Inverse kinematics for Puma 500

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Base actually backs up for a while, while
the arm extends.
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Inverse kinematics for Puma 500
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Inverse kinematics for Puma 500

• Based upon forward kinematics

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Inverse kinematics for Puma 500

• Based upon forward kinematics

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Puma 500.
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D-H Example Puma 560
Can we solve the inverse kinematics in closed
form for this six-axis robot?
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Target specified relative to the stationary base
frame.
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The idea is to find the internal rotations, q1 -
q6 such that the 6 (end-member) unit vectors
are coincident with the target-frame.
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This objective is completely specified in terms
of
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Components px py pz referred to base frame.
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Direction-cosine, or rotation, matrix orients
target frame relative to base frame.
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This target is tied to the object with which the
robot is to interact.
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Forward kinematics for Puma 500
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• 12 Equations for six unknowns
• q1 q2 q3 q4 q5 q6

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• 12 Equations for six unknowns
• q1 q2 q3 q4 q5 q6

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• 12 Equations for six unknowns
• q1 q2 q3 q4 q5 q6

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• 12 Equations for six unknowns
• q1 q2 q3 q4 q5 q6

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• 12 Equations for six unknowns
• q1 q2 q3 q4 q5 q6

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• 12 Equations for six unknowns
• q1 q2 q3 q4 q5 q6

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• 12 Equations for six unknowns
• q1 q2 q3 q4 q5 q6

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This may be solved for the single unknown, q1
but the user should resolve the quadrant
ambiguity.
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K is a function of known parameters its a
combination of the target or objective matrix
elements and the DH parameters of the 500.
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Note that this equation for q3 has the same
functional form as the earlier equation for q1.
K is a function of known parameters its a
combination of the target or objective matrix
elements and the DH parameters of the 500.
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Note that this equation for q3 has the same
functional form as the earlier equation for q1.
K is a function of known parameters its a
combination of the target or objective matrix
elements and the DH parameters of the 500.
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Note that this equation for q3 has the same
functional form as the earlier equation for q1.
K is a function of known parameters its a
combination of the target or objective matrix
elements and the DH parameters of the 500.
As with q1 we need to make deliberate
quadrant decisions. This means that there are
2x24 pose possibilities already. Some or all
of these may, for other reasons, be impossible.
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Inverse kinematics for nonholonomic, wheeled robot
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Initial and final conditions are constantly
changing must update wheel-rotation instructions
frequently.
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Convergence onto C1-C4.