Impact of control representations on efficiency of local nonholonomic motion planning

• Autorzy: Duleba I.
• Języki publikacji: EN

Abstrakty

EN

In this paper various control representations selected from a family of harmonic controls were examined for the task of locally optimal motion planning of nonholonomic systems. To avoid dependence of results either on a particular system or a current point in a state space, considerations were carried out in a sub-space of a formal Lie algebra associated with a family of controlled systems. Analytical and simulation results are presented for two inputs and three dimensional state space and some hints for higher dimensional state spaces were given. Results of the paper are important for designers of motion planning algorithms not only to preserve controllability of the systems but also to optimize their motion.

Słowa kluczowe

EN

motion planning; nonholonomic systems; Lie-algebraic methods; controllability; optimization

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2011
• Tom: Vol. 59, nr 2
• Strony: 213--218
• Opis fizyczny: Bibliogr. 15 poz., rys., tab.

Twórcy

autor

Duleba I.

• Institute of Computer Engineering, Control and Robotics, Wroclaw University of Technology, 11/17 Janiszewski St., 50-372 Wroclaw, Poland,

Bibliografia

• [1] J. Szrek and P. Wójtowicz, “Idea of wheel-legged robot and its control system”, Bull. Pol. Ac.: Tech. 58 (1), 43–50 (2010).
• [2] I. Duleba, Algorithms of Motion Planning for Nonholonomic Robots, Wroclaw Univ. Publ. House, Wrocław, 1998.
• [3] D.B. Reister and F.G. Pin, “Time-optimal trajectories for mobile robots with two independently driven wheels”, Int. J. Robotics Research 13 (1), 38–54 (1991).
• [4] C. Fernandez, L. Gurvits, and Z.X. Li, “A variational approach to optimal nonholonomic motion planning”, Proc. IEEE Conf. Robotics and Automat.1, 680–685 (1991).
• [5] S. LaValle, Planning Algorithms, Cambridge Univ. Press, Cambridge, 2006.
• [6] C. Zieliński and T. Winiarski, “General specification of multirobot control system structures”, Bull. Pol. Ac.: Tech. 58 (1), 15–28 (2010).
• [7] K. Tchon and J. Jakubiak, “Endogenous configuration space approach to mobile manipulators: a derivation and performance assessment of jacobian inverse kinematics algorithms”, Int. J. Control 26 (14), 1387–1419 (2003).
• [8] J-P. Serre, Lie Algebras and Lie Groups, Springer, Berlin, 1964.
• [9] W.L. Chow, “uber Systeme von linearen partiellen Differentialgleichungen erster Ordnung”, Math. Annallen 117 (1), 98–105 (1939).
• [10] R.S. Strichartz, “The Campbell-Baker-Hausdorff-Dynkin formula and solutions of differential equations”, J. Funct. Analysis 72 (2), 320–345 (1987).
• [11] I. Duleba, “Pre-control form of the generalized Campbell-Baker-Hausdorff-Dynkin formula for affine nonholonomic systems”, Systems & Control Letters 55 (2), 146–157 (2006).
• [12] M. Spong and M. Vidyasagar, Robot Dynamics and Control, MIT Press, Cambridge, 1989.
• [13] A. Belaiche, F. Jean, and J.J. Risler, “Geometry of nonholonomic systems”, Robot Motion Planning and Control, Lecture Notes in Control and Information Sciences 229, 55–92 (1993).
• [14] D.P. Bertsekas, Constrained Optimization and Lagrange Multiplier Methods, Athena Scientific, Nashua, 1999.
• [15] Y. Nakamura, Advanced Robotics: Redundancy and Optimization, Addison Wesley, New York, 1991.