hassan thesis presentation - dec16

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KINEMATICS AND OPTIMAL CONTROL OF A MOBILE PARALLEL ROBOT FOR INSPECTION OF PIPE-LIKE ENVIRONMENTSHassan Sarfraz

The Ottawa-Carleton Institute for Electrical and Computer Engineering

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Snake-like Pipeline Inspection Robot

Explorer 10/14 [Photograph]. Retrieved 11 December, 2013, from Pipetel technologies Inc. http://www.pipetelone.com/explorer_10-14.html

http://www.pipetelone.com/explorer_10-14.html

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Problem Statement Goal: To maximize the reachable

workspace

00

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Contribution

Analysis of a single module of a snake-like pipeline inspection robot. Study of Workspace and Singularities Determination of Optimal Geometry Optimal Control in a Geometrically

Singular pipe

Explorer 10/14 [Photograph]. Retrieved 11 December, 2013, from Pipetel technologies Inc. http://www.pipetelone.com/explorer_10-14.html

http://www.pipetelone.com/explorer_10-14.html

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Single Module: a Mobile Parallel Robot

qJxJ qx

2121 ,,, ssq

,, GG yxx

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Single Module: a Mobile Parallel Robot

cossinsin00sincoscos00

cossin2

sin2110

cossin2

cos2101

21

21

1

1

wllwll

lwah

lwah

J x

2

22

1

1121

2

22

1

1121

1

111

1

111

sinsin

coscos

00sin

00cos

dssdy

dssdyll

dssdx

dssdxll

dssdyl

dssdxl

J

PP

PP

P

P

q

qJxJ qx

2121 ,,, ssq ,, GG yxx

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Singular ConfigurationsSerial Singularity

222222

111111

sin'cos'sin'cos'

sxsysxsy

PP

PP

0det TqqJJ

Active joints motion resulting in no motion in the end-effector

Applied to this robot

Singularity occurs when at least one arm is perpendicular to pipe wall

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Singular ConfigurationsParallel Singularity

0det TxxJJ

,4,2,0,0

0sinsin2cos12

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212122

iiw

wllw

Motion in the end-effector is admitted for motionless active joints

Practically, the above condition is not possible

Analytical expression defining parallel singularity

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Singularity-free Workspace, Гsf

Introduction to four pipe-like structures

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Discretization Method

1. Forming a Grid on test area, Гref

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1. Forming a Grid on surface area, Гref

2. Direct Search Algorithm, Inverse Kinematic Sol.

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3. Collision Avoidance Algorithm

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10

1

max

min

KCI

KCI



3. Collision Avoidance Algorithm

4. Proximity to singularity Kinematic Conditioning Index



14Proximity to singularity in a Straight pipe

0

5

5

15

15


15

0

10

10

20

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Proximity to singularity in 135° elbowSingularity-free Workspace, Гsf

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Optimization of Geometric ParametersOptimization Problem Formulation

sf

ref

sfahwl

of ContinuityConstraintContact

Constraint AvoidanceCollision Constraint Avoidancey Singularit: tosubjected

,,,FMaximize

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PWl 26.0 PWw 5.0

PWhPWa 25.0

Optimization of Geometric ParametersConstrained Optimization in a Straight Pipe

Initial Design Parameters

015

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PWw 5.0

PWh

Optimization of Geometric ParametersConstrained Optimization in a Straight Pipe

PWl 58.0

PWa 96.0

Converged Design Parameters

015

19Constrained Optimization in a Straight Pipe

Converged Design Parameters,l

PWa 96.0

Cost function v.s. θ for values of l Average Cost function v.s. l

PWw 5.0

PWh

Optimization of Geometric Parameters

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PWw 5.0

PWh

Constrained Optimization in 135° elbow

PWl 75.0

PWa 91.0


0

Optimization of Geometric Parameters

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Critical Mobility Scenario

• Collision • Singular Configuration

• Discontinuity in Гsf

Optimal Control in a Geometrically Singular pipe

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• Prismatic Joints on the arms

• Additional degrees of freedom to overcome singularities at the corner

Modified Parallel Mobile RobotOptimal Control in a Geometrically Singular pipe

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Modified Parallel Mobile Robot (continued)Optimal Control in a Geometrically Singular pipe

2

22

1

112211

2

22

1

112211

1

1111

1

1111

sinsin

coscos

00sin

00cos

dssdy

dssdyldld

dssdx

dssdxldld

dssdyld

dssdxld

J

PP

PP

P

P

q

qJxJ qx

2121 ,,, ssq 21,,,, ddyxx GG

212211

212211

111

111

coscoscossinsin00sinsinsincoscos00

0coscossin2

sin2110

0sincossin2

cos2101

wldldwldld

ldwah

ldwah

J x

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1. Forward motion using Path-Following Control with proportional term• Xg, Yg, θ

2. Optimal arm length using gradient ascent

Path Following and Optimal TrajectoriesOptimal Control in a Geometrically Singular pipe

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Discrete-time Simulation ResultsOptimal Control in a Geometrically Singular pipe

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Prismatic Arm length vs. Path AbscissaSingularity measure vs. Path Abscissa

Performance EvaluationOptimal Control in a Geometrically Singular pipe

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• Continuous Singularity-free Workspace using Mobile Parallel Robot with prismatic arms

• Discontinuity in Singularity-free Workspace using Mobile Parallel Robot with rigid arms

vs.

Comparison of Singularity-free WorkspaceOptimal Control in a Geometrically Singular pipe

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Summary and Conclusion Singular configurations Singularity-free workspace Optimization of Geometric Parameters Mobile robot with discontinuous workspace when

crossing a sharp corner. Formulated and simulated a kinematical model to

navigate singularity-free across a corner An Optimal control strategy used to maximize a

performance index and deal with collisions Proposed Solution leads to continuous singularity-

free workspace.

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Publication

Journal Paper Lounis Douadi, Davide Spinello, Wail Gueaieb and Hassan Sarfraz. “Planar

kinematics analysis of a snake-like robot”. Robotica. doi:10.1017/S026357471300091X.

Conference Paper Davide Spinello, Hassan Sarfraz, Wail Gueaieb, Lounis Douadi, “Critical

Maneuvers of an Autonomous Parallel Robot in a Confined Environment”, In Proceedings of the International Conference on Mechanical Engineering and Mechatronics (ICMEM), 8 pp. Paper no. 196, 2013.

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Thank you for your time

Any questions or comments?

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Contact Constraint

Continuity of Гsf

PWwl 2

Optimization of Geometric MethodOptimization Problem Formulation (continued)

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Step 1:

Step 2:

]0[l ]0[w ]0[h ]0[a

0001 ,,,Fmax ahwllldl

]1[l

Optimization of Geometric MethodOptimization Technique: Parametric Variation

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Step 1:

Step 2:

]0[l ]0[w ]0[h ]0[a

0001 ,,,Fmax ahwlwwdw

]1[l ]1[w


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Step 1:

Step 2:

]0[l ]0[w ]0[h ]0[a

ahwlaada

,,,Fmax 0001

]1[l ]1[w ]1[h ]1[a


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Step 1:

Step 2:

Step 3: Repeat the above process

]0[l ]0[w ]0[h ]0[a

]1[l ]1[w ]1[h ]1[a

qq 1

][ql ][qw ][qh ][qa ][q


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PWl 5.0 PWw 5.0

PWhPWa 5.0

Optimization of Geometric MethodConstrained Optimization in a Straight Pipe

Initial Design Parameters

0

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PWw 5.0

PWh

Optimization of Geometric MethodConstrained Optimization in a Straight Pipe

PWl 58.0

PWa 96.0


0

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0w0h

Optimization of Geometric MethodUnconstrained Optimization in a Straight Pipe

PWl

PWa


0

hassan thesis presentation - dec16

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