KINEMATICS AND OPTIMAL CONTROL OF A MOBILE PARALLEL ROBOT FOR INSPECTION OF PIPE-LIKE ENVIRONMENTS Hassan Sarfraz The Ottawa-Carleton Institute for Electrical and Computer Engineering 1
1
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
2
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
3
Problem Statement Goal: To maximize the reachable
workspace
00
4
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
5
Single Module: a Mobile Parallel Robot
qJxJ qx
2121 ,,, ssq
,, GG yxx
6
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
7
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
8
Singular ConfigurationsParallel Singularity
0det TxxJJ
,4,2,0,0
0sinsin2cos12
21
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
9
Singularity-free Workspace, Гsf
Introduction to four pipe-like structures
10
Singularity-free Workspace, Гsf
Discretization Method
1. Forming a Grid on test area, Гref
11
Singularity-free Workspace, Гsf
Discretization Method
1. Forming a Grid on surface area, Гref
2. Direct Search Algorithm, Inverse Kinematic Sol.
12
Singularity-free Workspace, Гsf
Discretization Method
1. Forming a Grid on surface area, Гref
2. Direct Search Algorithm, Inverse Kinematic Sol.
3. Collision Avoidance Algorithm
13
10
1
max
min
KCI
KCI
1. Forming a Grid on surface area, Гref
2. Direct Search Algorithm, Inverse Kinematic Sol.
3. Collision Avoidance Algorithm
4. Proximity to singularity Kinematic Conditioning Index
Singularity-free Workspace, Гsf
Discretization Method
14Proximity to singularity in a Straight pipe
0
5
5
15
15
Singularity-free Workspace, Гsf
15
0
10
10
20
20
Proximity to singularity in 135° elbowSingularity-free Workspace, Гsf
16
Optimization of Geometric ParametersOptimization Problem Formulation
sf
ref
sfahwl
of ContinuityConstraintContact
Constraint AvoidanceCollision Constraint Avoidancey Singularit: tosubjected
,,,FMaximize
17
PWl 26.0 PWw 5.0
PWhPWa 25.0
Optimization of Geometric ParametersConstrained Optimization in a Straight Pipe
Initial Design Parameters
015
18
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
20
PWw 5.0
PWh
Constrained Optimization in 135° elbow
PWl 75.0
PWa 91.0
Converged Design Parameters
0
Optimization of Geometric Parameters
21
Critical Mobility Scenario
• Collision • Singular Configuration
• Discontinuity in Гsf
Optimal Control in a Geometrically Singular pipe
22
• 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
23
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
24
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
25
Discrete-time Simulation ResultsOptimal Control in a Geometrically Singular pipe
26
Prismatic Arm length vs. Path AbscissaSingularity measure vs. Path Abscissa
Performance EvaluationOptimal Control in a Geometrically Singular pipe
27
• 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
28
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.
29
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.
30
Thank you for your time
Any questions or comments?
31
Contact Constraint
Continuity of Гsf
PWwl 2
Optimization of Geometric MethodOptimization Problem Formulation (continued)
32
Step 1:
Step 2:
]0[l ]0[w ]0[h ]0[a
0001 ,,,Fmax ahwllldl
]1[l
Optimization of Geometric MethodOptimization Technique: Parametric Variation
33
Step 1:
Step 2:
]0[l ]0[w ]0[h ]0[a
0001 ,,,Fmax ahwlwwdw
]1[l ]1[w
Optimization of Geometric MethodOptimization Technique: Parametric Variation
34
Step 1:
Step 2:
]0[l ]0[w ]0[h ]0[a
ahwlaada
,,,Fmax 0001
]1[l ]1[w ]1[h ]1[a
Optimization of Geometric MethodOptimization Technique: Parametric Variation
35
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
Optimization of Geometric MethodOptimization Technique: Parametric Variation
36
PWl 5.0 PWw 5.0
PWhPWa 5.0
Optimization of Geometric MethodConstrained Optimization in a Straight Pipe
Initial Design Parameters
0
37
PWw 5.0
PWh
Optimization of Geometric MethodConstrained Optimization in a Straight Pipe
PWl 58.0
PWa 96.0
Converged Design Parameters
0
38
0w0h
Optimization of Geometric MethodUnconstrained Optimization in a Straight Pipe
PWl
PWa
Converged Design Parameters
0