[CS686] Paper presentation 1

KAIST School of Computing

Generation of Dynamically Feasible and Collision Free Trajectoryby Applying Six-order Bezier Curve and Local Optimal Reshaping

Liang Yang et al.

IROS 2015

Heechan Shin

2017.04.27

CS686

[CS686] Paper presentation 1

KAIST School of Computing

Contents

• Problem of the paper• Backgrounds• Framework• Methods• Result• Summary• Limitation• Quiz

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[CS686] Paper presentation 1

KAIST School of Computing

Problems of the paper

• UAVs(or other robots) can follow a path, which is designed by previous path planner, with relatively slow speed.

• Piecewise linear paths are generated by RRT, RRT*, etc.

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[CS686] Paper presentation 1

KAIST School of Computing

Backgrounds

• Curvature

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[CS686] Paper presentation 1

KAIST School of Computing

Backgrounds

• Curvature

• Why is the curvature important?• Non-holonomic robots can’t go through piecewise linear path with high speed

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Low speed High speed

[CS686] Paper presentation 1

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Backgrounds

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• G2-Continuity

• End point• Tangent• Curvature radius

[CS686] Paper presentation 1

KAIST School of Computing

Backgrounds

• Bezier curve• Using Bernstein polynomial• N-1 order Bezier curve with N points• Continuous curvature at joint of two curves

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[CS686] Paper presentation 1

KAIST School of Computing

Framework

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[CS686] Paper presentation 1

KAIST School of Computing

Framework

• Path planner : Guiding Attraction based Random Tree(GART)• Attraction to the goal & Repulsion by the obstacles

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[CS686] Paper presentation 1

KAIST School of Computing

Methods

• Bezier curve based path smoothing

• Dangerous region finding

• Local optimal reshaping

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[CS686] Paper presentation 1

KAIST School of Computing

Methods – Bezier curve based path smoothing

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Six-order → 7 points

From path planner

From interpolation

[CS686] Paper presentation 1

KAIST School of Computing

Methods – Bezier curve based path smoothing

• How can we get interpolation points?

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[CS686] Paper presentation 1

KAIST School of Computing

Methods – Bezier curve based path smoothing

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• Tuning Rotation(TR)• Turning adjacent node until smooth

enough• Making the curve be consistent

[CS686] Paper presentation 1

KAIST School of Computing

Methods – Dangerous region finding

• “UAV simulations with dynamics show that the dangerous region”

• Performing fast simulation

• Obtaining dangerous regions (collision-expected)

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[CS686] Paper presentation 1

KAIST School of Computing

Methods – Local optimal reshaping

• Nodes near dangerous region should be reshaped

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Path length Curvature(1)

(1) Minimum distance from center of object𝒅𝒅𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 = 𝟒𝟒𝟒𝟒

(2),(3) Redistribution region

(2)

(3)

(4) Bezier curve

(4)

[CS686] Paper presentation 1

KAIST School of Computing

• Curvature within maximum curvature after smoothing and reshaping• Not enough to their target curvature 0.1

Result

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[CS686] Paper presentation 1

KAIST School of Computing

Result

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• After Tuning Rotation, curvature becomes lower than 0.1

[CS686] Paper presentation 1

KAIST School of Computing

Result

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• With speed disturbance 0.2m/s magnitude of WGN

[CS686] Paper presentation 1

KAIST School of Computing

Summary

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Guiding Attraction based Random Tree(GART)Six-order Bezier curve and Tuning RotationForward simulation to find dangerous regionLocal Optimal Reshaping

[CS686] Paper presentation 1

KAIST School of Computing

Limitation

• No mention about computational time

• No dynamics

• No difficult obstacles

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[CS686] Paper presentation 1

KAIST School of Computing

QnA

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THANK YOU

References• Generation of Dynamically Feasible and Collision Free Trajectory by Applying Six-order Bezier Curve and Local Optimal Reshaping (IROS 2015)• Guiding attraction based random tree path planning under uncertainty: Dedicate for UAV (IROS 2014)