Abstract
This paper presents the synthesis of a control system for a biped, walking dynamic robot. Such control system should provide the stable walking [3]. In this paper, stability is defined as limited deviations of speed and coordinates of the center of gravity of the robot from its required values at the end of each step. The control system has a feedback containing “the ideal mechanism” [16]. The equations of the ideal mechanism enable to define the time and place of putting down the feet at the end of each step, on the basis of the general requirements of walking. An ideal mechanism should be similar to the object of control [2, 7]. In this case, such ideal mechanism is the turned spatial mathematical pendulum. To check the described control system, as a physical model of the object of control employs a solid body on two weightless feet [4, 10]. For stable walking, it is convenient to develop algorithms that define the coordinates and speed of the center of gravity at the end of a step. In this paper the limitation of a general member of the sequence of coordinates and speed is investigated on the simple examples of walking [14], and the operation of the control system of the mentioned physical model is illustrated.
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References
Borina A, Tereshin V (2015) Control of biped walking robot using equations. In: Advances in mechanical engineering, lecture notes in mechanical engineering. Springer, Switzerland, pp 23–31
Borina AP, Tereshin VA (2013) Problem of spatial movement of dynamic walking device. In: Modern mechanical engineering, science and education, Saint-Petersburg, pp 631–641
Borina AP, Tereshin VA (2014) Even movement of humanoid robot. In: Modern mechanical engineering, science and education, Saint-Petersburg, pp 160–162
Borina AP, Tereshin VA (2012) Spatial movement of walking device under the influence of operating force from a foot. Modern mechanical engineering, science and education, Saint-Petersburg, pp 177–188
Brogliato B (2003) Some perspectives on the analysis and control of complementarity-systems. IEEE Trans Autom Control 48(6):918–935
Brogliato B, Niculescu SI, Monteiro-Marques M (2000) On the tracking control of a class of complementarity-slackness hybrid mechanical systems. Syst Control Lett 39:255–266
Brogliato B, ten Dam AA, Paoli L, Genot F, Abadie M (2002) Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. ASME Appl Mech Rev 55:107–150
Chevallereau C (2003) Time-scaling control of an underactuated biped robot. IEEE Trans Robot Autom 19(2):362–368
Chevallereau C, Aoustin Y (2001) Optimal reference trajectories for walking and running of a biped robot. Robotica 19:557–569
Collins S, Wisse M, Ruina A (2001) 3-d passive dynamic walking robot with two legs and knees. Int J Robot Res 20(7):607–615
Dankowicz H, Adolfsson J, Nordmark A (2001) 3D passive walkers: finding periodic gaits in the presence of discontinuities. Nonlinear Dyn 24:205–229
Das SL, Chatterjee A (2002) An alternative stability analysis technique for the simplest walker. Nonlinear Dyn 28(3):273–284
Gienger M, Loffer K, Pfeiffer F (2003) Practical aspects of biped locomotion. In: Siciliano B, Dario P (eds) Experimental robotics. Springer, Berlin, Heidelberg, pp 95–104
Kar DC, Kurien IK, Jayarajan K (2003) Gaits and energetics in terrestrial legged locomotion. Mech Mach Theory 38:355–366
Lum HK, Zribi M, Soh YC (1999) Planning and control of a biped robot. Int J Eng Sci 37:1319–1349
Pervozvansky AA (2010) Course of automatic control theory. LAN, Saint-Petersburg
Saidouni T, Bessonnet G (2003) Generating globally optimised sagittal gait cycles of a biped robot. Robotica 21:199–210
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Borina, A., Tereshin, V. (2017). Stability of Walking Algorithms. In: Evgrafov, A. (eds) Advances in Mechanical Engineering. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-53363-6_3
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DOI: https://doi.org/10.1007/978-3-319-53363-6_3
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