Kinematics: Degeneracies, Redundancies, Precision

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KinematicsDegeneracies, Redundancies, Precision

• Professor Nicola Ferrier
• ME 2246, 265-8793
• ferrier_at_engr.wisc.edu

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Redundancy and Degeneracies

• Redundant a manipulator can reach a specified
  position with more than one configuration of the
  linkages
• More than one solution to the inverse kinematic
  transform (usually from a sqrt function or
  arccos)
• Robot with more DOF than task demands
• Redundancy is not bad
• Reach into holes
• keep away from joint limits
• avoid collisions with obstacles
• Avoid degenerate states where manipulator could
  lose degrees of freedom

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Multiple Solutions
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Redundancy and Degeneracies
But redundancy can be useful.
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Redundancy and Degeneracies

• Degenerate infinitely many solutions
• Lose control of one or more degrees of freedom
• Occurs in wrist when two axes align

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Infinitely Many Solutions!

• Two link arm (L1 L2) with the origin as the
  goal position

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Static Precision of Manipulators

• Accuracy
• Repeatability
• Resolution

• difference between the actual location and the
  commanded location
• variation in the actual location when the
  manipulator repeatedly moves the
  end-effector/tool center point, Pe, to the same
  commanded location
• the minimum distance that the tool center point
  can be guaranteed to move

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Accuracy and Repeatability
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Resolution
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What causes inaccuracies?

• Non geometric parameters
• Compliance
• Gear backlash, eccentricity transmission errors
• Encoder resolution
• Temperature related expansion
• Linkage wobble due to bearing slop
• Cross coupling between joints due to robot
  construction
• Rotation of joint n due to a rotation about a
  joint n-I
• Occurs in cable driven systems

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What causes inaccuracies?

• For a Cartesian robot (prismatic joints in
  orthogonal directions) errors do not accumulate
• Errors accumulate for revolute robots

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What causes inaccuracies?

• Geometric parameters
• Errors in link parameters (manufacturing
  tolerances)
• Axes can be up to 0.5o from the design angle
• Error in joint placement (gripper flange not flat
  or not orthogonal to roll axis)