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Functional Gradient Motion Planning in Reproducing Kernel Hilbert - - PowerPoint PPT Presentation

Functional Gradient Motion Planning in Reproducing Kernel Hilbert Spaces RSS Robotics Science and Systems June 18-26, 2016 University of Michigan Joint work with: Zita Marinho Geoffrey J. Gordon (CMU) zmarinho@cmu.edu Siddhartha Srinivasa


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Functional Gradient Motion Planning in Reproducing Kernel Hilbert Spaces

RSS Robotics Science and Systems

June 18-26, 2016 University of Michigan

Zita Marinho

zmarinho@cmu.edu

Personal Robotics Lab Institute for Systems and Robotics CMU/Portugal

Joint work with:

Geoffrey J. Gordon (CMU) Siddhartha Srinivasa (CMU) Anca Dragan (UC Berkeley) Byron Boots (Georgia Tech) Arunkumar Byravan (University of Washington)

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zmarinho@cmu.edu

  • Functional Gradient Motion Planning in RKHSs - RSS Robotics Science and Systems 2016

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Main Contribution

all possible trajectories

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SLIDE 3

zmarinho@cmu.edu

  • Functional Gradient Motion Planning in RKHSs - RSS Robotics Science and Systems 2016

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Main Contribution

all possible trajectories

RKHS

interpolated waypoints

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SLIDE 4

zmarinho@cmu.edu

  • Functional Gradient Motion Planning in RKHSs - RSS Robotics Science and Systems 2016

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Main Contribution

all possible trajectories

interpolated waypoints in RKHSs

RKHS

interpolated waypoints

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SLIDE 5

zmarinho@cmu.edu

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Waypoints trajectory

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( CHOMP being used to grab a plate inside the microwave )

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zmarinho@cmu.edu

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Waypoints trajectory

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( CHOMP being used to grab a plate inside the microwave )

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SLIDE 7

zmarinho@cmu.edu

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RKHS - Trajectory

Reproducing Kernel Hilbert Space (RKHS)

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time points ∈ [0,1]

t1 t2 t3

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SLIDE 8

zmarinho@cmu.edu

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RKHS - Trajectory

Reproducing Kernel Hilbert Space (RKHS)

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time points ∈ [0,1]

t1 t2 t3

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SLIDE 9

zmarinho@cmu.edu

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RKHS - Trajectory

Reproducing Kernel Hilbert Space (RKHS)

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time points ∈ [0,1]

t1 t2 t3

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SLIDE 10

zmarinho@cmu.edu

  • Functional Gradient Motion Planning in RKHSs - RSS Robotics Science and Systems 2016

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RKHS - Trajectory

Reproducing Kernel Hilbert Space (RKHS)

7

time points ∈ [0,1]

t1 t2 t3

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SLIDE 11

zmarinho@cmu.edu

  • Functional Gradient Motion Planning in RKHSs - RSS Robotics Science and Systems 2016

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RKHS - Trajectory

Reproducing Kernel Hilbert Space (RKHS)

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time points ∈ [0,1]

t1 t2 t3

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SLIDE 12

zmarinho@cmu.edu

  • Functional Gradient Motion Planning in RKHSs - RSS Robotics Science and Systems 2016

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Planning in RKHS - Optimization

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SLIDE 13

zmarinho@cmu.edu

  • Functional Gradient Motion Planning in RKHSs - RSS Robotics Science and Systems 2016

/ 7 9

Planning in RKHS - Optimization

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SLIDE 14

zmarinho@cmu.edu

  • Functional Gradient Motion Planning in RKHSs - RSS Robotics Science and Systems 2016

/ 7 9

Planning in RKHS - Optimization

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SLIDE 15

zmarinho@cmu.edu

  • Functional Gradient Motion Planning in RKHSs - RSS Robotics Science and Systems 2016

/ 7 9

Planning in RKHS - Optimization

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SLIDE 16

zmarinho@cmu.edu

  • Functional Gradient Motion Planning in RKHSs - RSS Robotics Science and Systems 2016

/ 7 9

Planning in RKHS - Optimization

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SLIDE 17

zmarinho@cmu.edu

  • Functional Gradient Motion Planning in RKHSs - RSS Robotics Science and Systems 2016

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Results - RKHS require few iterations

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(b) Original CHOMP , large steps (a) RBF RKHS, large steps (c) Original CHOMP , smaller steps

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zmarinho@cmu.edu

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Results - 6D Robot arm : more complex scenes

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Waypoints Gaussian RBF w/ joint interactions Gaussian RBF w/ diagonal kernel

  • 5 iterations
  • 20 iterations
  • 20 iterations

Waypoints Gaussian RBF derivative Gaussian RBF Waypoints Gaussian RBF derivative Gaussian RBF

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zmarinho@cmu.edu

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Planning in RKHS - RKHS derivative trajectory

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( RKHS derivative kernel used to grab a plate inside the microwave )

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SLIDE 20

zmarinho@cmu.edu

  • Functional Gradient Motion Planning in RKHSs - RSS Robotics Science and Systems 2016

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Planning in RKHS - RKHS derivative trajectory

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( RKHS derivative kernel used to grab a plate inside the microwave )