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