Intuitive dynamic modeling and flatness-based nonlinear control of a mobile robot

Abstract

In this paper, a bond graph model of a mobile robot with four Mecanum wheels is developed to extract a dynamic model of the robot. This is achieved using the BG_V21 tool box of MATLAB. The dynamic model thus obtained is used to derive the control law for trajectory tracking by the robot. There are two control algorithms that are used, namely, the flatness-based controller and the backstepping controller. From the simulation results, it is evident that the extracted dynamic model of the robot is accurate. Moreover, the flatness-based controller proved to have the upper hand in performance over the backstepping controller.

Keywords

Omnidirectional robot dynamic modeling bond graph flatness-based control trajectory planning

Get full access to this article

View all access options for this article.

References

Hui

. An omnidirectional mobile robot. Sci China Inf Sci 2011; 54: 2631–2638.

Campion

Bastin

Andrea-Novel

. Structural properties and classification of kinematic and dynamic models of wheeled mobile robots. Proceedings IEEE International Conference on Robotics and Automation; Atlanta, GA, 2–6 May 1993. Piscataway, NJ: IEEE.

Tzafestas

. Introduction to mobile robot control. London: Elsevier, 2013.

Killough

. A new family of omnidirectional and holonomic wheeled platforms for mobile robots. IEEE Trans Robot Autom 1994; 10: 480–489.

Muir

Neuman

. Kinematic modeling for feedback control of an omnidirectional wheeled mobile robot. Proceedings 1987 IEEE International Conference on Robotics and Automation, Raleigh, NC, March 1987. Piscataway, NJ: IEEE.

Conceição

Moreira

Costa

. Practical approach of modeling and parameters estimation for omnidirectional mobile robots. IEEE/ASME Trans Mechatron 2009; 14: 377–381.

Jia

Song

SSD

. Modeling and motion analysis of four-Mecanum wheel omni-directional mobile platform. 2013 CACS International Automatic Control Conference (CACS), Nantou, Taiwan, 2–4 December 2013. Piscataway, NJ: IEEE.

Tlale

de Villiers

. Kinematics and dynamics modeling of a Mecanum wheeled mobile platform. Mechatronics and Machine Vision in Practice, M2VIP 2008 15th International Conference, Auckland, 2–4 December 2008. Piscataway, NJ: IEEE.

Mosterman

Biswas

. A theory of discontinuities in physical system models. J Franklin Inst 1998; 335: 401–439.

10.

Gawthrop

. Bond graphs: A representation for mechatronic systems. Mechatronics 1991; 1: 127–156.

11.

Van Amerongen

Breedveld

. Modeling of physical systems for the design and control of mechatronic systems. Ann Rev Contr 2003; 27: 87–117.

12.

Damic

Cohodar

. Dynamic analysis of Stewart platform by bond graphs. Proc Eng 2015; 100: 226–233.

13.

Patnaik

Umanand

. Kinematics and dynamics of Jansen leg mechanism: A bond graph approach. Sim Model Pract Th 2016; 60: 160–169.

14.

Pathak

Kumar

Mukherjee

et al . A scheme for robust trajectory control of space robots. Sim Model Pract Th 2008; 16: 1337–1349.

15.

Ragusila

Emami

. Modeling of a robotic leg using bond graphs. Sim Model Pract Th 2014; 40: 132–143.

16.

Tabatabaei

Behbahani

de Silva

. Self-adjusting multidisciplinary design of hydraulic engine mount using bond graphs and inductive genetic programming. Eng App Artif Intel 2016; 48: 32–39.

17.

Sutar

Pathak

Mehta

et al . Inverse kinematics and control of 4-degree-of-freedom wire-actuated in vivo robot. Proc Inst Mech Eng I J Syst Control Eng 2015; 229: 77–91.

18.

Kumar

Rastogi

Gupta

. A hybrid impedance control scheme for underwater welding robots with a passive foundation in the controller domain. Simulation 2017; 93(7): 619–630.

19.

Fliess

Lévine

Martin

et al . Flatness and defect of non-linear systems: Introductory theory and examples. Int J Control 1995; 61: 1327–1361.

20.

Murray

Rathinam

Sluis

. Differential flatness of mechanical control systems: A catalog of prototype systems. ASME International Mechanical Engineering Congress and Exposition, San Francisco, CA, 12–17 November 1995.

21.

Tang

Miller

Krovi

et al . Differential-flatness-based planning and control of a wheeled mobile manipulator—Theory and experiment. IEEE/ASME Trans Mechatronics 2011; 16: 768–773.

22.

Kim

Won

Tomizuka

. Flatness-based nonlinear control for position tracking of electrohydraulic systems. IEEE/ASME Trans Mechatronics 2015; 20: 197–206.

23.

Chamseddine

Zhang

Rabbath

et al . Flatness-based trajectory planning/replanning for a quadrotor unmanned aerial vehicle. IEEE Trans Aerosp Electron Syst 2012; 48: 2832–2848.

24.

Menhour

D’Andréa-Novel

Boussard

et al . Algebraic nonlinear estimation and flatness-based lateral/longitudinal control for automotive vehicles. Intelligent Transportation Systems (ITSC), 14th International IEEE Conference, Washington, D.C, 5–7 October 2011. Piscataway, NJ: IEEE.

25.

Şolea

Cernega

. Obstacle avoidance for trajectory tracking control of wheeled mobile robots. Service orientation in holonic and multi agent manufacturing and robotics. Berlin: Springer, 2013, pp. 279–290.

26.

Walambe

Agarwal

Kale

et al . Optimal trajectory generation for car-type mobile robot using spline interpolation. 2016; 49(1): 601–606.

27.

Markus

Agee

Jimoh

. Flat control of industrial robotic manipulators. Robot Autonom Syst 2017; 87: 226–236.

28.

Xia

et al . Lateral path tracking control of autonomous land vehicle based on ADRC and differential flatness. IEEE Trans Ind Elect 2016; 63: 3091–3099.

29.

Huang

H-C

Tsai

C-C

. Adaptive robust control of an omnidirectional mobile platform for autonomous service robots in polar coordinates. J Intel Robot Syst 2008; 51: 439–460.

30.

Shun-Hung

Juang

J-C

. Integrated backstepping mobile robot controller design by applying sum of squares approach. SICE JCMSI 2010; 3: 442–447.

31.

Chwa

. Tracking control of differential-drive wheeled mobile robots using a backstepping-like feedback linearization. IEEE Trans Syst Man Cybern A Syst Humans 2010; 40: 1285–1295.

32.

Hou

Z-G

Zou

A-M

Cheng

et al . Adaptive control of an electrically driven nonholonomic mobile robot via backstepping and fuzzy approach. IEEE Trans Control Syst Technol 2009; 17: 803–815.

33.

Roy

Nandy

Kar

et al . Robust control of nonholonomic wheeled mobile robot with past information: Theory and experiment. Proc Inst Mech Eng I J Syst Control Eng 2017; 231: 178–188.

34.

Fatahi

Khabbaz

et al . Numerical optimization applying trust-region reflective least squares algorithm with constraints to optimize the non-linear creep parameters of soft soil. Appl Math Model 2017; 41: 236–256.