Numerical and Experimental Validation of the Prototype of a BioInspired Piping Inspection Robot
Abstract
:1. Introduction
2. Locomotion Principle and Kinematic Equations of the Robot
3. Static Force Analysis on the Robot
 ${N}_{i}$—Normal Force
 ${T}_{li}$—Tangential longitudinal Force
 ${T}_{ri}$—Tangential radial Force
3.1. Results of Static Force Analysis
Forces Inside Horizontal and Vertical Orientations of Pipeline
4. Experimental Validation of the Prototype
Algorithm 1 Forward sequence force algorithm. 

 Forward motion (twice)
 Reverse motion (twice)
4.1. Estimation of Currents and Forces of the Motors from Experiments
5. Discussions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
DKM  Direct Kinematic Model 
IKM  Inverse Kinematic Model 
CG  Center of Gravity 
PWM  Pulse width modulation 
GPIO  Generalpurpose Input/Output 
ADC  Analog to Digital convertor 
BB  BeagleBone 
Nomenclature  
Symbol  Description 
$\rho $  Leg module actuation units 
${\rho}_{c}$  Central module actuation unit 
${l}_{1}$  Length of leg used in slotfollower mechanism 
$\theta $  Rotation angle of robot 
$\alpha $  Rotation angle of pipeline 
${\mathbf{R}}_{z}$  Rotation matrix about zaxis 
${\mathbf{n}}_{i}$  Vector coordinates for ${P}_{i}$ 
l  CG distance between clamped points and free end 
w  Selfweight of the robot 
${\mathbf{f}}_{i}$  Force vector 
${\mathbf{m}}_{i}$  Moment vector 
${}^{i}{\tau}_{0}$  Wrench at CG 
${T}_{li}$  Tangential longitudinal force 
${T}_{ri}$  Tangential radial force 
${N}_{i}$  Normal forces 
$\phi $  Coefficient of friction 
${F}_{a}$  Magnitude of actuator force 
${F}_{p}$,${N}_{total}$  Magnitude of contact force/Total normal force 
${\eta}_{f}$  Force transmission factor 
I  Current induced on actuators 
${V}_{t}$  Magnitude of measured voltage at time t 
${\tau}_{Mi}$  Magnitude of torque measured in experiments 
p  Pitch of screw in spindle drive 
${F}_{Mi}$  Output force of spindle drive 
Appendix
Parameters  Value 

Nominal voltage  12 V 
Nominal current (${I}_{c}$)  0.456 A 
No load speed  13,500 rpm 
No load current (${I}_{n}$)  60.2 mA 
Nominal speed  5840 rpm 
Efficiency (${\eta}_{m}$)  54% 
Torque constant (${K}_{T}$)  7.82 mNm/A 
Speed constant (${N}_{v}$)  1220 rpm/V 
Terminal resistance  15.7 $\mathsf{\Omega}$ 
Parameters  Value 

Spindle screw diameter and pitch (p)  $\varphi $5 × 2 mm 
Reduction ratio (G)  455:1 
Max. static axial load  500 N 
Max. spindle length  102 mm 
Efficiency (${\eta}_{s}$)  63% 
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Lengths  Dimensions [mm] 

${l}_{1}$  57 
${l}_{2}$  7 
e  11 
$\rho $  8.5–45.5 
Position of Central Actuator  Radius of the Pipeline (mm)  Position of CG from Clamped End (mm) 

Fully retracted  27  128 
Fully extended  27  149 
Fully retracted  37  123 
Fully extended  37  144 
Position of Central Actuator  Pipeline Radius (mm)  Actuator Force (N) Horizontal Pipe  Actuator Force (N) Vertical Pipe 

Fully retracted  27  60.6–63.7  20.4 
Fully extended  27  68.8–73.1  20.4 
Fully retracted  37  111.3–115  49.7 
Fully extended  37  125.7–130.8  49.7 
PWM Duty Cycle  ADC Voltage Range (V)  Nominal cUrrent Settings (A)  Motor Speed (rpm) 

20%  0  −0.46  10,800 (Counterclockwise) 
50% (idle)  0.9  0  0 
80%  1.8  0.46  10,800 (Clockwise) 
Orientation of Pipeline  Phase  Initial Force (N)  Final Force (N)  Force under Operation (N) 

Horizontal  Clamping (M1 & M3)  1000  1000  170–250 
Horizontal  Declamping (M1 & M3)  900  0  80–150 
Vertical  Clamping (M1 & M3)  1000  1000  160–330 
Vertical  Declamping (M1 & M3)  900  0  100–180 
Horizontal & Vertical  Elongation (M2)  1000  0  110–160 
Horizontal & Vertical  Retraction (M2)  1100  1100  100–150 
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Venkateswaran, S.; Chablat, D.; Boyer, F. Numerical and Experimental Validation of the Prototype of a BioInspired Piping Inspection Robot. Robotics 2019, 8, 32. https://doi.org/10.3390/robotics8020032
Venkateswaran S, Chablat D, Boyer F. Numerical and Experimental Validation of the Prototype of a BioInspired Piping Inspection Robot. Robotics. 2019; 8(2):32. https://doi.org/10.3390/robotics8020032
Chicago/Turabian StyleVenkateswaran, Swaminath, Damien Chablat, and Frédéric Boyer. 2019. "Numerical and Experimental Validation of the Prototype of a BioInspired Piping Inspection Robot" Robotics 8, no. 2: 32. https://doi.org/10.3390/robotics8020032