Modeling of dynamics of cooperating wheeled mobile robots
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Rzeszow University of Technology, Faculty of Mechanical Engineering and Aeronautics, Rzeszów, Poland
Submission date: 2021-04-17
Final revision date: 2021-07-18
Acceptance date: 2021-08-04
Online publication date: 2021-09-28
Publication date: 2021-10-20
Corresponding author
Andrzej Burghardt   

Faculty of Mechanical Engineering and Aeronautics, Department of Applied Mechanics and Robotics,, Rzeszow University of Technology, al. Powstańców Warszawy 12, 35-959, Rzeszow, Poland
Journal of Theoretical and Applied Mechanics 2021;59(4):649-659
The work presents dynamics of a system of two wheeled mobile robots cooperating in the transport of large-size cargo in the form of a beam. The purpose of modeling of such a system was to obtain a mathematical model in an applicable form. Lagrange equations of the second type were used to describe dynamics, and then the projective method was used to eliminate Lagrange multipliers. Thanks to this approach, unknown dry friction forces at the contact points of robot wheels with the ground were eliminated from the description, and dynamics in controllable coordinates was obtained. In addition, the obtained model has structural properties that enable its use in synthesis of a control system based on the mathematical model.
Abbaspour A., Alipour K., Jafari H.Z., Moosavian S.A., 2015, Optimal formation and control of cooperative wheeled mobile robots, Comptes Rendus Mécanique, 343, 5-6, 307-321.
Alipour K., Robat A.B., Tarvirdizadeh B., 2019, Dynamics modeling and sliding mode control of tractor-trailer wheeled mobile robots subject to wheels slip, Mechanism and Machine Theory, 138, 16-37.
Blajer W., 1998, Methods of Dynamics of Multi-Member Systems (in Polish), Politechnika Radomska, Radom.
Burghardt A., 2008, Proposal for a rapid prototyping environment for algorithms intended for autonomous mobile robot control, Mechanics and Mechanical Engineering, 1, 5-16.
Burghardt A., 2010, Modelling of dynamics of a wheeled robot by Appell’s equation (in Polish), Acta Mechanica et Automatica, 4, 9-12.
Burghardt A., Szybicki D., Kurc K., Muszynska M., 2020, Mechatronic designing and prototyping of a mobile wheeled robot driven by a microcontroller, Journal of Theoretical and Applied Mechanics, 58, 1, 127-142.
Dhaouadi R., Hatab A., 2013, Dynamic modelling of differential-drive mobile robots using Lagrange and Newton-Euler methodologies: a unified framework, Advances in Robotics and Automation, 2, 2, 1-7.
Giergiel J., Żylski W., 2005, Description of motion of a mobile robot by Maggie’s equations, Journal of Theoretical and Applied Mechanics, 43, 3, 511-521.
Hendzel Z., Burghardt A., Szuster M., 2013, Adaptive Critic Designs in Control of Robots Formation in Unknown Environment, Proceedings of International Conference on Artificial Intelligence and Soft Computing, ICAISC 2013, DOI:10.1007/978-3-642-38610-7 33, 351-362.
Hendzel Z., Burghardt A., Szuster M., 2015, Artificial intelligence algorithms in behavioural control of wheeled mobile robots formation, [In:] Computational Intelligence. Studies in Computational Intelligence, V. 577, Madani K., Correia A., Rosa A., Filipe J. (Eds), Springer, Cham.
Hoang N.B., Kang H.J., 2016, Neural network-based adaptive tracking control of mobile robots in the presence of wheel slip and external disturbance force, Neurocomputing, 188, 12-22.
Kurc K., Szybicki D., Burghardt A., Muszyńska M., 2016, The application of virtual prototyping methods to determine the dynamic parameters of mobile robot, Open Engineering, 6, 1, 55-63.
Mohammadpour E., Naraghi M., 2011, Robust adaptive stabilization of skid steer wheeled mobile robots considering slipping effects, Advanced Robotics, 25, 1-2, 205-227.
Szuster M., Hendzel Z., Burghardt A., 2014, Fuzzy sensor-based navigation with neural tracking control of the wheeled mobile robot, Artificial Intelligence and Soft Computing, Lecture Notes in Computer Science, Springer Verlag, 8468, 302-313.
Tanner H.G., Kyriakopoulos K.J., 2001, Mobile manipulator modeling with Kane’s approach, Robotica, 19, 6, 675-690.
Thanjavur K., Rajagopalan R., 1997, Ease of dynamic modelling of wheeled mobile robots (WMRs) using Kane’s approach, Proceedings of International Conference on Robotics and Automation, 4, IEEE, 2926-2931.
Wang D., Low C.B., 2008, Modeling and analysis of skidding and slipping in wheeled mobile robots: control design perspective, IEEE Transactions on Robotics, 24, 3, 676-687.
Yoo S.J., 2012, Approximation-based adaptive control for a class of mobile robots with unknown skidding and slipping, International Journal of Control, Automation, and Systems, 10, 4, 703-710.
Yun X., Sarkar N., 1998, Unified formulation of robotic systems with holonomic and nonholonomic constraints, IEEE Transactions on Robotics and Automation, 14, 4, 640-650.
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