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Vision Based Motion Control

Vision Based Motion Control. CMPUT 610 2001 Martin Jagersand. How to go from Visual sensation to Motor action?. Camera -> Robot coord Robot -> Object. Closed loop servoing. We focus on the geometric transforms. EE. Camera Center of projection Different models. Robot Base frame

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Vision Based Motion Control

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  1. Vision Based Motion Control CMPUT 610 2001 Martin Jagersand

  2. How to go from Visual sensationto Motor action? • Camera -> Robot coord Robot -> Object

  3. Closed loop servoing • We focus on the geometric transforms EE

  4. Camera Center of projection Different models Robot Base frame End-effector frame Object Lots of possible coordinates

  5. Coordinate rotation • Example: Around y-axis Z’ P X’ X

  6. Euler angles • Note: Successive rotations. Order matters.

  7. Rotation and translation • Translation t’ in new o’ coordinates Z’ P X’ X

  8. Successive translation and rotation % robocop Simulates a 3 joint robot function Jpos = robocop(theta1,theta2,theta3,L1,L2,L3,P0) Rxy1 = [cos(theta1) sin(theta1) 0 -sin(theta1) cos(theta1) 0 0 0 1]; Rxz2 = [cos(theta2) 0 sin(theta2) 0 1 0 -sin(theta2) 0 cos(theta2)]; Rxz3 = [cos(theta3) 0 sin(theta3) 0 1 0 -sin(theta3) 0 cos(theta3)]; P1 = P0 + Rxy1*[L1 0 0]'; P2 = P1 + Rxy1*Rxz2*[L2 0 0]'; P3 = P2 + Rxy1*Rxz2*Rxz3*[L3 0 0]'; Jpos = [P0 P1 P2 P3]; ExampleMatlab robot

  9. Homogeneous coordinates • Write as matrix multiplications only • 3-vectors -> 4 vectors • Affine -> homogeneous

  10. Denavit-Hartenberg • Particular choice of homogeneous parameterization, see eq. 2.8 in Alexa’s thesis

  11. Perspective Camera • In homogeneous 4-vector • Remove 3rd row for standard camera plane proj

  12. Hand-Eye system Motor-Visual function: y=f(x)

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