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 Wrist 1 University of Maryland IEEE_ICRA’02.Carignan/Howard.15-May-2002
Outline • Objectives • 4-Axis Wrist Design • Joint/Tool Workspace • Singularities • Inverse Kinematics • Simulation Results • Experiments • Conclusions Space Systems Laboratory 4-Axis Skew Wrist 2 University of Maryland IEEE_ICRA’02.Carignan/Howard.15-May-2002
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 operation Space Systems Laboratory 4-Axis Skew Wrist 3 University of Maryland IEEE_ICRA’02.Carignan/Howard.15-May-2002
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 Space Systems Laboratory 4-Axis Skew Wrist 4 University of Maryland IEEE_ICRA’02.Carignan/Howard.15-May-2002
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 Orthogonal 4-axis Skew 4-axis Yaw Drive Pitch Drive Yaw Drive Wrist Roll Wrist Roll Drive (aft) Drive (aft) Hand Roll & Wrist Roll & Tool Drives Tool Drives Pitch Drive Space Systems Laboratory 4-Axis Skew Wrist 5 University of Maryland IEEE_ICRA’02.Carignan/Howard.15-May-2002
4-Axis Skew Wrist Design Space Systems Laboratory 4-Axis Skew Wrist 6 University of Maryland IEEE_ICRA’02.Carignan/Howard.15-May-2002
Jointspace Comparison 4-AXIS SKEW 4-AXIS ORTHOGONAL Yaw Yaw 180° 270° HAND HAND ROLL ROLL 135° 225° YAW YAW YAW, 90° 180° WRIST ROLL H H H C C C T T T I I I P 45° P P 135° YAW, PITCH 0° WRIST 90° ROLL H H H -45° C C C 45° T T T P I I I P P YAW, -90° 0° WRIST YAW ROLL HAND HAND HAND HAND -45° YAW -135° ROLL ROLL ROLL ROLL -180° -90° -270° -225° -180° -135° -90° -45° 0° 45° 90° -360° -315° -270° -225° -180° -135° -90° -45° 0° 45° 90° 135° 180° Pitch Pitch Type I singularity (3DOF) -- Type II singularity (2DOF) Space Systems Laboratory 4-Axis Skew Wrist 7 University of Maryland IEEE_ICRA’02.Carignan/Howard.15-May-2002
Toolspace Comparison f (deg) Space Systems Laboratory 4-Axis Skew Wrist 8 University of Maryland IEEE_ICRA’02.Carignan/Howard.15-May-2002
Workspace Singularities Type I Type I – – 3 3 Axes Axes Become Become Coplanar Coplanar Coplanar Axes Condition 1, 2, 3 q 2 = 0º, ±180º 1, 2, 4 q 2 = ±90º or q 3 = 0º 1, 3, 4 tan( q 3 ) = -sin( q 2 ) 2, 3, 4 q 3 = 0º, ±180º Type Type II II – – 4 4 Axes Axes Become Become Coplanar Coplanar q 2 = 0º, ±180º & q 3 = 0º, ±180º Space Systems Laboratory 4-Axis Skew Wrist 9 University of Maryland IEEE_ICRA’02.Carignan/Howard.15-May-2002
Manipulability Index T H M = J w J w Pseudoinverse: T J W J W † = J W - 1 ( T ) J W 2 1.5 HM 2 1 0.5 1 0 0 q3 - 2 - 2 - 1 0 0 q2 q2 - 2 2 2 Space Systems Laboratory 4-Axis Skew Wrist 10 University of Maryland IEEE_ICRA’02.Carignan/Howard.15-May-2002
Inverse Kinematics Approaches Full 4-axis control with 3-axis control to get self-motion for singularity Rotational command, and joint limit avoidance Independent hand roll Joystick Joystick Joystick Joystick Command Command Command Command † D r + ( I - J W † J W ) r - 1 D r D q W = J W D q 1 - 3 = J 123 ∅ [ ] D t r ∅ = k M — H M + k J — H J D q 4 = D q HR Hand Hand Roll Roll Manipulability Manipulability Joint Limit Joint Limit Command Command Gradient Gradient Gradient Gradient Space Systems Laboratory 4-Axis Skew Wrist 11 University of Maryland IEEE_ICRA’02.Carignan/Howard.15-May-2002
Generalized Inverse Kinematics HAND WRIST JOINT CONTROLLER ANGLES f,q,y 0 0 R T R T WRIST des DESIRED ROTATIONAL FORWARD TOOL CHANGE KINEMATICS ORIENATION D r † Dq p J W WRIST PSEUDOINVERSE WRIST JACOBIAN J W JACOBIAN + 0 / Dq 0 J W + / WRIST NULLSPACE JACOBIAN r 0 / MANIPULABILITY, NULLSPACE JOINT LIMIT INDEX VELOCITY Dq W Space Systems Laboratory 4-Axis Skew Wrist 12 University of Maryland IEEE_ICRA’02.Carignan/Howard.15-May-2002
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 Space Systems Laboratory 4-Axis Skew Wrist 13 University of Maryland IEEE_ICRA’02.Carignan/Howard.15-May-2002
Wrist Run-In Testing 0:20 Space Systems Laboratory 4-Axis Skew Wrist 14 University of Maryland IEEE_ICRA’02.Carignan/Howard.15-May-2002
Inverse Kinematics Modes 1:33 4-DOF w/self-motion 3-DOF/Hand Roll Control Space Systems Laboratory 4-Axis Skew Wrist 15 University of Maryland IEEE_ICRA’02.Carignan/Howard.15-May-2002
Joint Limit Avoidance 0:31 CCW yaw limit during 3-DOF control; wrist transitions to 4-DOF control Space Systems Laboratory 4-Axis Skew Wrist 16 University of Maryland IEEE_ICRA’02.Carignan/Howard.15-May-2002
Singularity Avoidance (Simulation) 0:44 Tool Roll Simulation: - Pseudoinverse - Pseudoinverse with self-motion Space Systems Laboratory 4-Axis Skew Wrist 17 University of Maryland IEEE_ICRA’02.Carignan/Howard.15-May-2002
Singularity Avoidance (Experiment) 0:13 Forearm rolls to avoid singularity Space Systems Laboratory 4-Axis Skew Wrist 18 University of Maryland IEEE_ICRA’02.Carignan/Howard.15-May-2002
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 Space Systems Laboratory 4-Axis Skew Wrist 19 University of Maryland IEEE_ICRA’02.Carignan/Howard.15-May-2002
Acknowledgements This research was sponsored by NASA Headquarters under NASA Cooperative Agreement NCC5-243 The Ranger Team Space Systems Laboratory 4-Axis Skew Wrist 20 University of Maryland IEEE_ICRA’02.Carignan/Howard.15-May-2002
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