# Dynamic Modeling of an Out-Pipe Inspection Robot and Experimental Validation of the Proposed Model using Image Processing Technique

• Alborz Aghamaleki Sarvestani
• Farimah Fazlollahi
• Alireza Goshtasbi
• Kasra Mokhtari
Technical Note

## Abstract

Gas and liquid pipelines surround us. To ensure reliable product delivery and to maintain pipeline integrity, asset managers should consider routine pipeline inspection and holistic management programs to extend pipeline life and prevent risk. Therefore, pipe inspection robots are of special interest to industries. In this paper, we present a new and simple locomotion strategy for an out-pipe inspection robot which can provide adjustable tractive force and can also be utilized to support active diameter adaptability. The advantages proposed by this design include simplicity, low manufacturing costs, online inspection capability and short operational time. Here a dynamic model of the robot is presented with the required assumptions. The mathematical model of 2-DOF robot is obtained using the well-known Lagrange equation. Modeling and simulations were conducted to test the validity and practicality of the proposed design and strategies. The prototype has successfully traveled along a pipe of 20 cm diameter. The results obtained from our dynamic model are then validated by experimental data.

## Keywords

Inspection robots Image processing Out-pipe robots Dynamic modeling of out-pipe robots

## List of symbols

$$q_{1}$$

Center height of driving wheels

$$q_{2}$$

Angle of rotation of rigid guides with respect to the horizon

R

$$d_{\text{wheel}}$$

Distance between closer sides of driving wheels

$$\alpha_{\text{w}}$$

Included angle between the vertical axis and the line from the supporting point of driving wheels to the pipe center

$$\alpha_{\text{wi}}$$

Included angle between the vertical axis and the line from the supporting point of idler wheels to the pipe center

$$d_{\text{wheelidler}}$$

Distance between centers of idler wheels

$$d_{p1}$$

Distance between center of mass of sliding plate and four rigid guides and axis of driving wheels

$$d_{p2}$$

Distance between axis of driving wheels and mass center of sliding plate

$$l_{\text{hor}}$$

Projected distance between axis of driving wheels and idler wheels on horizontal axis

$$l_{{{\text{base}} \times {\text{w}}}}$$

Normal distance between center of the idler wheels and base plate

P

Potential energy

Q

Vector of generalized forces

q

Vector of generalized coordinates

$$\dot{q}$$

Vector of generalized velocities

$$\ddot{q}$$

Vector of generalized accelerations

$$M(q)$$

Inertia matrix

$$C(q,\dot{q})$$

Coriolis and centrifugal force vector

$$g(t)$$

Gravitational force vector

$$\tau (t)$$

Applied torque/force vector

$$l_{0}$$

Initial length of springs

$$d_{\text{spring}}$$

Deflection of the springs

$$y_{c1}$$

Center of mass height of the frame

$$y_{c2}$$

Center of mass height of base plate with respect to reference frame

$$v_{c1}$$

Center of mass velocity of the frame

$$v_{c2}$$

Center of mass velocity of the sliding plate

K

Kinetic energy

$$l_{\text{tot}}$$

Total length of guides

$$tp1$$

Thickness of sliding plate

$$r_{\text{iw}}$$

$$r_{\text{w}}$$

## References

1. Aoshima S-I, Tsujimura T, Yabuta T (1993) A miniature mobile robot using piezo vibration for mobility in a thin tube. J Dyn Syst Meas Control 115:270–278
2. Aracil R, Saltarén R, Reinoso O (2003) Parallel robots for autonomous climbing along tubular structures. Robot Auton Syst 42:125–134
3. Choi C, Park B, Jung S (2010) The design and analysis of a feeder pipe inspection robot with an automatic pipe tracking system. IEEE/ASME Trans Mechatron 15:736–745
4. Durali M, Fazeli A, Azimi M (2008) Investigation of dynamics and vibration of a three unit pig in oil and gas pipelines. In: ASME 2008 International Mechanical Engineering Congress and Exposition, pp 265–275Google Scholar
5. Harris C, Stephens M (1988) A combined corner and edge detector. In: Alvey Vision Conference, p 50Google Scholar
6. Horodinca M, Doroftei I, Mignon E, Preumont A (2002) A simple architecture for in-pipe inspection robots. In: Proceedings of International Colloquium on Mobile and Autonomous Systems, pp 61–64Google Scholar
7. Hu Z, Appleton E (2005) Dynamic characteristics of a novel self-drive pipeline pig. IEEE Trans Robot 21:781–789
8. Kurata M, Takayama T, Omata T (2010) Helical rotation in-pipe mobile robot. In: 2010 3rd IEEE RAS and EMBS International Conference on Biomedical Robotics and Biomechatronics (BioRob), pp 313–318Google Scholar
9. Lee D, Park J, Hyun D, Yook G, Yang H-S (2012) Novel mechanisms and simple locomotion strategies for an in-pipe robot that can inspect various pipe types. Mech Mach Theory 56:52–68
10. Lim J, Park H, An J, Hong Y-S, Kim B, Yi B-J (2008) One pneumatic line based inchworm-like micro robot for half-inch pipe inspection. Mechatronics 18:315–322
11. Liu W, Jia X, Wang F, Jia Z (2010) An in-pipe wireless swimming microrobot driven by giant magnetostrictive thin film. Sens Actuators, A 160:101–108
12. Lopez JM, Sadovnychiy S (2007) Small PIG for inspection pipeline. In: Electronics, Robotics and Automotive Mechanics Conference, 2007. CERMA 2007, pp 585–590Google Scholar
13. Matuliauskas A, Spruogis B, Pikūnas A (2006) Wall press walking in-pipe robot. Solid State Phenom 113:296–300
14. Miyagawa T, Iwatsuki N (2007) Characteristics of in-pipe mobile robot with wheel drive mechanism using planetary gears. In: International Conference on Mechatronics and Automation, 2007. ICMA 2007, pp 3646–3651Google Scholar
15. Moghaddam MM, Tafti MRA (2005) Design, modeling and prototyping of a pipe inspection robot. In: 22nd International Symposium on Automation and Robotics in Construction ISARC 11–14 September 2005, FerraraGoogle Scholar
16. Neubauer W (1994) A spider-like robot that climbs vertically in ducts or pipes. In: Proceedings of the IEEE/RSJ/GI International Conference on Intelligent Robots and Systems’ 94. Advanced Robotic Systems and the Real World, IROS’94, pp 1178–1185Google Scholar
17. Okada T, Sanemori T (1987) MOGRER: a vehicle study and realization for in-pipe inspection tasks. IEEE J Robot Autom 3:573–582
18. Ono M, Kato S (2010) A study of an earthworm type inspection robot movable in long pipes. Int J Adv Rob Syst 7:085–090Google Scholar
19. Oya T, Okada T (2005) Development of a steerable, wheel-type, in-pipe robot and its path planning. Adv Robot 19:635–650
20. Park J, Hyun D, Cho W-H, Kim T-H, Yang H-S (2011) Normal-force control for an in-pipe robot according to the inclination of pipelines. IEEE Trans Ind Electron 58:5304–5310
21. Qiao J, Shang J, Goldenberg A (2013) Development of inchworm in-pipe robot based on self-locking mechanism. IEEE/ASME Trans Mechatron 18:799–806
22. Roh S-G, Choi HR (2005) Differential-drive in-pipe robot for moving inside urban gas pipelines. IEEE Trans Robot 21:1–17
23. Roh S, Lee J-S, Moon H, Choi HR (2008) Modularized in-pipe robot capable of selective navigation inside of pipelines. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, 2008. IROS 2008, pp 1724–1729Google Scholar
24. Schempf H, Mutschler E, Goltsberg V, Skoptsov G, Gavaert A, Vradis G (2003) Explorer: untethered real-time gas main assessment robot system. In: Proceedings of the Workshop on Advances in Service Robotics, ASERGoogle Scholar
25. Suzumori K, Miyagawa T, Kimura M, Hasegawa Y (1999) Micro inspection robot for 1-in pipes. IEEE/ASME Trans Mechatron 4:286–292
26. Vahabi M, Mehdizadeh E, Kabganian M, Barazandeh F (2011) Modelling of a novel in-pipe microrobot design with IPMC legs. Proc Inst Mech Eng Part I J Syst Control Eng 225:63–73
27. Wakimoto S, Nakajima J, Takata M, Kanda T, Suzumori K (2003) A micro snake-like robot for small pipe inspection. In: Proceedings of 2003 International Symposium on Micromechatronics and Human Science, 2003. MHS 2003, pp 303–308Google Scholar
28. Zagler A, Pfeiffer F (2003) “MORITZ” a pipe crawler for tube junctions. In: IEEE International Conference on Robotics and Automation, 2003. Proceedings. ICRA’03, pp 2954–2959Google Scholar
29. Zhang Y, Yan G (2007) In-pipe inspection robot with active pipe-diameter adaptability and automatic tractive force adjusting. Mech Mach Theory 42:1618–1631
30. Zhang Y, Jiang S, Zhang X, Yu H, Wang D, Guo D (2010) Dynamic characteristics of an intestine capsule robot with variable diameter. Chin Sci Bull 55:1813–1821

## Authors and Affiliations

• Alborz Aghamaleki Sarvestani
• 1
Email author