The Use of the Limit Cycles of Dynamic Systems for Formation of Program Trajectories of Points Feet of the Anthropomorphous Robot
The movement of points feet of the anthropomorphous robot in space occurs along some stable trajectory of a known form. A large number of modifications to the methods of control of biped robots indicate the fundamental complexity of the problem of stability of the program trajectory and, consequently, the stability of the control for the deviation for this trajectory. Existing gait generators use piecewise interpolation of program trajectories. This leads to jumps in the acceleration at the boundaries of sites. Another interpolation can be realized using differential equations with fractional derivatives. In work, the approach to synthesis of generators of program trajectories is considered. The resulting system of nonlinear differential equations describes a smooth trajectory of movement having rectilinear sites. The method is based on the theory of an asymptotic stability of invariant sets. The stability of such systems in the area of localization of oscillatory processes is investigated. The boundary of the area is a bounded closed surface. In the corresponding subspaces of the oscillatory circuits, the resulting stable limit cycles are curves having rectilinear sites. The solution of the problem is carried out by means of synthesis of a set of the continuous smooth controls with feedback. The necessary geometry of closed trajectories of movement is obtained due to the introduction of high-order nonlinearities in the control of stabilization systems. The offered method was used for the generation of trajectories of movement of point’s feet of the anthropomorphous robot. The synthesis of the robot's program movement was carried out by means of the inverse method.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1131860Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF
 Andrievskii B. R., Guzenko P. Yu., Fradkov A. L., “Control of Nonlinear Oscillation in Mechanic Systems by the Steepest Gradient Method”, Avtomat. i Telemekh., 1996, no. 4, 4–17
 Gorobtsov A.S., Grigoryeva O.E., Ryzhov E.N. Attracting ellipsoids and synthesis of oscillatory regimes. Automation and Remote Control, 2009, no. 8, p. 40 – 48.
 Gorobtsov A. Lame - manifolds in problems of synthesis of nonlinear oscillatory modes / Gorobtsov A., Ryzhov E., Churzina A. // JVE. Journal of Vibroengineering, Vol. 10, Issue 4, 2008, p. 456–459.
 Gorobtsov A. Principals of Multilinked Nonlinear Stabilization and Lame-Manifolds in Dynamic Systems / Gorobtsov A., Ryzhov E., Churzina A. // Rare Attractors and Rare Phenomena in Nonlinear Dynamics: mater. of the Int. Symposium RA08, Riga–Jurmala (Latvia), 8–12 September 2008 / Riga Techn. Univ., Inst. of Mechanics RTU (etc.). – Riga, 2008, p. 29-32.
 Gorobtsov A.S., Ryzhov E.N. Analytical synthesis of generators of self-oscillations on two oscillatory links//Automatics and telemechanics. − 2007. − № 6. p.35–44.
 Lyapunov A.M. The General problem of movement stability. – M.: Gostekhizdat, 1950 − 472 p.
 Zubov V.I. Stability of movement− М: The Higher school, 1973 − 272 p.
 Gorobtsov A.S., Ryzhov E. N., Churzina A.S. Detecting of Oscillations Close to Explosive. Biomedical Radioelectronics, 2009, no. 8, p. 32-34.
 Gorobtsov A. About formation of the stable modes of the movement of multilink mechanical systems / Gorobtsov A., Ryzhov E., Polyanina A. // Vibroengineering Procedia. Vol. 8: proc. of 22nd International Conference on Vibroengineering (Moscow, Russia, 4-7 October 2016) / Publisher JVE International Ltd. - Kaunas (Lithuania), 2016. - P. 522-526.
 Polyanina A.S. Problem of synthesis of the self-oscillatory modes in multivariate dynamic systems. International journal of applied and fundamental research, 2015, no. 12-4, p. 618-621.
 Gorobtsov A.S., Ryzhov E.N., Polyanina A.S. Calculation of the parameters of synthesis of oscillations with multi-channel stabilization (Proc. Xth all-Russian scientific conference of Yu. I. Neymark "Nonlinear oscillations of mechanical systems"), Nizhny Novgorod, 2016, p. 268-273.
 Gorobtsov A. Theoretically Investigations of the Control Movement of the CLAWAR at Statically Unstable Regimes. Walking and Climbing robots. Vienna, Austria, 2007, p. 95 – 106.
 Fumagalli, A., Gaias, G., Masarati, P.: A simple approach to kinematic inversion of redundant mechanisms. In: IDETC/CIE 2007 ASME 2007 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Las Vegas, NE, USA, 4–7 September 2007
 Shabana, A.A.: Dynamics of Multibody Systems, 3rd edn. Cambridge University, New York (2005)
 Cristina P. Santos, Nuno Alves, Juan C. Moreno.: Biped Locomotion Control through a Biomimetic CPG-based Controller. Nonlinear Dyn (2010) 62: 27–37.