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lecture10

# lecture10 - Implementation of Inverse Kinematics and...

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역역역역역 역역역 역역 Implementation of Inverse Kinematics and Application 역역역역역 역역역역역 역역역역역역역역역역 역역역 [email protected]

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Content What is Inverse Kinematics? Redundancy Basic Method NLP-based method Jacobian-based method Issues Resolving Redundancy Multiple Goals Application : Motion Retargetting
What is Inverse Kinematics? Forward Kinematics Base 1 θ 2 θ ) f( θ x = End Effector 3 θ ?

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What is Inverse Kinematics? Inverse Kinematics Base 1 θ 2 θ 3 θ End Effector ) ( f 1 x θ - =
What does looks like? ) sin( ) sin( ) sin( ) cos( ) cos( ) cos( 3 3 2 2 1 1 3 3 2 2 1 1 θ θ θ θ θ θ l l l y l l l x + + = + + = ) f( θ ? Base 1 θ 2 θ End Effector 3 θ 1 l 2 l 3 l

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Solution to Our example ) ( f 1 x θ - = ) sin( ) sin( ) sin( ) cos( ) cos( ) cos( 3 3 2 2 1 1 3 3 2 2 1 1 θ θ θ θ θ θ l l l y l l l x + + = + + = Number of equation : 2 Unknown variables : 3 Infinite number of solutions !
Redundancy System DOF > End Effector DOF ) sin( ) sin( ) sin( ) cos( ) cos( ) cos( 3 3 2 2 1 1 3 3 2 2 1 1 θ θ θ θ θ θ l l l y l l l x + + = + + = Our example System DOF = 3 End Effector DOF = 2

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Redundancy A redundant system has infinite number of solutions Human skeleton has 70 DOF Ultra-super redundant How to solve highly redundant system?
Content What is Inverse Kinematics? Redundancy Basic Method NLP-based method Jacobian-based method Issues Resolving Redundancy Multiple Goals Application : Motion Retargetting

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What is NLP? Non Linear Programming Method to optimize a nonlinear function Example Objective function Constraint Iterative algorithm 0 y 0, x subject to ) sin( ) 1 ( minimize 2 + + + y x y x
NLP-based Method Inverse Kinematics problem as non-linear optimization problem Minimization of Goal Potential Function Zhao and Badler, 1994, ACMTOG

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Goal Potential Function “Distance” from the end effector to the goal Function of joint angles : G( θ )
Our Example Base 1 θ 2 θ 3 θ End Effector Goal distance

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