Automatic Stabilization of a Riderless Bicycle using the Active Disturbance Rejection Control Approach

[ES] Este trabajo propone una estrategia de Control por Rechazo Activo de Perturbaciones (ADRC), usando observadores extendidos de perturbación, para estabilizar una bicicleta en movimiento, sin conductor y con una velocidad de avance variable. Aunque la bicicleta tiene una dinámica inestable y no lineal alrededor de su posición vertical, que puede modelarse como un sistema Lineal de Parámetros Variantes (LPV) dependientes de la velocidad, el diseño del controlador usa un modelo simplificado de parámetros concentrados invariantes en el tiempo y una velocidad nominal constante. El esquema ADRC agrupa las discrepancias entre el modelo simplificado y la planta, junto con las perturbaciones externas en una señal aditiva unificada, que es estimada a través del observador y realimentada mediante una ley de control lineal para rechazarla. La efectividad de la estrategia es validada mediante una co-simulación entre ADAMS y MATLAB, la cual exhibe un alto desempeño y robustez sobre un modelo dinámico virtual de la bicicleta, sometida a perturbaciones externas severas y variaciones de parámetros.[EN] This work proposes an ADRC (Active Disturbance Rejection Control) strategy by disturbance extended observers to stabilize a moving riderless bicycle with a variant forward speed. Although the bicycle has an unstable and non-linear dynamics when in its upright position, which can be modeled as a LPV (Linear-Parameter-Varying) system that depends on the forward speed, a simplified time-invariant and lumped-parameter model, with an nominal constant forward speed is used in the controller design. ADRC scheme groups discrepancies between the simplified model and the plant, with external disturbances into an equivalent additive unified disturbance signal at input, which is estimated via the observer and rejected through a linear control law. The effectiveness of this strategy is validated by a co-simulation between ADAMS and MATLAB, which exhibits a high performance and robustness in a virtual dynamic model of the bicycle, submitted to severe external disturbances and parameter variations. Baquero-Suárez, M.; Cortes-Romero, J.; Arcos-Legarda, J.; Coral-Enriquez, H. (2017). Estabilización Automática de una Bicicleta sin Conductor mediante el Enfoque de Control por Rechazo Activo de Perturbaciones. Revista Iberoamericana de Automática e Informática industrial. 15(1):86-100. https://doi.org/10.4995/riai.2017.8832OJS86100151Ai-Buraiki, O., Thabit, M. B., Jun 2014. Model Predictive Control Design Approach for Autonomous Bicycle Kinematics Stabilization. In: 22nd Mediterranean Conference of Control and Automation (MED). pp. 380-383. https://doi.org/10.1109/MED.2014.6961401Bickford, D., Davison, D. E., May 2013. Systematic Multi-Loop Control for Autonomous Bicycle Path following. In: 2013 26th IEEE Canadian Conference on Electrical and Computer Engineering (CCECE). pp. 1-5. https://doi.org/10.1109/CCECE.2013.6567714Brizuela, J., Astorga, C., Zavala, A., Pattalochi, L., Canales, F., Dec 2016. State and Actuator Fault Estimation Observer Design Integrated in a Riderless Bicycle Stabilization System. fISAg Transactions 61, 199-210.Canudas deWit, C., Tsiotras, P., 1999. Dynamic Tire Friction Models for Vehicle Traction Control. In: Proceedings of the 38th IEEE Conference on Decision and Control. Vol. 4. pp. 3746-3751. https://doi.org/10.1109/CDC.1999.827937Cerone, V., Andreo, D., Larsson, M., Regruto, D., Oct 2010. Stabilization of a Riderless Bicycle, A Linear-Parameter-Varying Approach [applications of control]. Control Systems, IEEE 30 (5), 23-32. https://doi.org/10.1109/MCS.2010.937745Cortés Romero, J., Luviano Juárez, A., Álvarez Salas, R., Sira Ramírez, H., Aug 2010. Fast Identification and Control of an Uncertain Brushless DC Motor Using Algebraic Methods. In: 12th International Power Electronics Congress (CIEP). pp. 9-14. https://doi.org/10.1109/CIEP.2010.5598844Cortés Romero, J., Ramos, G., Coral Enriquez, H., Aug 2014. Generalized Proportional Integral Control for Periodic Signals under Active Disturbance Rejection Approach. ISA Transactions 53 (6), 1901-1909. https://doi.org/10.1016/j.isatra.2014.07.001Emaru, T., Tsuchiya, T., Dec 2005. Research on Estimating Smoothed Value and Differential Value by using Sliding Mode System. IEEE Transactions on Robotics and Automation 21 (6), 391-402.Gao, B., Junpeng Shao, Xiaodong Yang, Nov 2014. A Compound Control Strategy Combining Velocity Compensation with ADRC of Electroydraulic Position Servo Control System. ISA Transactions 53 (6), 1910-1918. https://doi.org/10.1016/j.isatra.2014.06.011Goldstein, H., 1953. Classical Mechanics, 3rd Edition. Addison-Wesley, Ch. 5, pp. 184-188.Gordon Wilson, D., Jim Papadopoulos, 2004. Bicycling Science, 3rd Edition. The MIT Press, Ch. 8, pp. 263-310.Hwang, C.-L., Hsiu-Ming Wu, Shih, C.-L., May 2009. Fuzzy Sliding Mode Underactuated Control for Autonomous Dynamic Balance of an Electrical Bicycle. IEEE Transactions on Control Systems Technology 17 (3), 658-670. https://doi.org/10.1109/TCST.2008.2004349Jin, H., Yang, D., Liu, Z., Zang, X., Li, G., Zhu, Y., Dec 2015. A Gyroscope-Based Inverted Pendulum with Application to Posture Stabilization of Bicycle Vehicle. In: 2015 IEEE International Conference on Robotics and Biomimetics (ROBIO). pp. 2103-2108. https://doi.org/10.1109/ROBIO.2015.7419084Kooijman, J. D. G., Meijaard, J. P., Papadopoulos, J. M., Ruina, A., Schwab, A. L., 2011. A Bicycle can be Self-Stable without Gyroscopic or Caster Effects. Science 332 (6027), 339-342. https://doi.org/10.1126/science.1201959Kooijman, J. D. G., Schwab, A. L., Meijaard, J. P., May 2008. Experimental Validation of a Model for the Motion of an Uncontrolled Bicycle. Multibody System Dynamics 19 (1), 115-132. https://doi.org/10.1007/s11044-007-9050-xLam, P. Y., Sep 2011. Gyroscopic Stabilization of a Kid-Size Bicycle. In: 2011 IEEE 5th International Conference on Cybernetics and Intelligent Systems (CIS). pp. 247-252. https://doi.org/10.1109/ICCIS.2011.6070336Lewis, F. L., Popa, L. X. D., 2008. Optimal and Robust Estimation, with an Introduction to Stochastic Control Theory, 2nd Edition. CRC Press, Ch. 3, pp. 151-204.Limebeer, D. J. N., Sharp, R. S., Oct 2006. Bicycles, Motorcycles, and Models. IEEE Control Systems 26 (5), 34-61. https://doi.org/10.1109/MCS.2006.1700044Meijaard, J., Papadopoulos, J. M., Ruina, A., Schwab, A., 2007. Linearized Dynamics Equations for the Balance and Steer of a Bicycle: a Benchmark and Review. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 463 (2084), 1955-1982. https://doi.org/10.1098/rspa.2007.1857Michini, B., Sean Torrez, 2007. Autonomous Stability Control of a Moving Bicycle. Tech. rep., Massachusetts Institute of Technology, USA, 77 Massachusetts Ave, Rm 33-336 - Cambridge MA 02139.Neimark, J. I., N. A. Fufaev, 2004. Translations of Mathematical Monographs. In: Dynamics of Nonholonomic Systems. Vol. 33. American Mathematical Society, Ch. 6, pp. 330-373.Nenner, U., Linker, R., Gutman, P.-O., 2010. Robust Feedback Stabilization of an Unmanned Motorcycle. Control Engineering Practice 18 (8), 970-978. https://doi.org/10.1016/j.conengprac.2010.04.003Papadopoulos, J. M., 1987. Bicycle Steering Dynamics and Self-stability: A Summary Report on Work in Progress. Cornell bicycle research project, Cornell University, Ithaca, NY.Schwab, A., Meijaard, J., Papadopoulos, J., 2005a. Benchmark Results on the Linearized Equations of Motion of an Uncontrolled Bicycle. Journal of Mechanical Science and Technology 19 (1), 292-304. https://doi.org/10.1007/BF02916147Schwab, A. L., J. P. Meijaard, Papadopoulos, J. M., Aug 2005b. A Multibody Dynamics Benchmark on the Equations of Motion of an Uncontrolled Bicycle. In: Proceedings of the Fifth EUROMECH Nonlinear Dynamics Conference. pp. 511-521.Schwab, A. L., Meijaard, J. P., May 2013. A Review on Bicycle Dynamics and Rider Control. Vehicle System Dynamics 51 (7), 1059-1090. https://doi.org/10.1080/00423114.2013.793365Schwab, A. L., Meijaard, J. P., Kooijman, J. D. G., Aug 2012. Lateral Dynamics of a Bicycle with a Passive Rider Model: Stability and Controllability. Vehicle System Dynamics 50 (8), 1209-1224. https://doi.org/10.1080/00423114.2011.610898Srivastava, S., Pandit, V., 2016. A PI/PID Controller for Time Delay Systems with Desired Closed Loop Time Response and Guaranteed Gain and Phase Margins. Journal of Process Control 37, 70-77. https://doi.org/10.1016/j.jprocont.2015.11.001Åström, K. J., Hägglund, T., 1995. PID Controllers: Theory, Design, and Tuning, 2nd Edition. ISA, Ch. 3, pp. 80-92.Åström, K. J., Klein, R. E., Lennartsson, A., Aug 2005. Bicycle Dynamics and Control: Adapted Bicycles for Education and Research. IEEE Control Systems 25 (4), 26-47. https://doi.org/10.1109/MCS.2005.1499389Su, Y. X., Zheng, C. H., Dong Sun, Duan, B. Y., Aug 2005. A Simple Nonlinear Velocity Estimator for High-Performance Motion Control. IEEE Transactions on Industrial Electronics 52 (4), 1161-1169. https://doi.org/10.1109/TIE.2005.851598Sun, B., Zhiqiang Gao, Oct 2005. A DSP-based Active Disturbance Rejection Control Design for a 1-Kw H-bridge DC-DC Power Converter. IEEE Transactions on Industrial Electronics 52 (5), 1271-1277. https://doi.org/10.1109/TIE.2005.855679Tanelli, M., Schiavo, F., Savaresi, S. M., Ferretti, G., Oct 2006. Object-Oriented Multibody Motorcycle Modelling for Control Systems Prototyping. In: IEEE International Conference on Control Applications. pp. 2695-2700.Whipple, F., 1899. The Stability of the Motion of a Bicycle. Quart. J. Pure Appl. Math. 30 (120), 312-348.Yuanyuan, F., Runjia, D., Yuping, X., 2017. Steering Angle Balance Control Method for Rider-Less Bicycle Based on ADAMS. Springer Singapore, Singapore, Ch. 1, pp. 15-31