RoboticsChapter 6 – Visual Servoing

Dr. Amit Goradia

Topics

• Introduction – 2 hrs• Coordinate transformations – 6 hrs• Forward Kinematics - 6 hrs• Inverse Kinematics - 6 hrs• Velocity Kinematics - 2 hrs• Trajectory Planning - 6 hrs• Robot Dynamics (Introduction) - 2 hrs• Force Control (Introduction) - 1 hrs• Task Planning - 6 hrs• Machine Vision - 6 hrs

Visual Servoing

• Control the movement of a robot using information collected from cameras.

• Operates in closed loop. • Provides better accuracy than look and

move systems

Camera Configurations

End-Effector Mounted Fixed

Servoing Architectures

• Position based.

• Coordinates extracted from the image

• Control law derived from extracted coordinates

Servoing Architectures

• Image based

• Positions are not extracted from image

• Control directly applied in image space

Position Based

• Position based– Alignment in target coordinate

system– The 3D structure of the target

is rconstructed– The end-effector is tracked– Sensitive to calibration errors– Sensitive to reconstruction

errors

target

End-effector

Image Based

• Image Based– Alignment in image coordinates– No explicit reconstruction

necessary– Insensitive to calibration errors– Only special problems solvable– Depends on initial pose– Depends on selected features

Image of target

Image of end effector

EOL and ECL Configurations

• EOL: endpoint open-loop; – only the target is observed by the camera

• ECL: endpoint closed-loop; – target as well as end-effector are observed by

the camera

EOL ECL

Position Based Algorithm

• Position based– Estimation of relative pose– Computation of error between current pose

and target pose– Movement of robot

p1

p2

Position Based Point Alignment

• Goal: Bring e to 0 by moving p1

– pxm is subject to the following measurement errors: sensor position, sensor calibration, sensor measurement error

– pxm is independent of the following errors: end effector position, target position

p1m p2m

d

e = |p2m – p1m|u = k*(p2m – p1m)

Image based Point Alignment

• uxm, vxm is subject only to sensor measurement error

• uxm, vxm is independent of the following measurement errors: sensor position, end effector position, sensor calibration, target position

p1 p2

c1 c2

u1

u2

v1 v2

d1d2

Goal: Bring e to 0 by moving p1

e = |u1m – v1m| + |u2m – v2m|

Image Jacobian

• f is the feature point in image space

• r is the real-world position

• Image Jacobian relates the rates of change from f to r

• Image Jacobian for perspective projection model

rrJf )(

Examples – Image Space Servoing