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Control of a planar robot in the flight phase using transverse function approach

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper deals with stabilization and tracking control problems defined with respect to a planar mechanical structure similar to Raibert’s robot. The proposed control solution is based on formal analysis of the control system on a Lie group. In order to take advantage of Lie group theory a dynamic extension of the robot kinematics is introduced. To cope with non-zero angular momentum the controller based on transverse functions is employed. Properties of the closed-loop control system are investigated based on simulations including practical stabilization at neighborhood of a constant point or a reference trajectory.
Rocznik
Strony
759--770
Opis fizyczny
Bibliogr. 36 poz., rys., wykr.
Twórcy
autor
  • Chair of Control and Systems Engineering, Poznań University of Technology, 3a Piotrowo St., 60-965 Poznań, Poland
  • Chair of Control and Systems Engineering, Poznań University of Technology, 3a Piotrowo St., 60-965 Poznań, Poland
Bibliografia
  • [1] I. Dulęba, Algorithms of Motion Planning for Nonholonomic Robots, Publishing House of Wrocław University of Technology, Wrocław, 1998.
  • [2] E. Westervelt, J. Grizzle, C. Chevallereau, J.H. Choi, and B. Morris, Feedback Control of Dynamic Bipedal Robot Locomotion, Control and Automation, CRC Press, Boca Raton, 2007.
  • [3] N. Carlesi and A. Chemori, “Nonlinear model predictive running control of kanagaroo robot: a one-leg planar underactuated hopping robot”, Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Systems (IROS) 1, 3634–3639 (2010).
  • [4] T. Rybus, T. Barciński, J. Lisowski, K. Seweryn, J. Nicolau-Kukliński, J. Grygorczuk, M. Krzewski, K. Skup, T. Szewczyk, and R. Wawrzaszek, “Experimental demonstration of singularity avoidance with trajectories based on the Bézier curves for free-floating manipulator”, Lecture Notes in Control and Inform. Sci. Robot Motion Control: Recent Developments 335, 141–146 (2013).
  • [5] X. Xin, T. Mita, and M. Kaneda, “The posture control of a two-link free flying acrobot with initial angular momentum”, IEEE Trans. Autom. Control 49 (7), 1201–1206 (2004).
  • [6] J. Grizzle, C. Moog, and C. Chevallereau, “Nonlinear control of mechanical systems with an unactuated cyclic variable”, IEEE Trans. Autom. Control 50 (5), 559–576 (2005).
  • [7] F. Rehman and H. Michalska, “Geometric approach to feedback stabilization of a hopping robot in the flight phase”, Proc. Int. Conf. Advanced Robotics (ICAR) 1, 551–556 (1997).
  • [8] M. Raibert, H. Brown, and M. Chepponis, “Experiments in balance with a 3D one-legged hopping machine”, Int. J. Robot. Res. 3 (2), 75–92 (1984).
  • [9] P. Morin and C. Samson, “A characterization of the Lie Algebra Rank Condition by transverse periodic functions”, SIAM J. Control Optim. 40 (4), 1227–1249 (2001).
  • [10] P. Morin and C. Samson, “Control of nonholonomic mobile robots based on the transverse function approach”, IEEE Trans. Robot. 25 (5), 1058–1073 (2009).
  • [11] P. Morin and C. Samson, “Transverse function control of a class of non-invariant driftless systems, application to vehicles with trailers”, Proc. 47th IEEE Conf. on Decision and Control (CDC) 1, 4312–4319 (2008).
  • [12] D. Pazderski, K. Kozłowski, and D.K. Waśkowicz, “Control of a unicycle-like robot with trailers using transverse function approach”, Bull. Pol. Ac.: Tech. 60 (3), 537–546 (2012).
  • [13] P. Morin and C. Samson, “Stabilization of trajectories for systems on Lie groups. Application to the rolling sphere”, Proc. 17th IFAC World Congress 1, 508–513 (2008).
  • [14] W. Magiera, “Nonsymetric trident snake: the transverse function approach”, Robotics Advances 1, 451–460 (2012), (in Polish).
  • [15] D. Lizárraga, P. Morin, and C. Samson, “Non-robustness of continuous homogeneous stabilizers for affine control systems”, Proc. Conf. on Decision and Control (CDC) 1, 855–860 (1999).
  • [16] Z.-P. Jiang, “Robust exponential regulation of nonholonomic systems with uncertainties”, Automatica 36 (2), 189–209 (2000).
  • [17] D. Pazderski, B. Krysiak, and K. Kozłowski, “A comparison study of discontinuous control algorithms for three-link nonholonomic manipulator”, Lecture Notes in Control and Inform. Sci. Robot Motion Control: Recent Developments 1, 35–44 (2012).
  • [18] U. Libal and J. Płaskonka, “Noise sensitivity of selected kinematic path following controllers for a unicycle”, Bull. Pol. Ac.: Tech. 62 (1), 3–13 (2014).
  • [19] B. Jakubczyk and W. Respondek, “On linearization of control systems”, Bull. Pol. Ac.: Math. 28, 517–522 (1980).
  • [20] R.W. Brockett, “Asymptotic stability and feedback stabilization”, in Differential Geometric Control Theory, pp. 181–191, Birkhäuser, Boston, 1983.
  • [21] H. Nijmeijer and A. van der Schaft, Nonlinear Dynamical Control Systems, Springer, Berlin, 1990.
  • [22] H. Hermes, “Nilpotent and high-order approximations of vector field systems”, SIAM Rev. 33 (2), 238–264 (1991).
  • [23] R. Murray, S. Sastry, and L. Zexiang, A Mathematical Introduction to Robotic Manipulation, CRC Press, Inc., Boca Raton, 1994.
  • [24] K. Tchoń, “Differential topology of the inverse kinematic problem for redundant robot manipulators”, Int. J. Robot. Res. 10 (5), 492–504 (1991).
  • [25] J. Selig, Geometric Fundamentals of Robotics, Monographs in Computer Science, Springer, Berlin, 2005.
  • [26] C. de Wit, G. Bastin, and B. Siciliano, Theory of Robot Control, Springer-Verlag, New York, 1996.
  • [27] A.M. Bloch, Nonholonomic Mechanics and Control, Systems and Control, Springer, New York, 2003.
  • [28] J. Hilgert and K. Neeb, Structure and Geometry of Lie Groups, Springer, London, 2012.
  • [29] A. Isidori, Nonlinear Control Systems, Springer-Verlag, New York, 1995.
  • [30] I. Dulęba, “Impact of control representations on efficiency of local nonholonomic motion planning”, Bull. Pol. Ac.: Tech. 59 (2), 213–218 (2011).
  • [31] G. Blankenship and H. Kwatny, Nonlinear Control and Analytical Mechanics: a Computational Approach, Control engineering, Birkhäuser, Boston, 2000.
  • [32] P. Morin and C. Samson, “Practical stabilization of driftless systems on Lie groups: the transverse function approach”, IEEE Trans. Autom. Control 48 (9), 1496–1508 (2003).
  • [33] M. Vendittelli, G. Oriolo, F. Jean, and J.-P. Laumond, “Nonhomogeneous nilpotent approximations for nonholonomic systems with singularities”, IEEE Trans. Automat. Control 49 (2), 261–266 (2004).
  • [34] P. Morin and C. Samson, “Trajectory tracking for nonholonomic systems. Theoretical background and applications”, Rapport de Recherche RR-6464, CD-ROM (2008).
  • [35] P. Morin and C. Samson, “Practical stabilization of driftless homogeneous systems based on the use of transverse periodic functions”, Proc. 40th IEEE Conf. Decision and Control (CDC) 1, 1761–1766 (2001).
  • [36] D. Pazderski, D.K. Waśkowicz, and K. Kozłowski, “Motion control of vehicles with trailers using transverse function approach”, Int. J. Intell. Syst. 77 (3–4), 457–479 (2015).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-99d25f67-a8a4-4cbb-934d-9fecfbfc075c
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