In this paper, we study the dynamics of an articulated planar mobile robot for confined environment exploration. The mobile vehicle is composed of n identical modules hitched together with passive revolute joints. Each module has the structure of a four-bar parallel mechanism on a mobile platform. The dynamic model is derived using Lagrange formulation. Computer simulations illustrate the model by addressing a path following problem inside a pipe. The dynamic model presented in this paper is the basis for the design of motion control algorithms that encode energy optimization and sensor performance maximization.
Issue Section:
Research Papers
References
1.
Hirose
, S.
, and Morishima
, A.
, 1990
, “Design and Control of a Mobile Robot With an Articulated Body
,” J. Robot. Res.
, 9
(2
), pp. 99
–114
.10.1177/0278364990009002082.
Mirats Tur
, J.
, and Garthwaite
, W.
, 2010
, “Robotic Devices for Water Main In-Pipe Inspection: A Survey
,” J. Field Rob.
, 27
(4
), pp. 491
–508
.10.1002/rob.203473.
Mazumdar
, A.
, and Asada
, H. H.
, 2010
, “An Underactuated, Magnetic-Foot Robot for Steel Bridge Inspection
,” ASME J. Mech. Rob.
, 2
(3
), p. 031007
.10.1115/1.40017784.
Suzumori
, K.
, Wakimoto
, S.
, and Takata
, M.
, 2003
, “A Miniature Inspection Robot Negotiating Pipes of Widely Varying Diameter
,” Proceedings of IEEE International Conference on Robotics and Automation
, Vol. 1–3
, pp. 2735
–2740
.5.
Schempf
, H.
, Mutschler
, E.
, Goltsberg
, V.
, Skoptsov
, G.
, Gavaert
, A.
, and Vradis
, G.
, 2003
, “Explorer: Untethered Real-Time Gas Main Assessment Robot System
,” Proceedings of International Workshop on Advances in Service Robotics
, ASER’03, Bardolino, Italy.6.
Jamoussi
, A.
, 2005
, “Robotic NDE: A New Solution for In-Line Pipe Inspection
,” Middle East Nondestructive Testing Conference and Exhibition
, Manama, Bahrain, Nov. 27–30.7.
Fjerdingen
, S. A.
, Liljebäck
, P.
, and Transeth
, A. A.
, 2009
, “A Snake-Like Robot for Internal Inspection of Complex Pipe Structures (PIKo)
,” IEEE/RSJ International Conference on Intelligent Robots and Systems
, pp. 5665
–5671
.8.
Shin
, H.
, Jeong
, K.-M.
, and Kwon
, J.-J.
, 2010
, “Development of a Snake Robot Moving in a Small Diameter Pipe
,” International Conference on Control, Automation and Systems (ICCAS 2010)
, pp. 1826
–1829
.9.
Dertien
, E.
, Stramigioli
, S.
, and Pulles
, K.
, 2011
, “Development of an Inspection Robot for Small Diameter Gas Distribution Mains
,” IEEE International Conference on Robotics and Automation (ICRA)
, pp. 5044
–5049
.10.
Transeth
, A. A.
, and Pettersen
, K. Y.
, 2006
, “Developments in Snake Robot Modeling and Locomotion
,” International Conference on Control, Automation, Robotics and Vision ICARCV
, pp. 1
–8
.11.
Wiriyacharoensunthorn
, P.
, and Laowattana
, S.
, 2002
, “Analysis and Design of a Multi-Link Mobile Robot (Serpentine)
,” IEEE International Conference on Industrial Technology
, Vol. 2
, pp. 694
–699
.12.
Ostrowski
, J.
, and Burdick
, J.
, 1996
, “Gait Kinematics for a Serpentine Robot
,” Proceedings of the IEEE International Conference on Robotics and Automation
, Vol. 2
, pp. 1294
–1299
.13.
Transeth
, A. A.
, Leine
, R. I.
, Glocker
, C.
, Pettersen
, K. Y.
, and Liljebäck
, P.
, 2008
, “Snake Robot Obstacle-Aided Locomotion: Modeling, Simulations, and Experiments
,” IEEE Trans. Rob.
, 24
(1
), pp. 88
–104
.10.1109/TRO.2007.91484914.
Ma
, S.
, and Tadokoro
, N.
, 2006
, “Analysis of Creeping Locomotion of a Snake-Like Robot on a Slope
,” Auton. Rob.
, 20
(1
), pp. 15
–23
.10.1007/s10514-006-5204-615.
Bayraktaroglu
, Z. Y.
, and Blazevic
, P.
, 2005
, “Understanding Snakelike Locomotion Through a Novel Push-Point Approach
,” ASME J. Dyn. Syst., Meas., Control
, 127
(1
), pp. 146
–152
.10.1115/1.187004516.
Hopkins
, J. K.
, Spranklin
, B. W.
, and Gupta
, S. K.
, 2011
, “A Case Study in Optimization of Gait and Physical Parameters for a Snake-Inspired Robot Based on a Rectilinear Gait
,” ASME J. Mech. Rob.
, 3
(1
), p. 014503
.10.1115/1.400307717.
Briot
, S.
, Glazunov
, V.
, and Arakelian
, V.
, 2013
, “Investigation on the Effort Transmission in Planar Parallel Manipulators
,” ASME J. Mech. Rob.
, 5
(1
), p. 011011
.10.1115/1.402332518.
Carretero
, J. A.
, Ebrahimi
, I.
, and Boudreau
, R.
, 2012
, “Overall Motion Planning for Kinematically Redundant Parallel Manipulators
,” ASME J. Mech. Rob.
, 4
(2
), p. 024502
.10.1115/1.400652319.
Hu
, B.
, Yu
, J.
, Lu
, Y.
, Sui
, C.
, and Han
, J.
, 2012
, “Statics and Stiffness Model of Serial-Parallel Manipulator Formed by k Parallel Manipulators Connected in Series
,” Trans. ASME J. Mech. Rob.
, 4
(2
), p. 021012
.10.1115/1.400619020.
Bolzern
, P.
, DeSantis
, R.
, Locatelli
, A.
, and Togno
, S.
, 1996
, “Dynamic Model of a Two-Trailer Articulated Vehicle Subject to Nonholonomic Constraints
,” Robotica
, 14
(4
), pp. 445
–450
.10.1017/S026357470001985821.
Ute
, J.
, and Ono
, K.
, 2002
, “Fast and Efficient Locomotion of a Snake Robot Based on Self-Excitation Principle
,” Proceedings of the 7th International Workshop on Advanced Motion Control
, pp. 532
–539
.22.
Transeth
, A. A.
, Leine
, R. I.
, Glocker
, C.
, and Pettersen
, K. Y.
, 2008
, “3-D Snake Robot Motion: Nonsmooth Modeling, Simulations, and Experiments
,” IEEE Trans. Rob.
, 24
(2
), pp. 361
–376
.10.1109/TRO.2008.91700323.
Liljebäck
, P.
, Pettersen
, K. Y.
, Stavdahl
, O.
, and Gravdahl
, J. T.
, 2010
, “A Simplified Model of Planar Snake Robot Locomotion
,” IEEE/RSJ 2010 International Conference on Intelligent Robots and Systems (IROS 2010)
, pp. 2868
–2875
.24.
Liljebäck
, P.
, Pettersen
, K.
, Stavdahl
, O.
, and Gravdahl
, J.
, 2010
, “Hybrid Modelling and Control of Obstacle-Aided Snake Robot Locomotion
,” IEEE Trans. Rob.
, 26
(5
), pp. 781
–799
.10.1109/TRO.2010.205621125.
Murugendran
, B.
, Transeth
, A. A.
, and Fjerdingen
, S. A.
, 2009
, “Modeling and Path-Following for a Snake Robot With Active Wheels
,” IEEE-RSJ International Conference on Intelligent Robots and Systems
, pp. 3643
–3650
.26.
Li
, N.
, Zhao
, T.
, and Zhao
, Y.
, 2008
, “The Dynamic Modeling of Snake-Like Robot by Using Nominal Mechanism Method
,” ICIRA’08 Proceedings of the First International Conference on Intelligent Robotics and Applications: Part I
, pp. 1185
–1194
.27.
Liljebäck
, P.
, Pettersen
, K.
, Stavdahl
, O.
, and Gravdahl
, J.
, 2012
, “A Review on Modelling, Implementation, and Control of Snake Robots
,” Rob. Auton. Syst.
, 60
(1
), pp. 29
–40
.10.1016/j.robot.2011.08.01028.
Samin
, J.-C.
, and Fisette
, P.
, 2003
, “Symbolic Modeling of Multibody Systems,” Solid Mechanics and Its Applications
, Vol. 112, Springer
, New York
.29.
Bendtsen
, C.
, and Thomsen
, P.
, 1999
, Numerical Solution of Differential Algebraic Equations
, IMM, Department of Mathematical Modeling, Technical University of Denmark
, Kongens Lyngby, Denmark.30.
Wijckmans
, P.
, 1996
, “Conditioning of Differential Algebraic Equations and Numerical Solution of Multibody Dynamics
,” Ph.D. thesis, Technische Universiteit Eindhoven, Eindhoven, The Netherlands.31.
Baumgarte
, J.
, 1972
, “Stabilization of Constraints and Integrals of Motion in Dynamical Systems
,” Comput. Methods Appl. Mech. Eng.
, 1
(1
), pp. 1
–16
.10.1016/0045-7825(72)90018-732.
Cline
, M. B.
, and Pai
, D. K.
, 2003
, “Post-Stabilization for Rigid Body Simulation With Contact and Constraints
,” Proceedings of the IEEE International Conference on Robotics and Automation
, Vol. 1–3
, pp. 3744
–3751
.33.
Ascher
, U.
, Chin
, H.
, Petzold
, L.
, and Reich
, S.
, 1995
, “Stabilization of Constrained Mechanical Systems With DAEs and Invariant Manifolds
,” Mech. Struct. Mach.
, 23
, pp. 135
–157
.10.1080/0890545950890523234.
Bauchau
, O.
, and Laulusa
, A.
, 2008
, “Review of Contemporary Approaches for Constraint Enforcement in Multibody Systems
,” J. Comput. Nonlinear Dyn.
, 3
(1
), pp. 1
–8
.35.
Sarfraz
, H.
, Spinello
, D.
, Gueaieb
, W.
, and Douadi
, L.
, 2013
, “Critical Maneuvers of an Autonomous Parallel Robot in a Confined Environment
,” Proceedings of the International Conference of Mechanical Engineering and Mechatronics (ICMEM)
, p. 196
.36.
Gosselin
, C.
, and Angeles
, J.
, 1990
, “Singularity Analysis of Closed-Loop Kinematic Chains
,” IEEE Trans. Rob. Autom.
, 6
(3
), pp. 281
–290
.10.1109/70.5666037.
Merlet
, J. P.
, 2006
, Parallel Robots
, Springer
, New York
.38.
Bernstein
, D. S.
, 2011
, Matrix Mathematics: Theory, Facts, and Formulas
, 2nd ed., Princeton University Press
, Princeton, NJ
.39.
Spong
, M. W.
, Hutchinson
, S.
, and Vidyasagar
, M.
, 2006
, Robot Modeling and Control
, Wiley
, New York
.40.
Flannery
, M.
, 2004
, “The Enigma of Nonholonomic Constraints
,” Am. J. Phys.
, 73
(3
), pp. 265
–272
.10.1119/1.183050141.
Hemami
, H.
, and Weimer
, F. C.
, 1981
, “Modeling of Nonholonomic Dynamic Systems With Applications
,” ASME J. Appl. Mech.
, 48
(1
), pp. 177
–182
.10.1115/1.315756342.
Metiku
, R.
, 2004
, “Computer-Aided Dynamic Force Analysis of Four-Bar Planar Mechanism
,” Master's thesis, Addis Ababa University, School of Graduate Studies, Addis Ababa, Ethiopia.43.
Poursina
, M.
, and Anderson
, K. S.
, 2013
, “An Extended Divide-and-Conquer Algorithm for a Generalized Class of Multibody Constraints
,” Multibody Syst. Dyn.
, 29
(3
), pp. 235
–254
.10.1007/s11044-012-9324-944.
Kreutz-Delgado
, K.
, Jain
, A.
, and Rodriguez
, G.
, 1991
, “Recursive Formulation of Operational Space Control
,” Proceedings of the IEEE International Conference on Robotics and Automation
, pp. 1750
–1753
.45.
Poursina
, M.
, and Anderson
, K. S.
, 2013
, “Canonical Ensemble Simulation of Biopolymers Using a Coarse-Grained Articulated Generalized Divide-and-Conquer Scheme
,” Comput. Phys. Commun.
, 184
(3
), pp. 652
–660
.10.1016/j.cpc.2012.10.02946.
Yu
, Q.
, and Chen
, I.-M.
, 2000
, “A Direct Violation Correction Method in Numerical Simulation of Constrained Multibody Systems
,” Comput. Mech.
, 26
(1
), pp. 52
–57
.10.1007/s00466000014947.
Sastry
, S. S.
, 1999
, Nonlinear Systems: Analysis, Stability, and Control
, Springer
, New York
.48.
Altafini
, C.
, 2002
, “Following a Path of Varying Curvature as an Output Regulation Problem
,” IEEE Trans. Autom. Control
, 47
(9
), pp. 1551
–1556
.10.1109/TAC.2002.802750Copyright © 2015 by ASME
You do not currently have access to this content.