Analysis of the parametric configuration impact on BallBot control performance

Abstract

The BallBot, a versatile robot system, finds applications in various domains of life. It comprises a frame moved by three wheels mounted on a ball. The robot performance is significantly influenced by its parametric configuration, including body mass, chassis size, and ball diameter. This study examines the impact of these configuration parameters on the control of the BallBot. The mathematical model of the BallBot is discussed, considering the assumptions and coordinate systems. To control the robot, a Linear Quadratic Regulator controller is designed. Subsequently, the simulation model is used to assess the effects of changing the initial parametric configuration. It is observed that altering the robot mass has a notable impact on the BallBot response, while changes in the ball diameter have a relatively insignificant effect.

Keywords

BallBot / LQR / BallBot’s control performance / structural configuration

References

[1] Elliott A. The Culture of AI: Everyday Life and the Digital Revolution. Routledge;2019.

[2] Strazdas D, Hintz J, Khalifa A, Abdelrahman AA, Hempel T, Al-Hamadi A. Robot system assistant (RoSA): towards intuitive multi-modal and multi-device human-robot interaction. Sensors. 2022;22(3):923.

[3] Thanh VN, Vinh DP, Nghi NT, Nam LH, Toan DLH. Restaurant serving robot with double line sensors following approach. Paper presented at:2019 IEEE International Conference on Mechatronics and Automation;2019:235-239;Tianjin, China.

[4] Pham DB, Kim H, Kim J, Lee SG. Balancing and transferring control of a ball segway using a double-loop approach [applications of control]. IEEE Control Syst Mag. 2018;38(2):15-37.

[5] Cai C, Lu J, Li Z. Kinematic analysis and control algorithm for the BallBot. IEEE Access. 2019;7:38314-38321.

[6] Lauwers TB, Kantor GA, Hollis RL. A dynamically stable single-wheeled mobile robot with inverse mouse-ball drive. Paper presented at:2006 IEEE International Conference on Robotics and Automation;2006:2884-2889;Orlando, FL.

[7] Thanh VN, Vinh DP, Nam LH, Nghi NT, Anh DL. Reinforcement Q-learning PID controller for a restaurant mobile robot with double line-sensors Association for Computing Machinery. Paper presented at:4th International Conference on Machine Learning and Soft Computing ICMLSC;2020:164-167;New York, NY.

[8] Le HN, Dang PV, Pham AD, Vo NT. System identifications of a 2DOF pendulum controlled by QUBE-servo and its unwanted oscillation factors. Arch Mech Eng. 2020;67(4):435-450.

[9] Pham AD, Ahn HJ. Evaluation of input shaping methods for the nonlinear vibration system using a furuta pendulum. J Korean Soc Precis Eng. 2020;37(11):827-833.

[10] Pham DB, Weon IS, Lee SG. Partial feedback linearization double-loop control for a Pseudo-2D ridable BallBot. Int J Control Autom Syst. 2020;18:1310-1323.

[11] Fankhauser P, Gwerder C. Modeling and Control of a BallBot. Dissertation. ETH Zurich;2010.

[12] Lal I, Nicoara M, Codrean A, Busoniu L. Hardware and control design of a ball balancing robot. Paper presented at: IEEE 22nd International Symposium on Design and Diagnostics of Electronic Circuits &Systems;2019:1-6;Cluj-Napoca, Romania.

[13] Garcia-Garcia RA, Arias-Montiel M. Linear controllers for the NXT BallBot with parameter variations using linear matrix inequalities [lecture notes]. IEEE Control Syst Mag. 2016;36(3):121-136.

[14] Ortiz I, Jurado F, Ollervides-Vazquez E. Discrete-time linear quadratic regulator for a NXT BallBot system. Paper presented at:2022 International Conference on Mechatronics, Electronics and Automotive Engineering (ICMEAE);2022:95-100;Cuernavaca, Mexico.

[15] Ba Pham D, Quang Duong X, Sang Nguyen D, et al. Balancing and tracking control of BallBot mobile robots using a novel synchronization controller along with online system identification. IEEE Trans Ind Electron. 2023;70(1):657-668.

[16] Nguyen DN, Cao TB, Pham TH, Vo NT, Dang PV, Le HN. Design and control of a Ball-balancing robot. Paper presented at:4th International Conference on Green Technology and Sustainable Development;2018:317-322;Ho Chi Minh City, Vietnam.

[17] Blonk JW. Modeling and Control of a Ball-balancing robot. Dissertation. University of Twente;2014.

[18] Wang J, Rui X, Wang X, Zhang J, Zhou Q, Gu J. Eigenvalue analysis of planar linear multibody system under conservative force based on the transfer matrix method. Int J Mech Syst Dyn. 2023;3:12-24.

[19] Le HN, Vo NT. Modeling and analysis of an RUU delta robot using SolidWorks and SimMechanics. Int J Dyn Control. 2024;12(7):2467-2479.

[20] Do VT, Lee SG, Gwak KW. Passivity-based nonlinear control for a BallBot to balance and transfer. Int J Control Autom Syst. 2019;17:2929-2939.

[21] Wang P, Rui X, Liu F, et al. Generation mechanism and control of high-frequency vibration for tracked vehicles. Int J Mech Syst Dyn. 2023;3:146-161.

[22] Huang Y, Ding J. A multiscale differential-algebraic neural network-based method for learning dynamical systems. Int J Mech Syst Dyn. 2024;4:77-87.

[23] Do VT, Lee SG, Kim JH. Robust integral backstepping hierarchical sliding mode controller for a BallBot system. Mech Syst Signal Process. 2020;144:106866.

[24] Jespersen TK. Kugle-Modelling and Control of a Ball-balancing Robot. Master’s thesis. Aalborg University;2019.

[25] Jang H-G, Hyun C-H, Park BS. Virtual angle-based adaptive control for trajectory tracking and balancing of ball-balancing robots without velocity measurements. Int J Adapt Control Signal Process. 2023;37(8):2204-2215.

[26] Nguyen XM, Pham DB, Duong XQ, et al. Intelligent robust disturbance rejection control of a BallBot drive micromobility vehicle. IEEE Trans Intell Veh. 2024;9(2):3617-3629.

[27] Do V-T, Lee S-G. Van M. Adaptive hierarchical sliding mode control for full nonlinear dynamics of uncertain ridable BallBots under input saturation. Int J Robust Nonlinear Control. 2021;31:2882-2904.

[28] Vu DC, Pham MD, Nguyen TTH, Nguyen TVA, Nguyen TL. Time-optimal trajectory generation and observer-based hierarchical sliding mode control for BallBots with system constraints. Int J Robust Nonlinear Control. 2024;34(11):7580-7610.

[29] Navabi H, Sadeghnejad S, Ramezani S, Baltes J. Position control of the single spherical wheel mobile robot by using the fuzzy sliding mode controller. Adv Fuzzy Syst. 2017:2651976.

[30] Odry Á, Fullér R, Rudas IJ, Odry P. Fuzzy control of self-balancing robots: a control laboratory project. Comput Appl Eng Educ. 2020;28:512-535.

[31] Bhatti OS, Tariq OB, Manzar A, Khan OA. Adaptive intelligent cascade control of a ball-riding robot for optimal balancing and station-keeping. Adv Robot. 2017;32(2):63-76.

[32] Rui X, Zhang J, Wang X, Rong B, He B, Jin Z. Multibody system transfer matrix method: the past, the present, and the future. Int J Mech Syst Dyn. 2022;2:3-26.

[33] Alrasheed S. Rotation of rigid bodies. In: S Alrasheed, ed. Principles of Mechanics. Advances in Science, Technology &Innovation. Springer;2019:103-122.

[34] Jeff H. Basketball Size Chart-Recommended Sizes for Kids &Adults. Breakthrough Basketball, LLC. Accessed November 6, 2024. https://www.breakthroughbasketball.com/basketballs/size-chart.html

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2024 2024 The Author(s). International Journal of Mechanical System Dynamics published by John Wiley & Sons Australia, Ltd on behalf of Nanjing University of Science and Technology.