ME5286CourseNotes06-09 - Add a degree of freedom (The human...

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VELOCITY AND PATH CONTROL
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VELOCITY CONTROL We not only wish to control position and orientation of the hand, but also its velocity This requires the speciFcation of a velocity vector … which must be related to the manipulator joint velocities
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We know that the position and orientation of the hand is a function of the joint variables After calculating J, we can derive the joint angular velocities Velocities as By taking derivatives, we can calculate the six element vector x representing the command rates along the hand axes
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Commercial manipulators are designed based on small positional changes, thus many terms in J simplify dramatically However… J may not have an inverse for various positions of the manipulator (I.E. J is singular and its determinant is equal to zero) This is equivalent to one or more joints moving at inFnite velocity Physical signiFcance?
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Solutions to singularity problem: Add an intermediate point (Position and orientation)
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Unformatted text preview: Add a degree of freedom (The human arm can be considered to have at least 7 D.O.F when it should only need six) New problem: Must specify extra D.O.F Coordinated motion for path control For coordination, ensure that all joints start and stop motion simultaneously For point-to-point control: Joints must move at different angular velocities Coordinate all joints to the “slowest” joint by rate interpolation Problem: Using only the end positions of a motion as constraints results in unpredictable end effector motion Solution: Control path of end effector by interpolating in world (Cartesian) coordinates Manipulator Motion Motion requires changes in joint angles: JT0 = 90˚ JT1 = 45˚ JT2 = -45˚ Interpolated Path (All joints start/stop simultaneously) Path Control Straight line path (All joints start/stop simultaneously) Need to program via points to control path and speed up motion Computation of the Jacobian...
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ME5286CourseNotes06-09 - Add a degree of freedom (The human...

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