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Evgenia Selinger, and Lars Linsen, Efficient Error-bounded Curvature Optimization for Smooth Machining Paths. Journal of Virtual Reality and Broadcasting, 15(2018), no. 2. (urn:nbn:de:0009-6-48202)

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%0 Journal Article
%T Efficient Error-bounded Curvature Optimization for Smooth Machining Paths
%A Selinger, Evgenia
%A Linsen, Lars
%J Journal of Virtual Reality and Broadcasting
%D 2019
%V 15(2018)
%N 2
%@ 1860-2037
%F selinger2019
%X Automated machining with 3-axis robots requires thegeneration of tool paths in form of positions of the tooltip. For 5-axis robots, the orientations of the tool ateach position needs to be provided, as well. Such atool path can be described in form of two curves, onefor the positional information (as for 3-axis machining)and one for the orientational information, wherethe orientation is given by the vector that points froma point on the orientation curve to the respective pointon the position curve. As the robots need to slow downfor sharp turns, i.e., high curvatures in the tool pathlead to slow processing, our goal is to generate toolpaths with minimized curvatures and a guaranteed errorbound. Starting from an initial tool path, which isgiven in the form of polygonal representations of theposition and orientation curves, we generate optimizedversions of the curves in the form of B-spline curvesthat lie within some error bounds of the input path.Our approach first computes an optimized version ofthe position curve within a tolerance band of the inputcurve. The outcome of this first step can directly beapplied to 3-axis machining. Based on this first step,for 5-axis machining the orientation curve needs to beupdated to again fit the position curve. Then, the orientationcurve is optimized using a similar approach asfor the position curve, but the error bounds are givenin the form of tolerance frustums that define the tolerancein lead and tilt. For an efficient optimizationprocedure, our approach analyzes the input path andsplits it into small (partially overlapping) groups beforeoptimizing the position curve. The groups are categorizedaccording to their geometric complexity andhandled accordingly using two different optimizationprocedures. The simpler, but faster algorithm uses alocal spline approximation, while the slower, but betteralgorithm uses a local sleeve approach. These algorithmsare adapted to both the position and orientationcurve optimization. Subsequently, the groups arecombined into a complete tool path in the form of G2-continuous B-spline curves, where we have one suchcurve for 3-axis machining and two such curves definedover the same knot vector for 5-axis machining.
%L 004
%K 3-axis matching
%K 5-axis matching
%K NURBS curves
%K g²-continuity
%K machining
%R 10.20385/1860-2037/15.2018.2
%U http://nbn-resolving.de/urn:nbn:de:0009-6-48202
%U http://dx.doi.org/10.20385/1860-2037/15.2018.2
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Bibtex

@Article{selinger2019,
  author = 	"Selinger, Evgenia
		and Linsen, Lars",
  title = 	"Efficient Error-bounded Curvature Optimization for Smooth Machining Paths",
  journal = 	"Journal of Virtual Reality and Broadcasting",
  year = 	"2019",
  volume = 	"15(2018)",
  number = 	"2",
  keywords = 	"3-axis matching; 5-axis matching; NURBS curves; g{\texttwosuperior}-continuity; machining",
  abstract = 	"Automated machining with 3-axis robots requires thegeneration of tool paths in form of positions of the tooltip. For 5-axis robots, the orientations of the tool ateach position needs to be provided, as well. Such atool path can be described in form of two curves, onefor the positional information (as for 3-axis machining)and one for the orientational information, wherethe orientation is given by the vector that points froma point on the orientation curve to the respective pointon the position curve. As the robots need to slow downfor sharp turns, i.e., high curvatures in the tool pathlead to slow processing, our goal is to generate toolpaths with minimized curvatures and a guaranteed errorbound. Starting from an initial tool path, which isgiven in the form of polygonal representations of theposition and orientation curves, we generate optimizedversions of the curves in the form of B-spline curvesthat lie within some error bounds of the input path.Our approach first computes an optimized version ofthe position curve within a tolerance band of the inputcurve. The outcome of this first step can directly beapplied to 3-axis machining. Based on this first step,for 5-axis machining the orientation curve needs to beupdated to again fit the position curve. Then, the orientationcurve is optimized using a similar approach asfor the position curve, but the error bounds are givenin the form of tolerance frustums that define the tolerancein lead and tilt. For an efficient optimizationprocedure, our approach analyzes the input path andsplits it into small (partially overlapping) groups beforeoptimizing the position curve. The groups are categorizedaccording to their geometric complexity andhandled accordingly using two different optimizationprocedures. The simpler, but faster algorithm uses alocal spline approximation, while the slower, but betteralgorithm uses a local sleeve approach. These algorithmsare adapted to both the position and orientationcurve optimization. Subsequently, the groups arecombined into a complete tool path in the form of G2-continuous B-spline curves, where we have one suchcurve for 3-axis machining and two such curves definedover the same knot vector for 5-axis machining.",
  issn = 	"1860-2037",
  doi = 	"10.20385/1860-2037/15.2018.2",
  url = 	"http://nbn-resolving.de/urn:nbn:de:0009-6-48202"
}
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RIS

TY  - JOUR
AU  - Selinger, Evgenia
AU  - Linsen, Lars
PY  - 2019
DA  - 2019//
TI  - Efficient Error-bounded Curvature Optimization for Smooth Machining Paths
JO  - Journal of Virtual Reality and Broadcasting
VL  - 15(2018)
IS  - 2
KW  - 3-axis matching
KW  - 5-axis matching
KW  - NURBS curves
KW  - g²-continuity
KW  - machining
AB  - Automated machining with 3-axis robots requires thegeneration of tool paths in form of positions of the tooltip. For 5-axis robots, the orientations of the tool ateach position needs to be provided, as well. Such atool path can be described in form of two curves, onefor the positional information (as for 3-axis machining)and one for the orientational information, wherethe orientation is given by the vector that points froma point on the orientation curve to the respective pointon the position curve. As the robots need to slow downfor sharp turns, i.e., high curvatures in the tool pathlead to slow processing, our goal is to generate toolpaths with minimized curvatures and a guaranteed errorbound. Starting from an initial tool path, which isgiven in the form of polygonal representations of theposition and orientation curves, we generate optimizedversions of the curves in the form of B-spline curvesthat lie within some error bounds of the input path.Our approach first computes an optimized version ofthe position curve within a tolerance band of the inputcurve. The outcome of this first step can directly beapplied to 3-axis machining. Based on this first step,for 5-axis machining the orientation curve needs to beupdated to again fit the position curve. Then, the orientationcurve is optimized using a similar approach asfor the position curve, but the error bounds are givenin the form of tolerance frustums that define the tolerancein lead and tilt. For an efficient optimizationprocedure, our approach analyzes the input path andsplits it into small (partially overlapping) groups beforeoptimizing the position curve. The groups are categorizedaccording to their geometric complexity andhandled accordingly using two different optimizationprocedures. The simpler, but faster algorithm uses alocal spline approximation, while the slower, but betteralgorithm uses a local sleeve approach. These algorithmsare adapted to both the position and orientationcurve optimization. Subsequently, the groups arecombined into a complete tool path in the form of G2-continuous B-spline curves, where we have one suchcurve for 3-axis machining and two such curves definedover the same knot vector for 5-axis machining.
SN  - 1860-2037
UR  - http://nbn-resolving.de/urn:nbn:de:0009-6-48202
DO  - 10.20385/1860-2037/15.2018.2
ID  - selinger2019
ER  -
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Wordbib

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<b:Comments>Automated machining with 3-axis robots requires thegeneration of tool paths in form of positions of the tooltip. For 5-axis robots, the orientations of the tool ateach position needs to be provided, as well. Such atool path can be described in form of two curves, onefor the positional information (as for 3-axis machining)and one for the orientational information, wherethe orientation is given by the vector that points froma point on the orientation curve to the respective pointon the position curve. As the robots need to slow downfor sharp turns, i.e., high curvatures in the tool pathlead to slow processing, our goal is to generate toolpaths with minimized curvatures and a guaranteed errorbound. Starting from an initial tool path, which isgiven in the form of polygonal representations of theposition and orientation curves, we generate optimizedversions of the curves in the form of B-spline curvesthat lie within some error bounds of the input path.Our approach first computes an optimized version ofthe position curve within a tolerance band of the inputcurve. The outcome of this first step can directly beapplied to 3-axis machining. Based on this first step,for 5-axis machining the orientation curve needs to beupdated to again fit the position curve. Then, the orientationcurve is optimized using a similar approach asfor the position curve, but the error bounds are givenin the form of tolerance frustums that define the tolerancein lead and tilt. For an efficient optimizationprocedure, our approach analyzes the input path andsplits it into small (partially overlapping) groups beforeoptimizing the position curve. The groups are categorizedaccording to their geometric complexity andhandled accordingly using two different optimizationprocedures. The simpler, but faster algorithm uses alocal spline approximation, while the slower, but betteralgorithm uses a local sleeve approach. These algorithmsare adapted to both the position and orientationcurve optimization. Subsequently, the groups arecombined into a complete tool path in the form of G2-continuous B-spline curves, where we have one suchcurve for 3-axis machining and two such curves definedover the same knot vector for 5-axis machining.</b:Comments>
</b:Source>
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ISI

PT Journal
AU Selinger, E
   Linsen, L
TI Efficient Error-bounded Curvature Optimization for Smooth Machining Paths
SO Journal of Virtual Reality and Broadcasting
PY 2019
VL 15(2018)
IS 2
DI 10.20385/1860-2037/15.2018.2
DE 3-axis matching; 5-axis matching; NURBS curves; g²-continuity; machining
AB Automated machining with 3-axis robots requires thegeneration of tool paths in form of positions of the tooltip. For 5-axis robots, the orientations of the tool ateach position needs to be provided, as well. Such atool path can be described in form of two curves, onefor the positional information (as for 3-axis machining)and one for the orientational information, wherethe orientation is given by the vector that points froma point on the orientation curve to the respective pointon the position curve. As the robots need to slow downfor sharp turns, i.e., high curvatures in the tool pathlead to slow processing, our goal is to generate toolpaths with minimized curvatures and a guaranteed errorbound. Starting from an initial tool path, which isgiven in the form of polygonal representations of theposition and orientation curves, we generate optimizedversions of the curves in the form of B-spline curvesthat lie within some error bounds of the input path.Our approach first computes an optimized version ofthe position curve within a tolerance band of the inputcurve. The outcome of this first step can directly beapplied to 3-axis machining. Based on this first step,for 5-axis machining the orientation curve needs to beupdated to again fit the position curve. Then, the orientationcurve is optimized using a similar approach asfor the position curve, but the error bounds are givenin the form of tolerance frustums that define the tolerancein lead and tilt. For an efficient optimizationprocedure, our approach analyzes the input path andsplits it into small (partially overlapping) groups beforeoptimizing the position curve. The groups are categorizedaccording to their geometric complexity andhandled accordingly using two different optimizationprocedures. The simpler, but faster algorithm uses alocal spline approximation, while the slower, but betteralgorithm uses a local sleeve approach. These algorithmsare adapted to both the position and orientationcurve optimization. Subsequently, the groups arecombined into a complete tool path in the form of G2-continuous B-spline curves, where we have one suchcurve for 3-axis machining and two such curves definedover the same knot vector for 5-axis machining.
ER
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Mods

<mods>
  <titleInfo>
    <title>Efficient Error-bounded Curvature Optimization for Smooth Machining Paths</title>
  </titleInfo>
  <name type="personal">
    <namePart type="family">Selinger</namePart>
    <namePart type="given">Evgenia</namePart>
  </name>
  <name type="personal">
    <namePart type="family">Linsen</namePart>
    <namePart type="given">Lars</namePart>
  </name>
  <abstract>Automated machining with 3-axis robots requires the
generation of tool paths in form of positions of the tool
tip. For 5-axis robots, the orientations of the tool at
each position needs to be provided, as well. Such a
tool path can be described in form of two curves, one
for the positional information (as for 3-axis machining)
and one for the orientational information, where
the orientation is given by the vector that points from
a point on the orientation curve to the respective point
on the position curve. As the robots need to slow down
for sharp turns, i.e., high curvatures in the tool path
lead to slow processing, our goal is to generate tool
paths with minimized curvatures and a guaranteed error
bound. Starting from an initial tool path, which is
given in the form of polygonal representations of the
position and orientation curves, we generate optimized
versions of the curves in the form of B-spline curves
that lie within some error bounds of the input path.
Our approach first computes an optimized version of
the position curve within a tolerance band of the input
curve. The outcome of this first step can directly be
applied to 3-axis machining. Based on this first step,
for 5-axis machining the orientation curve needs to be
updated to again fit the position curve. Then, the orientation
curve is optimized using a similar approach as
for the position curve, but the error bounds are given
in the form of tolerance frustums that define the tolerance
in lead and tilt. For an efficient optimization
procedure, our approach analyzes the input path and
splits it into small (partially overlapping) groups before
optimizing the position curve. The groups are categorized
according to their geometric complexity and
handled accordingly using two different optimization
procedures. The simpler, but faster algorithm uses a
local spline approximation, while the slower, but better
algorithm uses a local sleeve approach. These algorithms
are adapted to both the position and orientation
curve optimization. Subsequently, the groups are
combined into a complete tool path in the form of G2-
continuous B-spline curves, where we have one such
curve for 3-axis machining and two such curves defined
over the same knot vector for 5-axis machining.</abstract>
  <subject>
    <topic>3-axis matching</topic>
    <topic>5-axis matching</topic>
    <topic>NURBS curves</topic>
    <topic>g²-continuity</topic>
    <topic>machining</topic>
  </subject>
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  <identifier type="uri">http://nbn-resolving.de/urn:nbn:de:0009-6-48202</identifier>
  <identifier type="citekey">selinger2019</identifier>
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Full Metadata

Bibliographic Citation JVRB, 15(2018), no. 2.
Title

Efficient Error-bounded Curvature Optimization for Smooth Machining Paths (eng)
Author Evgenia Selinger, Lars Linsen
Language eng
Abstract Automated machining with 3-axis robots requires the generation of tool paths in form of positions of the tool tip. For 5-axis robots, the orientations of the tool at each position needs to be provided, as well. Such a tool path can be described in form of two curves, one for the positional information (as for 3-axis machining) and one for the orientational information, where the orientation is given by the vector that points from a point on the orientation curve to the respective point on the position curve. As the robots need to slow down for sharp turns, i.e., high curvatures in the tool path lead to slow processing, our goal is to generate tool paths with minimized curvatures and a guaranteed error bound. Starting from an initial tool path, which is given in the form of polygonal representations of the position and orientation curves, we generate optimized versions of the curves in the form of B-spline curves that lie within some error bounds of the input path. Our approach first computes an optimized version of the position curve within a tolerance band of the input curve. The outcome of this first step can directly be applied to 3-axis machining. Based on this first step, for 5-axis machining the orientation curve needs to be updated to again fit the position curve. Then, the orientation curve is optimized using a similar approach as for the position curve, but the error bounds are given in the form of tolerance frustums that define the tolerance in lead and tilt. For an efficient optimization procedure, our approach analyzes the input path and splits it into small (partially overlapping) groups before optimizing the position curve. The groups are categorized according to their geometric complexity and handled accordingly using two different optimization procedures. The simpler, but faster algorithm uses a local spline approximation, while the slower, but better algorithm uses a local sleeve approach. These algorithms are adapted to both the position and orientation curve optimization. Subsequently, the groups are combined into a complete tool path in the form of G2- continuous B-spline curves, where we have one such curve for 3-axis machining and two such curves defined over the same knot vector for 5-axis machining.
Subject 3-axis matching, 5-axis matching, NURBS curves, g²-continuity, machining
Classified Subjects
swd
  • 4261462-4, Robotik
  • 4384798-5, B-Spline
  • 4390818-4, Optimierungsproblem
DDC 004
Rights DPPL
URN: urn:nbn:de:0009-6-48202
DOI https://doi.org/10.20385/1860-2037/15.2018.2