ﻦﻳﺪﺑ

، دﻮﻴﻗ ﻦﺘﻓﺮﮔ ﺮﻈﻧرد ﺎﺑ

خﺮﭼ ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ تﺎﺑر ﻲﻄﺧﺮﻴﻏ ﻲﻜﻴﻣﺎﻨﻳد تﻻدﺎﻌﻣ ،ﺎﻫ

ﺎﺑ كﺮﺤﺘﻣ ﻲﻣ جاﺮﺨﺘﺳا ﮋﻧاﺮﮔﻻ ﻞﺻا زا هدﺎﻔﺘﺳا

دﻮﺷ . ﻦﻳا ﺲﭙﺳ

ﻪﺑ و هﺪﺷ نﺎﻴﺑ ﺖﻟﺎﺣ يﺎﻀﻓ رد تﻻدﺎﻌﻣ ﻪﻠﺌﺴﻣ دﻮﻴﻗ ناﻮﻨﻋ

رد ﻪﻨﻴﻬﺑ لﺮﺘﻨﻛ ﻲﻣ ﻪﺘﻓﺮﮔ ﺮﻈﻧ

دﻮﺷ . ﻨﻳﺰﻫ ﻊﺑﺎﺗ ﻦﻴﻨﭽﻤﻫ ﻞﻣﺎﺷ ﻪ

مﺮﺗ رد ﺖﻋﺮﺳ و روﺎﺘﺸﮔ يﺎﻫ ﻲﻣ ﻪﺘﻓﺮﮔ ﺮﻈﻧ

دﻮﺷ ﻪﻠﺌﺴﻣ و

ﻲﻣ نﻮﻴﺳﻻﻮﻣﺮﻓ ﻪﻨﻴﻬﺑ لﺮﺘﻨﻛ دﻮﺷ

. ﺲﭙﺳ

، زا هدﺎﻔﺘﺳا ﺎﺑ ﻞﺻا

ﻦﻴﮔﺎﻳﺮﺘﻧﻮﭘ ﻢﻤﻴﻨﻴﻣ ،ﻪﻨﻴﻬﺑ لﺮﺘﻨﻛ ﻪﻠﺌﺴﻣ ﻢﻴﻘﺘﺴﻣﺮﻴﻏ ﻞﺣ و3

ﻞﻴﺴﻧاﺮﻔﻳد تﻻدﺎﻌﻣ ﻪﻋﻮﻤﺠﻣ ﻚﻳ ترﻮﺻ ﻪﺑ ﻲﮕﻨﻴﻬﺑ تﻻدﺎﻌﻣ شور زا هدﺎﻔﺘﺳا ﺎﺑ ﻪﻛ هﺪﺷ جاﺮﺨﺘﺳا ﻲﻄﺧﺮﻴﻏ ﻞﺣ يدﺪﻋ يﺎﻫ

ﻲﻣ دﻮﺷ . ﻦﻴﻨﭽﻤﻫ

، ﻪﻴﺒﺷ يزﺎﺳ ﺎﻫ مﺎﺠﻧا هﺪﺷ ﺖﺴﺗ ﺞﻳﺎﺘﻧ ﺎﺑ يﺎﻫ

يدﺎﻬﻨﺸﻴﭘ شور ﻲﻳارﺎﻛ ﺎﺗ هﺪﺷ ﻪﺴﻳﺎﻘﻣ ﻲﺑﺮﺠﺗ ﻲﺳرﺮﺑ درﻮﻣ

دﺮﻴﮔ راﺮﻗ .

ﻪﻟﺎﻘﻣ يﺪﻌﺑ ﺶﺨﺑ رد

، ﻲﻜﻴﻣﺎﻨﻳد تﻻدﺎﻌﻣ ﻲﻄﺧﺮﻴﻏ

خﺮﭼ كﺮﺤﺘﻣ تﺎﺑر ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ دﻮﻴﻗ ﻦﺘﻓﺮﮔ ﺮﻈﻧرد ﺎﺑ راد

ﻲﻣ نﺎﻴﺑ دﻮﺷ .

مﻮﺳ ﺶﺨﺑ رد

، ﺎﺑ تﺎﺑر ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻲﺣاﺮﻃ نﻮﻴﺳﻻﻮﻣﺮﻓ

جاﺮﺨﺘﺳا ﻲﮕﻨﻴﻬﺑ تﻻدﺎﻌﻣ و نﺎﻴﺑ ﻪﻨﻴﻬﺑ لﺮﺘﻨﻛ شور زا هدﺎﻔﺘﺳا ﻲﻣ دﻮﺷ . ﺞﻳﺎﺘﻧ ﻦﻴﻨﭽﻤﻫ ﻪﻴﺒﺷ

يزﺎﺳ ﻧ و ﺎﻫ درﻮﻣ ﻲﺑﺮﺠﺗ ﺞﻳﺎﺘ

ﻲﻣ راﺮﻗ ﻲﺳرﺮﺑ دﺮﻴﮔ

و ﻪﺠﻴﺘﻧ ﻪﻟﺎﻘﻣ ﺮﺧآ ﺶﺨﺑ رد ﺚﺣﺎﺒﻣ يﺮﻴﮔ

ﻲﻣ مﺎﺠﻧا دﻮﺷ .

2. Numerical explosion

(3)

2 - كﺮﺤﺘﻣ تﺎﺑر ﻲﻜﻴﻣﺎﻨﻳد تﻻدﺎﻌﻣ

ﺶﺨﺑ ﻦﻳا رد

، ﻌﻣ جاﺮﺨﺘﺳا ﻪﺑ ﺎﺑ كﺮﺤﺘﻣ تﺎﺑر ﻲﻜﻴﻣﺎﻨﻳد تﻻدﺎ

رد ﻲﻣ ﻪﺘﺧادﺮﭘ ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ دﻮﻴﻗ ﻦﺘﻓﺮﮔ ﺮﻈﻧ دﻮﺷ

. ﻞﻜﺷ 1

كﺮﺤﻣ خﺮﭼ ود ﺎﺑ كﺮﺤﺘﻣ تﺎﺑر اﺰﺠﻣ

ﻲﻣ نﺎﺸﻧ ار ﻪﺑ ﻪﻛ ﺪﻫد

ﻲﻣ رد ﺖﻛﺮﺣ ﻪﺑ رﻮﺗﻮﻣ ود ﻂﺳﻮﺗ اﺰﺠﻣ ترﻮﺻ ﺪﻳآ

.

ﻞﻜﺷ ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ كﺮﺤﺘﻣ تﺎﺑر1

هزاﺪﻧا و ﺎﻫﺮﺘﻣارﺎﭘ ﺮﻴﻏ كﺮﺤﺘﻣ تﺎﺑر ﻪﺑ طﻮﺑﺮﻣ يﺎﻫ

ﻚﻴﻣﻮﻧﻮﻟﻮﻫ

، ﻞﻜﺷ ﻖﺑﺎﻄﻣ 1

، ترﺎﺒﻋ ا زا ﺖﺳ :

،ﻪﻳﺎﭘ مﺮﺟ ﺰﻛﺮﻣ C ،ﻪﻳﺎﭘ ﻲﺳﺪﻨﻫ ﺰﻛﺮﻣ O

ﺰﻛﺮﻣ ﻪﻠﺻﺎﻓ b

خﺮﭼ زا ﻲﺳﺪﻨﻫ ،ﺎﻫ

،ﻲﺳﺪﻨﻫ ﺰﻛﺮﻣ و مﺮﺟ ﺰﻛﺮﻣ ﻪﻠﺻﺎﻓ d

) , (x_c y_c ،تﺎﺑر مﺮﺟ ﺰﻛﺮﻣ ﺖﻴﻌﻗﻮﻣ ﺖﻬﺟ ﻪﻳوازφ

،تﺎﺑر يﺮﻴﮔ

r l θ θ , ﻪﻳواز نارود راﺪﻘﻣ ﺐﻴﺗﺮﺗ ﻪﺑ ،ﭗﭼ و ﺖﺳار خﺮﭼ يا

r l θ θ^&,^&

ﻪﻳواز ﺖﻋﺮﺳ راﺪﻘﻣ ﺐﻴﺗﺮﺗ ﻪﺑ ،ﭗﭼ و ﺖﺳار خﺮﭼ يا

c

c m

I , ،ﻪﻳﺎﭘ ﻲﺳﺮﻨﻳا نﺎﻤﻣ و مﺮﺟ

w

w m

I , نﺎﻤﻣ و مﺮﺟ

خﺮﭼ ﻲﺳﺮﻨﻳا ،ﺎﻫ

r0

خﺮﭼ عﺎﻌﺷ ،تﺎﺑر يﺎﻫ

Tr

رﻮﺗﻮﻣ روﺎﺘﺸﮔ

و ﺖﺳار خﺮﭼ Tl

ﭗﭼ خﺮﭼ رﻮﺗﻮﻣ روﺎﺘﺸﮔ .

اﺪﺘﺑا ﺎﺑ ﺑﻴ نﺎ رادﺮﺑ تﺎﺼﺘﺨﻣ ﻣﻮﻤﻋ

[

x_c y_c _r _l

]

^Tﻲ

qr= φ θ θ

ﻗ ﻴ دﻮ ﺒﻧﺎﺟ شﺰﻐﻟ مﺪﻋ ﻲ

ﻟﻮﻃ شﺰﻐﻟ مﺪﻋ و تﺎﺑر ﻲ

خﺮﭼ ﺎﻫ ﺎﺑ ﺮﺑاﺮﺑ

ﻪﻄﺑار ) 1 ( ﺖﺳا :

) 1 (

l

c c

r c

c

c c

r b y

x

r b y

x

d x

y

θ φ φ φ

φ φ φ

&

0 0

sin cos

0 sin

cos

=

− +

= + +

=

−

دﻮﻴﻗ ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ ﻢﺘﺴﻴﺳ

ﻪﺑ ﻞﻜﺷ ﺮﺗﺎﻣ ﻳ ﺴ ﻲ ز ﻳ ﺮ ﺑﻴ نﺎ ﻣ ﻲ دﻮﺷ :

) 2 (

=0 q A&r

ﻻﺎﺑ ﻪﻄﺑار رد

، ﺲﻳﺮﺗﺎﻣ و ﺖﺳا ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ دﻮﻴﻗ ﺮﮕﻧﺎﻴﺑ A

ﺎﺑ ﺖﺳا ﺮﺑاﺮﺑ :

)

3 (

















−

=

r b

r b d A

0 sin

cos

0 sin

cos

0 0 cos

sin

φ φ

ﻪﺑ ﻢﺘﺴﻴﺳ ﻲﻜﻴﻣﺎﻨﻳد تﻻدﺎﻌﻣ ،ﮋﻧاﺮﮔﻻ ﻞﺻا زا هدﺎﻔﺘﺳا ﺎﺑ ﻲﻣ نﺎﻴﺑ ﺮﻳز ﻲﻳﺎﻬﻧ مﺮﻓ ددﺮﮔ

:

) 4 (

( )

^q^r ^&r^q^& ^V^r

( )

^q^r ^q^r^& ^B^T^r ^A^T^λ^r

M + , = +

،ﻻﺎﺑ ﻪﻄﺑار رد ،مﺮﺟ ﺲﻳﺮﺗﺎﻣ M

V r يﺎﻫوﺮﻴﻧ رادﺮﺑ

،ﻢﺘﺴﻴﺳ ﻲﺸﻧاﺮﮔ و ﻲﻄﺧﺮﻴﻏ روﺎﺘﺸﮔ ﺐﻳاﺮﺿ ﺲﻳﺮﺗﺎﻣ B

،يدورو

[

Tr Tl

]

^T

T = r رادﺮﺑ خﺮﭼ رﻮﺗﻮﻣ روﺎﺘﺸﮔ تﺎﺑر يﺎﻫ

و

λ^r ﻲﻣ ﮋﻧاﺮﮔﻻ ﺐﻳاﺮﺿ لﻮﻬﺠﻣ مﺮﺗ ﺪﺷﺎﺑ

. تﺎﺑر ﻪﺑ طﻮﺑﺮﻣ ﺮﻳدﺎﻘﻣ

رد كﺮﺤﺘﻣ ﻪﻄﺑار

) 4 ( زا ﺖﺳا ترﺎﺒﻋ :













−

− +

+

=

w w c

w w

c

w w

c

I I I

d m d

m

d m m

m

d m m

m

M

0 0

0 0 cos

2 sin 2

0 0 cos 2 2

0

0 0 sin 2 0

2

φ φ

) 5 (

) 6 (













=

0 0 0

sin 2

cos 2

2 2

φ φ

&

d m

d m V

w w

) 7 (













= 0 1

0 1

0 0

0 0 B

تﻻدﺎﻌﻣ زا ﮋﻧاﺮﮔﻻ ﺐﻳاﺮﺿ مﺮﺗ فﺬﺣ رﻮﻈﻨﻣ ﻪﺑ ﻪﻣادا رد ،ﻢﺘﺴﻴﺳ ﻲﻜﻴﻣﺎﻨﻳد ﺖﻋﺮﺳ رادﺮﺑ

[

θr θl

]

^T

υ^r= ^& ^&

ﺲﻳﺮﺗﺎﻣ و S

ﺎﺑ ﻲﮔﮋﻳو 0 .

, =

=S AS q^r^& υ^r ﻲﻣ ﻒﻳﺮﻌﺗ

دﻮﺷ . رد ﺖﻟﺎﺣ ﻦﻳا

ﺲﻳﺮﺗﺎﻣ ﺲﻳﺮﺗﺎﻣ ﻲﭼﻮﭘ يﺎﻀﻓ رد S

ﻪﻄﺑار زا و هدﻮﺑ A )

8 (

ﺑ ﻪ ﻲﻣ ﺖﺳد ﺪﻳآ

:

) 8 (

b

c r c

c

d b

c d

b c

d b

c d

b c

S 2

1 0

0 1

) cos sin

( ) cos sin

(

) sin cos

( ) sin cos

(

= 0













−

− +

+

−

=

φ φ

Y

X O

φ

d C b

(4)

تﻻدﺎﻌﻣ نﺎﻴﺑ ياﺮﺑ رد

يﺎﻀﻓ رادﺮﺑ ﻒﻳﺮﻌﺗ ﺎﺑ ،ﺖﻟﺎﺣ يﺎﻀﻓ

[

x_c y_c _r _l _r _l

]

^T

[

x x

]

^T ﺖﻟﺎﺣ

X^r = φ θ θ θ^& θ^& = ₁ ... ₇

ﻪﺑ ﺖﻳﺎﻬﻧ رد ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ كﺮﺤﺘﻣ تﺎﺑر ﺖﻟﺎﺣ يﺎﻀﻓ تﻻدﺎﻌﻣ دﻮﺑ ﺪﻫاﻮﺧ ﺮﻳز ﻞﻜﺷ :

) 9 (

) (

0

1 2

V S S M S MS S f

MS T S f X S

T T

r r

&

r r r

r

&

r

−

=



 

 +



 



=

−

υ υ

3 - ﺮﻴﺴﻣ ﻲﺣاﺮﻃ و ﻪﻨﻴﻬﺑ لﺮﺘﻨﻛ نﻮﻴﺳﻻﻮﻣﺮﻓ

كﺮﺤﺘﻣ تﺎﺑر ﻪﻨﻴﻬﺑ

ﻚﻳ ترﻮﺻ ﻪﺑ كﺮﺤﺘﻣ تﺎﺑر ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻲﺣاﺮﻃ ،ﺶﺨﺑ ﻦﻳا رد نﻮﻴﺳﻻﻮﻣﺮﻓ ﻪﻨﻴﻬﺑ لﺮﺘﻨﻛ ﻪﻠﺌﺴﻣ ﻲﻣ

دﻮﺷ . نﻮﻴﺳﻻﻮﻣﺮﻓ رد

ﻪﻄﺑار ﻪﻨﻴﻬﺑ لﺮﺘﻨﻛ ﻪﻠﺌﺴﻣ )

9 (،

ﻲﻜﻴﻣﺎﻨﻳد تﻻدﺎﻌﻣ ﺮﮕﻧﺎﻴﺑ ﻪﻛ

ﺖﺳا ﺖﻟﺎﺣ يﺎﻀﻓ رد ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ كﺮﺤﺘﻣ تﺎﺑر

، ناﻮﻨﻋ ﻪﺑ

ﻪﻠﺌﺴﻣ دﻮﻴﻗ رد

ﻲﻣ ﻪﺘﻓﺮﮔ ﺮﻈﻧ دﻮﺷ

رادﺮﺑ ﻦﺘﻓﺎﻳ فﺪﻫ و ﺖﻟﺎﺣ

ﻪﻨﻴﻬﺑ X∗

r و روﺎﺘﺸﮔ ﻪﻨﻴﻬﺑ يدورو T∗

r ﻪﻧﻮﮔ ﻪﺑ يا ا ﻪﻛ ﺖﺳ

دﻮﺷ ﻪﻨﻴﻤﻛ ﺮﻳز فﺪﻫ ﻊﺑﺎﺗ و راﺮﻗﺮﺑ ﻢﺘﺴﻴﺳ يﺪﻴﻗ تﻻدﺎﻌﻣ :

) 10 (

(

^X ^t ^T ^t ^t

)

^dt

L

J ^f

o t

∫

t

= ( ), ( ), r

r

ﻪﻄﺑار رد )

10 (،

ﻪﻨﻴﻬﺑ رﻮﻈﻨﻣ ﻪﺑ تﺎﺑر يژﺮﻧا فﺮﺼﻣ يزﺎﺳ

نآ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻲﻃ رد

، فﺪﻫ ﻊﺑﺎﺗ ﻳز ﻞﻜﺷ ﻪﺑ

رد ﺮ ﺮﻈﻧ

ﻲﻣ ﻪﺘﻓﺮﮔ دﻮﺷ

:

) 11 (

( )

⁼ _^ ² ⁺ ² _^

2 ) 1 ( ),

(t T t X W T R

X L

r r

11 (

2 مﺮﺗ

||

||X _W r ﻢﻴﻤﻌﺗ ﻲﻌﺑﺮﻣ مﺮﻧ ﻪﺘﻓﺎﻳ

رادﺮﺑ1

ﻪﺑ ﺖﺒﺴﻧ ﺖﻟﺎﺣ يﺎﻀﻓ ﻲﻧزو ﺲﻳﺮﺗﺎﻣW

ﺖﻟﺎﺣ يﺎﻀﻓ ﺖﻴﺻﺎﺧ ﺎﺑ

ﻪﻤﻴﻧ ﺖﺒﺜﻣ نرﺎﻘﺘﻣ ﻦﻴﻌﻣ

ﺖﺳا . مﺮﺗ ﻦﻴﻨﭽﻤﻫ

||2

||T _R r مﺮﻧ

ﻢﻴﻤﻌﺗ ﻲﻌﺑﺮﻣ ﻪﺘﻓﺎﻳ

رادﺮﺑ روﺎﺘﺸﮔ ﻢﺘﺴﻴﺳ يدورو

ﺖﺒﺴﻧ

ﻪﺑ ﻲﻧزو ﺲﻳﺮﺗﺎﻣ R لﺮﺘﻨﻛ

ﺎﺑ ﻲﮔﮋﻳو ﺖﺒﺜﻣ نرﺎﻘﺘﻣ ﻦﻴﻌﻣ

ﻲﻣ ﺪﺷﺎﺑ . ﻲﻣ اﺬﻟ ﺲﻳﺮﺗﺎﻣ ناﻮﺗ يﺮﻄﻗ ترﻮﺻ ﻪﺑ ار ﻲﻧزو يﺎﻫ

(

1 2

)

diagr r R=

(

₁ ... ₇

)

و

diagw w

W = ﺖﻓﺮﮔ ﺮﻈﻧرد .

و ﻢﻴﻘﺘﺴﻣ شور ود ،ﻪﻨﻴﻬﺑ لﺮﺘﻨﻛ ﻪﻠﺌﺴﻣ ﻞﺣ رﻮﻈﻨﻣ ﻪﺑ ﻲﻣ هدﺎﻔﺘﺳا ﻢﻴﻘﺘﺴﻣﺮﻴﻏ دﻮﺷ

] 19 [ . يﺎﻀﻓ ﻢﻴﻘﺘﺴﻣ شور رد

ﻪﺘﺴﺴﮔ ﻢﺘﺴﻴﺳ فﺪﻫ ﻊﺑﺎﺗ و ﺖﻟﺎﺣ تﻻدﺎﻌﻣ و هﺪﺷ يزﺎﺳ

ﻲﻣ جاﺮﺨﺘﺳا ﻪﺘﺴﺴﮔ يﺎﻀﻓ رد ﻲﮕﻨﻴﻬﺑ ددﺮﮔ

. ياراد شور ﻦﻳا

ﻢﺠﺣ هدﻮﺑ ﻲﻳﻻﺎﺑ تﺎﺒﺳﺎﺤﻣ و

ﻪﺑ ﻢﺘﺴﻴﺳ ياﺮﺑ هﮋﻳو ﻲﻄﺧﺮﻴﻏ يﺎﻫ

دراﺪﻧ دﺮﺑرﺎﻛ ﻻﺎﺑ يدازآ تﺎﺟرد ﺎﺑ

. ﻢﻴﻘﺘﺴﻣﺮﻴﻏ شور رد ﻪﻴﻀﻗ زا

ترﻮﺻ ﻪﺑ ﻲﮕﻨﻴﻬﺑ تﻻدﺎﻌﻣ و هدﺮﻛ هدﺎﻔﺘﺳا تاﺮﻴﻴﻐﺗ بﺎﺴﺣ ﻪﻠﭘﻮﻛ ﻞﻴﺴﻧاﺮﻔﻳد تﻻدﺎﻌﻣ ﻪﻋﻮﻤﺠﻣ ﻲﻣ جاﺮﺨﺘﺳا هﺪﺷ

ددﺮﮔ . رد

ﻪﻟﺎﻘﻣ ﻦﻳا

، ﻲﻣ هدﺎﻔﺘﺳا ﻦﻴﮔﺎﻳﺮﺘﻧﻮﭘ ﻢﻤﻴﻨﻴﻣ ﻞﺻا زا دﻮﺷ

. ﺎﺑ

ﻊﺑﺎﺗ اﺪﺘﺑا رد ،ﻢﻴﻘﺘﺴﻣﺮﻴﻏ شور ﻦﻳا زا هدﺎﻔﺘﺳا ﻪﺑ ﻦﻴﻧﻮﺘﻠﻴﻤﻫ

ترﻮﺻ X P L

H r^T r&

+ ﻲﻣ ﻒﻳﺮﻌﺗ =

رادﺮﺑ ﻪﻛ ددﺮﮔ P

r رادﺮﺑ

ﻪﺒﺷ ﻲﻣ هﺪﻴﻣﺎﻧ ﺖﻟﺎﺣ دﻮﺷ

. بﺎﺴﺣ شور زا هدﺎﻔﺘﺳا ﺎﺑ ﺲﭙﺳ

تﻻدﺎﻌﻣ ﻪﻋﻮﻤﺠﻣ ﻚﻳ ترﻮﺻ ﻪﺑ ﻲﮕﻨﻴﻬﺑ ﻂﻳاﺮﺷ تاﺮﻴﻴﻐﺗ ﻲﻣ جاﺮﺨﺘﺳا ﻲﻄﺧﺮﻴﻏ ﻞﻴﺴﻧاﺮﻔﻳد دﻮﺷ

] 19 :[

) 12 (

(

^X ^t ^T ^t ^P ^t ^t

)

P

t H

X^*( ) ^*(), ^*(), ^*(), r r r

& r r

∂

=∂

) 13 (

(

^X ^t ^T ^t ^P ^t ^t

)

X

t H

P^*() ^*(), ^*(), ^*(), r r r

& r r

∂

−∂

=

) 14 (

(

^X ^t ^T ^t ^P ^t ^t

)

T

H (), ( ), ( ),

0 ^* ^* ^*

r r r r r

∂

=∂

،كﺮﺤﺘﻣ تﺎﺑر ﻪﻄﻘﻧ ﻪﺑ ﻪﻄﻘﻧ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻲﺣاﺮﻃ ياﺮﺑ ﻲﮕﻨﻴﻬﺑ تﻻدﺎﻌﻣ )

12 ( ﺎﺗ ) 14 ( تﻻدﺎﻌﻣ ﻪﻋﻮﻤﺠﻣ ﻚﻳ ترﻮﺻ ﻪﺑ

ﻲﻣ ﻞﺻﺎﺣ ﺺﺨﺸﻣ يزﺮﻣ ﻂﻳاﺮﺷ ﺎﺑ ﻞﻴﺴﻧاﺮﻔﻳد دﻮﺷ

. ﻪﻠﺌﺴﻣ ﻦﻳا

ﻲﻣ ار يزﺮﻣ راﺪﻘﻣ شور زا هدﺎﻔﺘﺳا ﺎﺑ ناﻮﺗ

دﺮﻛ ﻞﺣ يدﺪﻋ يﺎﻫ .

رﻮﺘﺳد زا ،ﻪﻟﺎﻘﻣ ﻦﻳا رد bvp4c

مﺮﻧ ﻲﺳﺪﻨﻬﻣ راﺰﻓا ﺐﻠﺘﻣ

ﻪﺑ

ﻞﺻﺎﺣ يزﺮﻣ راﺪﻘﻣ ﻪﻠﺌﺴﻣ ﻞﺣ رﻮﻈﻨﻣ و هﺪﻳدﺮﮔ هدﺎﻔﺘﺳا هﺪﺷ

جاﺮﺨﺘﺳا ﻲﮕﻨﻴﻬﺑ تﻻدﺎﻌﻣ يدﺪﻋ ﻞﺣ ﺖﺳا هﺪﺷ مﺎﺠﻧا هﺪﺷ

.

4 - ﻪﻴﺒﺷ ﺞﻳﺎﺘﻧ ﺖﺴﺗ و يزﺎﺳ

ﻲﺑﺮﺠﺗ يﺎﻫ

ﺶﺨﺑ ﻦﻳا رد

، ﻪﻴﺒﺷ ﺞﻳﺎﺘﻧ ﺖﺴﺗ و يزﺎﺳ

تﺎﺑر ﻲﺑﺮﺠﺗ يﺎﻫ

تﺎﻜﺳا ﻲﻫﺎﮕﺸﻳﺎﻣزآ كﺮﺤﺘﻣ ارا2

ﺋ ﺖﺳا هﺪﺷ ﻪ .

ياراد تﺎﺑر ﻦﻳا

ﻞﻜﺷ رد ﻪﻛ ﺖﺳا ﻚﻴﻣﻮﻧﻮﻟﻮﻫﺮﻴﻏ كﺮﺤﺘﻣ ﻪﻳﺎﭘ ﻚﻳ 2

نﺎﺸﻧ

ﺖﺳا هﺪﺷ هداد .

ﻞﻜﺷ كﺮﺤﺘﻣ تﺎﺑر2 تﺎﻜﺳا

(5)

يﺎﻫﺮﺘﻣارﺎﭘ طﻮﺑﺮﻣ

ﻪﺑ ﻦﻳا تﺎﺑر رد لوﺪﺟ 1 ارا ﺋ ﺖﺳا هﺪﺷ ﻪ :

لوﺪﺟ

تﺎﻜﺳا كﺮﺤﺘﻣ تﺎﺑر يﺎﻫﺮﺘﻣارﺎﭘ1

ﺪﺣاو راﺪﻘﻣ تﺎﺑر ﺮﺘﻣارﺎﭘ

kg mc=6.0 ﻪﻳﺎﭘ مﺮﺟ

kg mc=0.32 خﺮﭼ مﺮﺟ

kg.m² I_c=0.06363 ﻪﺤﻔﺻ ﺮﺑ دﻮﻤﻋ رﻮﺤﻣ لﻮﺣ ﻪﻳﺎﭘ ﻲﺳﺮﻨﻳا نﺎﻤﻣ kg.m² Iw=0.0008 شرﻮﺤﻣ لﻮﺣ خﺮﭼ ﺮﻫ ﻲﺳﺮﻨﻳا نﺎﻤﻣ

m b=0.145 ﺎﻫخﺮﭼ زا ﻚﻳ ﺮﻫ زا ^O ﻪﻄﻘﻧ ﻪﻠﺻﺎﻓ

m r0=0.08 خﺮﭼ عﺎﻌﺷ

m d=0.065 ^C زا^O ﻪﻄﻘﻧ ﻪﻠﺻﺎﻓ

ﻦﻴﻨﭽﻤﻫ

، ﻪﺼﺨﺸﻣ ﺎﺑ تﺎﺑر ﻢﻴﻘﺘﺴﻣ نﺎﻳﺮﺟ يﺎﻫرﻮﺗﻮﻣ

ﻲﻣ نﺎﻴﺑ ﺮﻳز ﻪﻄﺑار زا هدﺎﻔﺘﺳا دﻮﺷ

:

) 13 (

[ ]

Nms rad

K

Nm K

K K T

T

/ 4956 . 0 4956 . 0

85 . 6 85 . 6

2 1

=

−

=

−

=

+

−

υ υ r r

r r r r

13 ( خﺮﭼ يﺎﻫروﺎﺘﺸﮔ ﻢﻣﺮﺘﺴﻛا و هدوﺪﺤﻣ يﺎﻫ

تﺎﻜﺳا كﺮﺤﺘﻣ تﺎﺑر

+

− T T

r r ﺖﺳا هﺪﺷ نﺎﻴﺑ , .

ﻪﻴﺒﺷ رﻮﻈﻨﻣ ﻪﺑ كﺮﺤﺘﻣ تﺎﺑر ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻲﺣاﺮﻃ يزﺎﺳ

،تﺎﻜﺳا رد ﻪﻴﺒﺷ ﻪﻴﻟوا ﻂﻳاﺮﺷ زا كﺮﺤﺘﻣ تﺎﺑر لوا يزﺎﺳ

4 ) , 0 , 0

(x m y m rad

P_i _c _C π

φ=

= ﻲﻳﺎﻬﻧ ﻂﻳاﺮﺷ ﻪﺑ =

4 ) , 1 , 0

(x m y m rad

P_f _c _C π

φ=

= رد =

تﺪﻣ نﺎﻣز ﺺﺨﺸﻣ

s t_f =3 ﻲﻣ ﺖﻛﺮﺣ ﺪﻨﻛ

. ﻲﻧزو ﺲﻳﺮﺗﺎﻣ رادﺮﺑ

ﺮﺑاﺮﺑ ﺖﻟﺎﺣ

(

0 ... 0 1 1

)

₇_*₇

=diag لﺮﺘﻨﻛ ﻲﻧزو ﺲﻳﺮﺗﺎﻣ وW

ﺎﺑ ﺮﺑاﺮﺑ يدورو

(

¹ ¹

)

=diag

ﻲﻣ ضﺮﻓ R

دﻮﺷ . مﺎﺠﻧا ﺎﺑ

ﻪﻴﺒﺷ ،يزﺎﺳ تﺎﺑر ﻪﻄﻘﻧ ﻪﺑ ﻪﻄﻘﻧ ﺖﻛﺮﺣ ياﺮﺑ ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ

ترﻮﺻ ﻪﺑ تﺎﻜﺳا كﺮﺤﺘﻣ ﻞﻜﺷ

3 ﻲﻣ ﻞﺻﺎﺣ دﻮﺷ

.

ﻦﻴﻨﭽﻤﻫ

، ﻪﻳواز ﺖﻋﺮﺳ خﺮﭼ يا

تﺎﻜﺳا كﺮﺤﺘﻣ تﺎﺑر يﺎﻫ

نآ ﻪﻄﻘﻧ ﻪﺑ ﻪﻄﻘﻧ ﺮﻴﺴﻣ ﻲﻃ رد ﻞﻜﺷ ﻖﺑﺎﻄﻣ

يﺎﻫ 4 و 5 ﺖﺳا .

نﺎﻤﻫ رد ﻪﻛ رﻮﻃ ﻞﻜﺷ

يﺎﻫ 4 و 5 ﻲﻣ هﺪﻫﺎﺸﻣ ﺖﻋﺮﺳ ،دﻮﺷ

يﺎﻫ

ﻪﻳواز خﺮﭼ يا رد و هدﻮﺑ راﻮﻤﻫ تﺎﻜﺳا كﺮﺤﺘﻣ تﺎﺑر يﺎﻫ

ﺖﺴﺗ دﻮﺑ ﺪﻫاﻮﺧ اﺮﺟا ﻞﺑﺎﻗ ﺰﻴﻧ ﻲﺑﺮﺠﺗ يﺎﻫ .

ﻞﻜﺷ تﺎﺑر ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ3 تﺎﻜﺳا كﺮﺤﺘﻣ

ﻞﻜﺷ ﻪﻳواز ﺖﻋﺮﺳ4 ﺖﺳار خﺮﭼ ﻪﻨﻴﻬﺑ يا

تﺎﺑر

ﻞﻜﺷ ﻪﻳواز ﺖﻋﺮﺳ5 خﺮﭼ ﻪﻨﻴﻬﺑ يا

تﺎﺑر ﭗﭼ

ﻦﻴﻨﭽﻤﻫ

، خﺮﭼ ﺮﺑ دراو ﻪﻨﻴﻬﺑ روﺎﺘﺸﮔ كﺮﺤﺘﻣ تﺎﺑر يﺎﻫ

ﻞﻜﺷ رد تﺎﻜﺳا يﺎﻫ

6 و 7 ﺖﺳا هﺪﺷ هداد ﺶﻳﺎﻤﻧ .

(6)

ﻞﻜﺷ تﺎﺑر ﺖﺳار خﺮﭼ ﺮﺑ دراو ﻪﻨﻴﻬﺑ روﺎﺘﺸﮔ6

ﻞﻜﺷ روﺎﺘﺸﮔ7 تﺎﺑر ﭗﭼ خﺮﭼ ﺮﺑ دراو ﻪﻨﻴﻬﺑ

نﺎﻤﻫ ﻞﻜﺷ رد ﻪﻛ رﻮﻃ يﺎﻫ

ﻲﻣ هﺪﻳد ﻻﺎﺑ يﺎﻫروﺎﺘﺸﮔ ،دﻮﺷ

دراو ﺮﺑ خﺮﭼ يﺎﻫ هدﻮﺑ راﻮﻤﻫ ﺰﻴﻧ تﺎﺑر ﻢﻣﺮﺘﺴﻛا ﺮﻳدﺎﻘﻣ زا ﺮﺘﻤﻛ و

خﺮﭼ كﺮﺤﻣ يﺎﻫرﻮﺗﻮﻣ ﺖﺳا تﺎﺑر يﺎﻫ

. ﻪﻨﻴﻬﺑ ﺮﻴﺴﻣ ﻲﻃ رد اﺬﻟ

ﺖﺴﺗ مﺎﺠﻧا رد و هﺪﻴﺳﺮﻧ عﺎﺒﺷا ﻪﺑ تﺎﺑر يﺎﻫرﻮﺗﻮﻣ ﻲﺑﺮﺠﺗ يﺎﻫ

خر تﺎﺑر كﺮﺤﻣ يﺎﻫرﻮﺗﻮﻣ عﺎﺒﺷا يازا ﻪﺑ ﺮﻴﺴﻣ يﺎﻄﺧ تﺎﺑر داد ﺪﻫاﻮﺨﻧ .

ﻪﻴﺒﺷ ياﺮﺑ ﻂﻳاﺮﺷ زا تﺎﻜﺳا كﺮﺤﺘﻣ تﺎﺑر ،ﺮﮕﻳد يزﺎﺳ

ﻪﻴﻟوا ) 0 , 0 , 0

(x m y m rad

P_i _c = _C = φ = ﻲﻳﺎﻬﻧ ﻂﻳاﺮﺷ ﻪﺑ

) 0 , 2 , 0

(x m y m rad

P_f _c = _C = φ= رد

تﺪﻣ نﺎﻣز ﺺﺨﺸﻣ

s t_f =5.5 ﻲﻣ ﺖﻛﺮﺣ

ﺪﻨﻛ . ﺑاﺮﺑ ﺖﻟﺎﺣ ﻲﻧزو ﺲﻳﺮﺗﺎﻣ ﺎﺑ ﺮ

(

0 ... 0 1 1

)

₇_*₇

diag W= لﺮﺘﻨﻛ ﻲﻧزو ﺲﻳﺮﺗﺎﻣ و

ﺎﺑ ﺮﺑاﺮﺑ يدورو

(

0.1 0.1

)

diag R= ﻲﻣ ضﺮﻓ دﻮﺷ . ﻞﻜﺷ رد

يﺎﻫ 8 و 9 ﻪﻳواز ﺖﻋﺮﺳ خﺮﭼ ﻪﻨﻴﻬﺑ يا

نﺎﺸﻧ ﺎﻫ

ﺖﺳا هﺪﺷ هداد :

ﻞﻜﺷ ﻪﻳواز ﺖﻋﺮﺳ8 ﺖﺳار خﺮﭼ ﻪﻨﻴﻬﺑ يا

تﺎﺑر

ﻞﻜﺷ ﻪﻳواز ﺖﻋﺮﺳ9 خﺮﭼ ﻪﻨﻴﻬﺑ يا

تﺎﺑر ﭗﭼ

ﻞﻜﺷ يﺎﻫ 8 و 9 ﻪﻳواز ﺖﻋﺮﺳ خﺮﭼ يا

ﺮﻴﺴﻣ لﻮﻃ رد ﺎﻫ

ار تﺎﻜﺳا كﺮﺤﺘﻣ تﺎﺑر ﺖﻛﺮﺣ ﻲﻣ نﺎﺸﻧ

ﺪﻫد . ﻪﺟﻮﺗ ﻲﺘﺴﻳﺎﺑ

ﺖﻋﺮﺳ ﻞﻴﻓوﺮﭘ ،تﺎﻜﺳا كﺮﺤﺘﻣ تﺎﺑر هﺪﻧزﺎﺳ ﻂﺳﻮﺗ ﻪﻛ ﺖﺷاد خﺮﭼ ﺮﻈﻧرد تﺎﺑر ﺮﻴﺴﻣ ﻲﻃ ياﺮﺑ و يدورو ناﻮﻨﻋ ﻪﺑ تﺎﺑر يﺎﻫ

ﺖﺳا هﺪﺷ ﻪﺘﻓﺮﮔ .

اﺬﻟ

، زا هدﺎﻔﺘﺳا ﺎﺑ ﻲﺑﺮﺠﺗ ﺖﺴﺗ مﺎﺠﻧا ياﺮﺑ

ﺖﻋﺮﺳ ﻲﺘﺴﻳﺎﺑ ،تﺎﻜﺳا ﻲﻫﺎﮕﺸﻳﺎﻣزآ تﺎﺑر ﺑ ﻪﻨﻴﻬﺑ يﺎﻫ

ﻪ ﺖﺳد

ﻪﻴﺒﺷ زا هﺪﻣآ ار يزﺎﺳ

يدورو ناﻮﻨﻋ ﻪﺑ تﺎﺑر ﻲﻟﺮﺘﻨﻛ ﺶﺨﺑ يﺎﻫ

دﺮﻛ لﺎﻤﻋا نآ ﻪﺑ .

ﻪﺑ ار تﺎﺑر ﺖﻛﺮﺣ ﻞﻛ نﺎﻣز ،رﺎﻛ ﻦﻳا ياﺮﺑ

خﺮﭼ ﺖﻋﺮﺳ راﺪﻘﻣ و هدﺮﻛ ﻢﻴﺴﻘﺗ يوﺎﺴﻣ ﺖﻤﺴﻗ هﺎﺠﻨﭘ رد ار ﺎﻫ

يﺎﻫرادﻮﻤﻧ زا ﻲﻧﺎﻣز ﻪﻠﺻﺎﻓ هﺎﺠﻨﭘ ﻦﻳا 8

و 9 ﻲﻣ جاﺮﺨﺘﺳا ﻢﻴﻨﻛ

.