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Original Articles

Logarithmic control, trajectory tracking, and formation for nonholonomic vehicles on Lie group SE(2)

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Pages 204-224 | Received 23 Nov 2016, Accepted 27 Jun 2017, Published online: 13 Jul 2017

References

  • Aguiar, A. , & Hespanha, J. (2007). Trajectory-tracking and path-following of underactuated autonomous vehicles with parametric modeling uncertainty. IEEE Transactions on Automatic Control, 52 , 1362–1379.
  • Brockett, R. W. (1983). Asymptotic stability and feedback stabilization. In R. W. Brockett , R. S. Millman , & H. J. Sussmann (Eds.), Differential geometric control theory (pp. 181–191). Boston, MA: Birkhauser.
  • Bullo, F. , & Murray, R . (1995). Proportional derivative (PD) control on the Euclidean group. In Proceedings of the European Control Conference (pp. 1091–1097). Rome: EUCA.
  • Bullo, F. , & Murray, R. (1999). Tracking for fully actuated mechanical systems: A geometric framework. Automatica, 35 , 17–34.
  • Canudas de Wit, C. , & Sordalen, O. J. (1992). Exponential stabilization of mobile robots with nonholonomic constraints. IEEE Transactions on Automatic Control, 37 , 1791–1797.
  • Coelho, P. , & Nunes, U. (2003). Lie algebra application to mobile robot control: A tutorial. Robotica, 21 , 483–493.
  • Dong, R. , & Geng, Z. (2015). Formation tracking control of multivehicle systems. Asian Journal of Control, 17 , 1–7.
  • Jakubek, S. , Seyr, M. , & Novak, G. (2008). Autonomous mobile robot propioceptive navigation and predictive trajectory tracking. International Journal of Control, 81 , 989–1001.
  • Jiang, Z. P. , & Nijmeijer, H. (1997). Tracking control of mobile robots: A case study in backstepping. Automatica, 33 , 1393–1399.
  • Khalil, H. K . (2002). Nonlinear systems (3rd ed.) . Upper Saddle River, NJ: Prentice Hall.
  • Lee, T. , Leok, M. , & McClamroch, N. H . (2010). Geometric tracking control of a quadrotor UAV on SE(3). In Proceedings of the IEEE Conference on Decision and Control (pp. 5420–5425). Atlanta, GA: IEEE.
  • Liu, Y. , & Geng, Z. (2013). Finite-time optimal formation control of multi-agent systems on the Lie group SE(3). International Journal of Control, 86 (10), 1675–1686.
  • Liu, Y. , & Geng, Z. (2014). Finite-time optimal formation tracking control of vehicles in horizontal plane. Nonlinear Dynamics, 76 , 481–495.
  • Luca, A. D. , Oriolo, G. , & Vendittelli, M. (2001). Control of wheeled mobile robots: An experimental overview. In S. Nicosia , B. Siciliano , A. Bicchi , & P. Valigi (Eds.), RAMSETE - Articulated and mobile robotics for services and technologies (pp. 181–226). London: Springer-Verlag.
  • Maithripala, D. S. , & Dayawansa, W. P. (2006). Almost-global tracking of simple mechanical systems on a general class of Lie groups. IEEE Transactions on Automatic Control, 51 , 216–225.
  • Morin, P. , & Samson, C. (2009). Control of nonholonomic mobile robots based on the transverse function approach. IEEE Transactions on Robotics, 25 , 1058–1073.
  • Morin, P. , & Samson, C. (2008). Motion control of wheeled mobile robots. In B. Siciliano , & O. Khatib (Eds.), Handbook of robotics (pp. 799–826). Berlin, Heidelberg: Springer.
  • Oriolo, G. , Luca, A. D. , & Vendittelli, M. (2002). WMR control via dynamic feedback linearization: Design, implementation, and experimental validation. IEEE Transactions on Control Systems Technology, 10 , 835–852.
  • Ostrowski, J. (1999). Computing reduced equations for robotic systems with constraints and symmetries. IEEE Transactions on Robotics and Automation, 15 , 111–123.
  • Peng, X. , Geng, Z. , & Tayefi, M . (2016). Containment control based formation tracking for multi-vehicles on Lie Group. In Proceedings of the Chinese Control Conference (pp. 7751–7756). Chengdu: IEEE.
  • Panteley, E. , Lefeber, E. , Loria, A. , & Nijmeijer, H . (1998). Exponential tracking control of a mobile car using a cascaded approach. In Proceedings IFAC Workshop on Motion Control (pp. 221–226). Grenoble: IFAC.
  • Sadowskaa, A. , Broekb, T. , Huijberts, H. , Wouw, N., Kostic, D., & Nijmeijer, H. (2011). A virtual structure approach to formation control of unicycle mobile robots using mutual coupling. International Journal of Control, 84 (11), 1886–1902.
  • Shi, X. N. , Zhang, Y. A. , & Zhou, D. (2015). A geometric approach for quadrotor trajectory tracking control. International Journal of Control, 88 (11), 2217–2227.
  • Sussmann, H. J. , & Liu, W. (1993). Lie bracket extentions and averaging: The single-bracket case. In Z. Li , & J. F. Canny (Eds.), Nonholonomic motion planning (pp. 109–147). Boston, MA: Springer.
  • Tayefi, M. , Geng, Z. , & Peng, X. (2017). Coordinated tracking for multiple nonholonomic vehicles on SE(2). Nonlinear Dynamics, 87 (1), 665–675.
  • Tchon, K. , & Jakubiak, J. (2006). Extended Jacobian inverse kinematics algorithm for nonholonomic mobile robots. International Journal of Control, 79 , 895–909.

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