Trajectory Generation

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Trajectory GenerationRobot Control

• Contents of lecture
• Trajectory Generation (chapter 7)
• Introduction
• Joint Space
• Cartesian Space
• A Generic Robot Controller

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Trajectory Generation
How do I move from this location
To this location
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Cartesian Space Trajectory
Move TCP from A to B
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User Specified Trajectory

• Location
• Start location
• End location
• Intermediate location (via points)
• Interpolation
• PTP-motion (ABB MoveJ/REIS PTP)
• Linear motion (ABB MoveL/REIS CP_LIN)
• Circular motion (ABB MoveC/REIS CP_CIRC1)
• Technological Instructions
• Velocity
• Acceleration
• Tool Functions and Settings

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ABB program

• VERSION1
• LANGUAGEENGLISH
• MODULE SVEJS
• PERS weavedata wv10,0,0,0,0,0,0,0,0,0,0,0,0,0
  ,0,0,0
• PERS welddata wd14,4,9,0,0,0
• PERS seamdata sm10,0,0,0,0,0
• PROC main()
• MoveJ 309.73,-125.76,509.36,0.246344,-0.69
  2778,0.62777,-0.255495,-1,0,-2,0,
  9E09,9E09,9E09,9E09,9E09,9E09,v100,z50,to
  ol0
• ArcL\On,382.56,48.51,429.57,0.242483,-0.70
  4985,0.62782,-0.223698,0,-1,-1,0,
  9E09,9E09,9E09,9E09,9E09,9E09,v200,sm1,wd
  1,wv1,fine,tool0
• ArcL\Off,388.2,109.07,429.57,0.242508,-0.7
  0503,0.627762,-0.223692,0,-1,-1,0,
  9E09,9E09,9E09,9E09,9E09,9E09,v100,sm1,wd
  1,wv1,fine,tool0
• MoveL 298.77,-104.68,534.41,0.246333,-0.69
  2792,0.627756,-0.255505,-1,0,-2,0,
  9E09,9E09,9E09,9E09,9E09,9E09,v200,fine,t
  ool0
• ENDPROC
• ENDMODULE

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Requirements to trajectory

• The motion of the manipulator must be smooth
• Continuous path
• Continuous velocity profile
• Sometimes continuous acceleration

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Cubic PolynominalsNo via points
Polynomials
Constraints
Þ
Þ
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Example
Starts and stops at rest q0 15 qf 75 tf 3
seconds
Position
Velocity
Acceleration
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With Via Point
And
ß
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Linear Function with Parabolic Blends
Simple Linear Function
With Parabolic Blends
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Cartesian Interpolation

• Move from a start frame to an end frame with a
  certain velocity.
• Start frame
• End frame

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Use Roll, Pitch Yaw (or another rep.)
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Method

• Transform start and end frames. 6x1 vectors
  (determine roll, pitch, yaw).
• Use cubic polynomials to represent a path that
  brings X1 to X2, Y1 to Y2, Z1 to Z2, roll1 to
  roll2, pitch1 to pitch2, yaw1 to yaw2.

ß
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Problems due to Cartesian Interpolation
Intermediate points unreachable
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Problems due to Cartesian Interpolation
Singularities in the cartesian path
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Problems due to Cartesian Interpolation
Path points reachable in different
solutions/configurations
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Problems due to Cartesian Interpolation

• Different start configurations of the robot

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A Generic Robot Controller
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Motion Controller
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The Trajectory Planner
Joint2
Joint21
Joint11
Joint12
Joint3
Joint22
Joint1
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The Joint Controller
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Generic Motion Controller
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Problems

• CRAIG
• 7.2
• 7.6
• Cartesian problem