Free Shape Paths in Industrial Robots
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Transcript of Free Shape Paths in Industrial Robots
Free Shape Paths in Industrial Robots
•Date: Octoer, 2012•Linked to: AESOP
Contact information
Tampere University of Technology,
FAST Laboratory,
P.O. Box 600,
FIN-33101 Tampere,
Finland
Email: [email protected]
www.tut.fi/fast
Conference: 38th Annual Conference of the IEEE Industrial Electronics Society
Title of the paper: Free Shape Paths in Industrial Robots
Authors: Luis E. Gonzalez Moctezuma, Andrei Lobov, Jose L. Martinez Lastra
If you would like to receive a reprint of the original paper, please contact us
Free Shape Paths in Industrial Robots
Authors: Luis E. Gonzalez Moctezuma, Andrei Lobov, Jose L. Martinez Lastra
Tampere University of TechnologyFactory Automation Systems and Technology Lab
IECON 2012, Montreal, Canada25-28.10.2012
Outline
• Motivation
• Bezier curves
• Curve approximation: arc and linear segments
• Comparison
• Implementation
• Conclusions
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Motivation (1/2)• 2008: 1.3 million of industrial robots
• Simple movements in industrial robots– Linear– Circular
• Need for free shape paths in robotic applications:– Welding– Fluid dispensing– Painting processes– Interaction and cooperation with humans
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Motivation (2/2)
• How to enable standard industrial robots to perform free shape paths?
09.04.23 5
Bezier curves (1/2)• Introduced by Pierre Bezier – Renault
• Curves described by a parametric function
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Bezier curves (2/2)
• Control, flexibility, intuitive
• Use and tools in:– Industrial design– CAD– 3D modelling– Vector-based drawing
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Approximation by arc segments
• Implementation of algorithm proposed by: Riskus, Aleksas. “Approximation of a Cubic Bezier Curve by Circular Arcs and Viceversa”
– Find inflection points (curvature change in sign)– Segments subdivided to reach biarcs <90°
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Approximation by linear segments• 1) Evaluate directly on the polynomial
function: Numerically unstable
• 2) Use the De Casteljau algorithm– Uses parameter t – and Bezier descriptors
Numerically stable
09.04.23 9
Comparison: arc Vs linear segments
*
*Interpolations can be computed in the target (industrial robot controller)
Implementation• SCARA robot (~15 years old)
• De Casteljau algorithm within the robot controller
• Transfer to controller just Bezier descriptors
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Conclusions
• Approach to implement free shape paths in generic industrial robots.
• Bezier curve descriptors can be storage as standard points
• Feasible to implement the Decasteljau algorithm within robot controllers
• Current and future industrial robotic applications might need free shape path capabilities to cooperate with humans and other machines
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Questions?
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