Trajectory reproduction and trajectory tracking problem for the nonholonomic systems

• Autorzy: Ratajczak A.

Identyfikatory

DOI

10.1515/bpasts-2016-0008

• Języki publikacji: EN

Abstrakty

EN

This paper introduces a new algorithm of trajectory reproduction and trajectory tracking for nonholonomic systems. The endogenous configuration space approach is employed as a guideline in the algorithm derivation. The derivation uses a trajectory reproduction error, which is an integral of the difference between the resultant trajectory and the desired trajectory over the motion horizon. Such a definition of the error allows to solve both the trajectory reproduction as well as the trajectory tracking problem. Considerable attention in the paper has been paid to the implementation aspects of the algorithm. The nonparametric approach is used together with a higher order of the integration method. The algorithm efficiency is illustrated with computer simulations accomplished for two nonholonomic systems: the dynamics of the double pendulum with a passive joint, and the kinematics of the unicycle.

Słowa kluczowe

EN

trajectory reproduction; trajectory tracking; nonholonomic system

PL

nieholonomiczny układ; śledzenie trajektorii

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2016
• Tom: Vol. 64, nr 1
• Strony: 63--70
• Opis fizyczny: Bibliogr. 20 poz., wykr.

Twórcy

autor

Ratajczak A.

• Department of Control Systems and Mechatronics, Wrocław University of Technology, 11/17 Janiszewski St., 50-372 Wroclaw, Poland

Bibliografia

• [1] S.M. LaValle, Planning Algorithms, Cambridge University, Cambridge, 2006.
• [2] R.W. Brockett and M.D. Mesarewić, “The reproducibility of multivariable systems”, J. Math. Anal. Appl. 11, 548-563 (1965).
• [3] W. Respondek, “Right and left invertibility of nonlinear control systems”, in ed. H. J. Sussmann, Non-linear Controllability and Optimal Control, Marcel Dekker, New York, 1990.
• [4] G. Walsh, D. Tilbury, S. Sastry, R. Murray, and J.P. Laumond, “Stabilization of trajectories for systems with nonholonomic constraints”, IEEE Trans. Autom. Control 39 (1), 216-222 (1994).
• [5] W. Kowalczyk, M. Michałek, and K. Kozłowski, “Trajectory tracking control with obstacle avoidance capability for unicycle-like mobile robot”, Bull. Pol. Ac.: Tech. 60 (3), 537-546 (2012).
• [6] J. Karpińska and K. Tchoń, “Continuation method approach to trajectory planning in robotic systems”, 16th Int. Conf. Methods and Models in Automation and Robotics, MMAR 2011, 51-56 (2011).
• [7] P. Morin and C. Samson, “Trajectory tracking for nonholonomic vehicles”, ed. K. Kozłowski, Robot Motion and Control, Lecture Notes in Control and Information Sciences, vol. 335, pp. 3-23, Springer, London, 2006.
• [8] P. Morin and C. Samson, “Trajectory tracking for nonholonomic systems. Theoretical background and applications”, Research Report RR-6464, CD-ROM (2008).
• [9] D. Pazderski and K. Kozłowski, “Motion control of a skidsteering robot using transverse function approach - experimental evaluation”, in 10th Int. Workshop on Robot Motion and Control, RoMoCo 2015, 72-77 (2015).
• [10] D. Chaos, R. Muñoz-Mansilla, D. Moreno-Salinas, and J. Aranda, “Nonlinear control for trajectory tracking of a nonholonomic rc-hovercraft with discrete inputs”, Mathematical Problems in Engineering 2013, ID 589267 (2013).
• [11] K. Tchoń and J. Jakubiak, “Endogenous configuration space approach to mobile manipulators: a derivation and performance assessment of Jacobian inverse kinematics algorithms”, Int. J. Control 76 (14), 1387-1419 (2003).
• [12] K. Tchoń and J. Jakubiak, “Simple algorithm for solving the continous inverse kinematics problem for stationary and mobile robots”, ed. K. Tchoń, Advances in Robotics, pp. 275-282, WKŁ, Warsaw, 2005, (in Polish).
• [13] D. Paszuk, K. Tchoń, and Z. Pietrowska, “Motion planning of the trident snake robot equipped with passive or active wheels”, Bull. Pol. Ac.: Tech. 60 (3), 547-555 (2012).
• [14] E.D. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems, Springer, New York, 1998.
• [15] K. Tchoń, “Continuation method in robotics”, 7th Conf. Computer Methods and Systems 1, 17-24 (2007).
• [16] A. Ratajczak and K. Tchoń, “Multiple-task motion planning of non-holonomic systems with dynamics”, Mech-Sci 4 (1), 153-166 (2013).
• [17] A. Ratajczak and K. Tchoń, “Parametric and non-parametric Jacobian motion planning for non-holonomic robotic systems”, J. Intell. Robot. Syst. 1, 1-12 (2013).
• [18] A. Ratajczak, “Output trajectory reproduction in nonholonomic systems”, eds. K. Tchoń and C. Zieliński, Advances in Robotics, vol. 2, pp. 671-680, OWPW, Warsaw, 2014.
• [19] I. Fantoni and R. Lozano, Non-linear Control for Underactuated Mechanical Systems, Springer, London, 2002.
• [20] M.W. Spong, “Underactuated mechanical systems”, ed. K.P. Valavanis, Control Problems in Robotics and Automation, Springer, London, 1998.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.