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# ECE 486 Lecture

June 06, 2012

## Transcript

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### ECE 486: Robot Dynamics and Control Practical Applications of the

Jacobian Safwan Choudhury May 31, 2012
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Components
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### Computing the Jacobian Columns The “Geometric” Approach Revolute Joints Ji

=  zi 1 ⇥ ( on oi 1) zi 1 Ji =  zi 1 0 Prismatic Joints Recall
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### Motivating Example q dq QUARC Visualization System Timebase Kp KP(1:7)

Knee Pitch 60 Kd KD(1:7)*5 Hip Yaw 0 Hip Roll 0 Hip Pitch -30 EN 1 D2R D2R D2R D2R D2R D2R D2R Biped τ q q′ q′′ Ankle Yaw 0 Ankle Roll 0 Ankle Pitch -20 Direct Joint Control
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˙ x
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### Jacobian Inverse Control 1. Compute Jacobian matrix w.r.t. end effector

2. Invert the matrix (pseudoinverse if ) 3. Obtain by multiplying 4. Obtain by integrating ˙ q q = Z ˙ q q ˙ q = J 1 ˙ x n > 6
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### Motivating Example Work Space Analysis QUARC Visualization Trajectory Reference Model

Configuration Joint Space Analysis Jacobian Inverse Transformation q′ = J-1x′ J x′ q q′ Jacobian Computation DQREF QREF q → x q x x dqref qref Jacobian Inverse Control
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### Motivating Example τ q q′ q′′ PD Controller q error

q′ error τ control erse Transformation q′ = J-1x′ q q′ an Computation Control Torques DQREF QREF q → x q q dq dqref qref Jacobian Inverse Control
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P ximi P mi
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### Jacobian Transpose Control 1. Compute the partial center of masses

for each joint 2. Form the COM Jacobian matrix 3. Obtain from the basic formula 4. Obtain by multiplying J com ~ FG = m~ g ~ F ⌧G ⌧ G = JT com ~ F G
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### Whole Body Control A Jacobian-Based Approach ˙ q = 2

6 6 4 JCOM J1 J2 J3 3 7 7 5 1 ˙ x
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