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.

1. Free Shape Paths in
Industrial Robots
•Date: Octoer, 2012 Conference: 38th Annual Conference of
•Linked to: AESOP 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
Contact information
Tampere University of Technology,
FAST Laboratory,
P.O. Box 600,
FIN-33101 Tampere, If you would like to receive a reprint of
Finland the original paper, please contact us
Email: fast@tut.fi
www.tut.fi/fast

2. Free Shape Paths in
Industrial Robots
Authors: Luis E. Gonzalez Moctezuma, Andrei Lobov,
Jose L. Martinez Lastra
Tampere University of Technology
Factory Automation Systems and Technology Lab
IECON 2012, Montreal, Canada
25-28.10.2012

3. Outline
• Motivation
• Bezier curves
• Curve approximation: arc and linear segments
• Comparison
• Implementation
• Conclusions
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4. 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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5. Motivation (2/2)
• How to enable standard industrial robots to
perform free shape paths?
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6. Bezier curves (1/2)
• Introduced by Pierre Bezier – Renault
• Curves described by a parametric function
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7. Bezier curves (2/2)
• Control, flexibility, intuitive
• Use and tools in:
– Industrial design
– CAD
– 3D modelling
– Vector-based drawing
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8. 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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9. 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
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10. Comparison: arc Vs linear
segments
*
*Interpolations can be computed in the
target (industrial robot controller)

11. Implementation
• SCARA robot (~15 years old)
• De Casteljau algorithm within the robot
controller
• Transfer to controller just Bezier descriptors
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12. System in action
Video link
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13. 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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14. Questions?
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