ECE 486 Lecture

ECE 486 Lecture

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Safwan Choudhury

June 06, 2012
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Transcript

  1. 1.
  2. 6.
  3. 7.
  4. 15.

    Computing the Jacobian Columns The “Geometric” Approach Revolute Joints Ji

    =  zi 1 ⇥ ( on oi 1) zi 1 Ji =  zi 1 0 Prismatic Joints Recall
  5. 16.
  6. 17.

    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
  7. 21.

    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
  8. 22.

    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
  9. 23.

    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
  10. 33.

    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
  11. 35.

    Whole Body Control A Jacobian-Based Approach ˙ q = 2

    6 6 4 JCOM J1 J2 J3 3 7 7 5 1 ˙ x