Mobile%20Robot%20Kinematics - PowerPoint PPT Presentation

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Mobile%20Robot%20Kinematics

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Holonomic Robots Nonholonomic systems Nonholonomic systems are characterized by constraint equations involving the time derivatives of the system conguration variables. – PowerPoint PPT presentation

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Title: Mobile%20Robot%20Kinematics


1
Mobile Robot Kinematics
???????? ???????? ?????
  • ???? ???? ???? ??????
  • ??? 3 ???? Introduction to Autonomous Mobile
    Robots

2
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  • ?????? ???????? ???????? ????? ?? ?? ????? ????
    ???
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  • ????? ??? ????? ?????? ????? ????? ???
  • ?? ?????? ??? ??? ????? ????? ? ????? ????? ??
    ?????? ???? ?????? ???. ????? ????? ?? ?? ????
    ???? ??? ??? ?????? ?????? ???? ???? ?? ??? ????
    ???? ?????? ????.

3
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  • ??? ????? ?????? ??????? ????? ?? ????? ????? ?
    ?????
  • ???????? ??????? ????? ???? ?? ???????? ????? ???
    ?? ??? ????? ?? ????? ????? ??????? ??????? ??
    ???? ???? ?????.
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    ????? ???? ? ?????? ?? ???? ?? ??? ???? ??
    ??????? ???? ?? ???? ??? ????? ??? ???? ????.
  • ?????? ???? ?? ????? ??? ?? ?????? ???? ????? ??.
  • ?????? ?? ??? ????? ??? ??????? ??? ?? ????? ???
    ????? ??????.
  • ???? ??? ???? ????? ???? ?? ??????????? ?? ?????
    ?? ?? ??? ???? ????? ?????? ???? ????.

4
????? ?????? ?? ?????
  • ???? ????? ?????? ?? ????? ???? ??? ?? ????? ???
    ?? ??????
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  • ????? ????- ????? ??????
  • ????? ?????? ?? ??????????? ???? ?? ???????
    ?????.

5
???? ???? ?????? ?????
  • ??? ????? ?? ????? ?? ??? ??? ???? ?? ??? ?????
    ???? ????? ? ?? ??? ?? ???? ???? ?????.
  • ?????? ????? ?? ?????? ?? ?? ????? x,y ?? ???? ?
    ?? ????? q ???? ???? ???? ??? ?? ???? ????

6
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  • ???? ?????? ?? ?? ???? ?????? ??????? ?????
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7
???? ???? ?????? ?????
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    ?? q ???? ? ???? ???? ????? (P) ?????? x,y ????
    ?? ???? ???? ???? ????? ???? ?? ??????? ????
    ????? ???? ?? ???? ???? ????? ??? ???? ???? ?????.

8
???? ???? ?????? ?????
  • ???? ????? ???? ????? ???? ??? ?? ???? ?? ??????
    ???? ???? ?? ???? ?? ???? ????? ????? ???. ????
    ?????? ?? ?????? ????? ??? ??????? ?????.
  • ???? ???? ???? ???? ??? ??? ?????

9
??? ???????? ??????
  • ??? ??? ???? ?????? ????? ? ????? ????? ???? ??
    ????? ????? ???? ????? ????? ????? ????

????? ??? ??? ????? ?? ??? ?? ?? ?? ???? r ???? ?
??????? l ?? ???? P ?? ?? ??? ??? ?? ??? ????
???? ????? ????. ???? ????? ????? ?? q1,q2
??????. ?? ??????? ??? ???????? ?????? ?????
????? ??? ????? ???
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????
12
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  • ???? ?????? ???? ????? ?? ???? ???? ?????? ?????
    ?? ?? ?? ????? ?? ???? ????? ?? ?????? ???? ?
    ????? ?? ?? ???? ???? ????? ??????.
  • ??? ??? ???? ?? ????? ?? ??? ???? X ?? ???? ????
    ???? ???? ???? P ????? ???? ?? ?? ?? ????? ?????
    ??? ????? ???
  • ?? ?? ????? ?? ????? ?????????? ?????? ??? ??
    ????? ?? ?? ?? ??? ????

13
?????? ???????? ??????
  • ????? y. ??? ???? ??? ????? ???.
  • ???? ?????? ????? q ?? ??? ????? ????? ??? ???
    ??? ???? ????? ??? ????? ??? ??? ?? ?? ???? ??
    ????? ???.???? ????? ?? ???? P ????? ????? ???
    ??
  • ?? ???? ????? ???? ??? ?? ?????

?? ????? ??? ????? ??? ????????? ????? ????? ???
????? ???
14
?????? ???????? ??????
  • ?? ??? ????? ????? ?????? ????? ?? ????? ??? ????
    ?????.
  • ?? ???? ??? ???? ????? ???? ????? ????? ??????
    ??? ?? ??????? ???? ?? ?? ??? ?? ???? ???? ?????
    ?? ??? ?? ??? ??????.

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25
Holonomic Robots
26
Nonholonomic systems
  • Nonholonomic systems are characterized by
    constraint equations involving the time
    derivatives of the system conguration variables.
    These equations are non integrable they
    typically arise when the system has less controls
    than configuration variables.
  • For instance a car-like robot has two controls
    (linear and angular velocities) while it moves in
    a 3-dimensional conguration space.
  • As a consequence, any path in the conguration
    space does not necessarily correspond to a
    feasible path for the system. This is basically
    why the purely geometric techniques developed in
    motion planning for holonomic systems do not
    apply directly to nonholonomic ones.

27
???? ??? ????
Nonholonomic Constraint
?? ?? ?????? ?? ?? ??? ???? ? ?? ??? ????? ????
??? ??? ?? ???? ????? ???
28
?????? ?? ?? ??? ????
1
  • ?? ??? ???? ??? ?? ????? holonomic ???

29
????? ???? ???
  • ????? ???? ??? ???? ??????? ????????? ??? ??? ???
    ??????? ?????????? ?????? ????. ??? ?? ????? ????
    ??? ????? holonomic ???.

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