A Skew-Axis Design for a 4-Joint Revolute Wrist Craig R. Carignan - - PowerPoint PPT Presentation

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A Skew-Axis Design for a 4-Joint Revolute Wrist Craig R. Carignan - - PowerPoint PPT Presentation

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A Skew-Axis Design for a 4-Joint Revolute Wrist Craig R. Carignan Russell D. Howard University of Maryland Space Systems Laboratory IEEE International Conference on Robotics and Automation May 15, 2002 Space Systems Laboratory 4-Axis Skew

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Space Systems Laboratory University of Maryland

IEEE_ICRA’02.Carignan/Howard.15-May-2002

4-Axis Skew Wrist

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A Skew-Axis Design for a 4-Joint Revolute Wrist

Craig R. Carignan Russell D. Howard University of Maryland Space Systems Laboratory IEEE International Conference

  • n Robotics and Automation

May 15, 2002

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Space Systems Laboratory University of Maryland

IEEE_ICRA’02.Carignan/Howard.15-May-2002

4-Axis Skew Wrist

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Outline

  • Objectives
  • 4-Axis Wrist Design
  • Joint/Tool Workspace
  • Singularities
  • Inverse Kinematics
  • Simulation Results
  • Experiments
  • Conclusions
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Space Systems Laboratory University of Maryland

IEEE_ICRA’02.Carignan/Howard.15-May-2002

4-Axis Skew Wrist

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Objectives

  • Introduce an alternative 4-axis wrist with

larger tool workspace

  • Map the wrist rotational workspace and

singularities

  • Present inverse kinematics options for

controlling the wrist

  • Simulation/hardware results for wrist
  • peration
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Space Systems Laboratory University of Maryland

IEEE_ICRA’02.Carignan/Howard.15-May-2002

4-Axis Skew Wrist

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Why a 4-Axis Wrist?

  • Advantages

– Singularity-free access to rotational workspace – Avoid joint limits through “self-motion” – Lower joint velocities than 3-axis designs

  • Disadvantages

– Additional hardware required – Greater computational complexity – More singularities in the workspace

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Space Systems Laboratory University of Maryland

IEEE_ICRA’02.Carignan/Howard.15-May-2002

4-Axis Skew Wrist

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Why a Skew Axis?

  • Lower interference of the tool with the

forearm extends pitch travel

  • Single-sided support of the inner wrist

allows for greater yaw range

  • Frontal area of the wrist reduced by

skew layback of pitch actuator

Skew 4-axis Orthogonal 4-axis

Wrist Roll & Tool Drives Pitch Drive Yaw Drive Wrist Roll Drive (aft)

Hand Roll & Tool Drives Pitch Drive Yaw Drive Wrist Roll Drive (aft)

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Space Systems Laboratory University of Maryland

IEEE_ICRA’02.Carignan/Howard.15-May-2002

4-Axis Skew Wrist

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4-Axis Skew Wrist Design

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Space Systems Laboratory University of Maryland

IEEE_ICRA’02.Carignan/Howard.15-May-2002

4-Axis Skew Wrist

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Jointspace Comparison

4-AXIS ORTHOGONAL 4-AXIS SKEW

  • 180°
  • 135°
  • 90°
  • 45°

0° 45° 90°

  • 90°
  • 45°

0° 45° 90° 135° 180° 225° 270°

  • 270°
  • 225°

HAND ROLL

Yaw Pitch

HAND ROLL YAW PITCH YAW, WRIST ROLL YAW, WRIST ROLL

  • 180°
  • 135°
  • 90°
  • 45°

0° 45° 90° 135° 180°

  • 180°
  • 135°
  • 90°
  • 45°

0° 45° 90° 135° 180°

Pitch Yaw

  • 225°
  • 270°
  • 315°
  • 360°

YAW YAW YAW HAND ROLL HAND ROLL HAND ROLL HAND ROLL YAW, WRIST ROLL P I T C H P I T C H P I T C H P I T C H P I T C H P I T C H

Type II singularity (2DOF) Type I singularity (3DOF)

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Space Systems Laboratory University of Maryland

IEEE_ICRA’02.Carignan/Howard.15-May-2002

4-Axis Skew Wrist

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Toolspace Comparison

f (deg)

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Space Systems Laboratory University of Maryland

IEEE_ICRA’02.Carignan/Howard.15-May-2002

4-Axis Skew Wrist

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Workspace Singularities

Coplanar Axes Condition 1, 2, 3 q2 = 0º, ±180º 1, 2, 4 q2 = ±90º or q3 = 0º 1, 3, 4 tan(q3) = -sin(q2) 2, 3, 4 q3 = 0º, ±180º Type Type I I – – 3 3 Axes Axes Become Become Coplanar Coplanar Type Type II II – – 4 4 Axes Axes Become Become Coplanar Coplanar q2 = 0º, ±180º & q3 = 0º, ±180º

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Space Systems Laboratory University of Maryland

IEEE_ICRA’02.Carignan/Howard.15-May-2002

4-Axis Skew Wrist

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Manipulability Index

  • 2

2 q2

  • 2
  • 1

1 2 q3 0.5 1 1.5 2 HM

  • 2

2 q2

HM = JwJw

T

JW

† = JW T JW JW T

( )

  • 1

Pseudoinverse:

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Space Systems Laboratory University of Maryland

IEEE_ICRA’02.Carignan/Howard.15-May-2002

4-Axis Skew Wrist

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Inverse Kinematics Approaches

DqW = JW

†Dr +(I - JW †JW )r ∅

r

∅ = kM—HM + kJ—H J

[ ]Dt

Full 4-axis control with self-motion for singularity and joint limit avoidance

Manipulability Manipulability Gradient Gradient Joint Joint Limit Limit Gradient Gradient Joystick Joystick Command Command

Dq1-3 = J123

  • 1Dr

Dq4 = DqHR

Joystick Joystick Command Command Hand Hand Roll Roll Command Command

3-axis control to get Rotational command, Independent hand roll

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Space Systems Laboratory University of Maryland

IEEE_ICRA’02.Carignan/Howard.15-May-2002

4-Axis Skew Wrist

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Generalized Inverse Kinematics

DESIRED TOOL ORIENATION

f,q,y

WRIST PSEUDOINVERSE JACOBIAN

Dr RT RT

des

ROTATIONAL CHANGE

WRIST JOINT ANGLES

JW Dqp

WRIST NULLSPACE JACOBIAN WRIST FORWARD KINEMATICS MANIPULABILITY, JOINT LIMIT INDEX NULLSPACE VELOCITY

r 0

/

Dq 0

/

Dq + +

WRIST JACOBIAN

HAND CONTROLLER

J W JW

/ † W

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Space Systems Laboratory University of Maryland

IEEE_ICRA’02.Carignan/Howard.15-May-2002

4-Axis Skew Wrist

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Inverse Kinematics Tradeoffs

  • Generalized Inverse

+ Automatic singularity and joint limit avoidance + Locally minimum joint velocities + Only 3-axis rotational input required

  • Self-motion can be disrupting to operator
  • Extended Jacobian

+ Cyclic motion + Direct control of yoke axis camera + Direct control of hand roll (tool axis)

  • Manual singularity avoidance
  • Greater motion of joints is more likely to cause joint limiting
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Space Systems Laboratory University of Maryland

IEEE_ICRA’02.Carignan/Howard.15-May-2002

4-Axis Skew Wrist

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Wrist Run-In Testing

0:20

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Space Systems Laboratory University of Maryland

IEEE_ICRA’02.Carignan/Howard.15-May-2002

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Inverse Kinematics Modes

4-DOF w/self-motion 3-DOF/Hand Roll Control 1:33

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Space Systems Laboratory University of Maryland

IEEE_ICRA’02.Carignan/Howard.15-May-2002

4-Axis Skew Wrist

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Joint Limit Avoidance

CCW yaw limit during 3-DOF control; wrist transitions to 4-DOF control 0:31

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Space Systems Laboratory University of Maryland

IEEE_ICRA’02.Carignan/Howard.15-May-2002

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Singularity Avoidance (Simulation)

Tool Roll Simulation:

  • Pseudoinverse
  • Pseudoinverse with self-motion

0:44

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Space Systems Laboratory University of Maryland

IEEE_ICRA’02.Carignan/Howard.15-May-2002

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Singularity Avoidance (Experiment)

Forearm rolls to avoid singularity 0:13

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Space Systems Laboratory University of Maryland

IEEE_ICRA’02.Carignan/Howard.15-May-2002

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Conclusions

  • Skewing the pitch axis significantly increases

the pitch and yaw range over the orthogonal design

  • The singularity regions for the skew design

are significantly more complex

  • The generalized inverse method is most

useful for large range of motion when singularities and joint limits are more likely to be encountered

  • The extended Jacobian approach is more

effective during close-proximity tasks when controlling the wrist camera and hand roll directly is critical

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Space Systems Laboratory University of Maryland

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Acknowledgements

This research was sponsored by NASA Headquarters under NASA Cooperative Agreement NCC5-243 The Ranger Team