Proceedings of COBEM 2007 19th International Congress of Mechanical Engineering Copyright © 2007 by ABCM November 5-9, 2007, Brasília, DF MODELING THE CENTRAL PATTERN GENERATOR OF HUMAN LOCOMOTION USING NONLINEAR OSCILLATORS Armando Carlos de Pina Filho, pina-filho@deg.ee.ufrj.br Department of Graphic Designing, Polytechnic School, Universidade Federal do Rio de Janeiro, Technology Center, bloco D, sala D-101, 21949-900, Ilha do Fundão, Rio de Janeiro - RJ, Brazil. Max Suell Dutra, max@mecanica.coppe.ufrj.br COPPE/PEM - Mechanical Engineering Program, Universidade Federal do Rio de Janeiro, Technology Center, P.O.Box 68503, 21945-970, Ilha do Fundão, Rio de Janeiro - RJ, Brazil. Abstract. Nervous nets in the spinal marrow are capable to produce rhythmic movements, such as: the locomotion. These specialized systems are known as nervous oscillators or central pattern generators (CPGs). Oscillators can be used as pattern generators similar to the human CPG; such oscillators obtain the approximate trajectories of the legs. The objective of this work is to present the modeling of the human CPG using a set of nonlinear oscillators. We consider a 2D model, with the three most important determinants of gait, that performs motions parallel to the sagittal plane. Using oscillators such as: van der Pol and Rayleigh oscillators, we determine the transient motion and the stable limit cycles of the oscillators, showing the behavior of the hip and knee angles. By changing a few parameters in the oscillators, modification of the step length and the frequency of the gait can be obtained. A comparison of the plotted graphs reveals that the system provides excellent results when compared to experimental analyses. Based on this results, we conclude that the use of coupled nonlinear oscillators can represent an excellent method for signal generation, allowing their application for simulate the CPG in a walking machine. Keywords: CPG, oscillator, locomotion. 1. INTRODUCTION Nervous nets in the spinal marrow are capable to produce rhythmic movements, such as: to swim, to jump, and to walk, when isolated from the brain and sensorial inputs. These specialized nervous systems are known as nervous oscillators or central pattern generators (CPGs)(Mackay-Lyons, 2002). According to Moraes (1999), the relation between spinal marrow and encephalus in domestic animals is most significant than relation in human beings. The animals perform motor activities by reflexes and not by the cerebral activity. It is estimated that exist approximately ten times more activity in the spinal marrow of dogs than in humans. Grillner (1985), Pearson (1993) and Collins and Richmond (1994) are some interesting works about the locomotion of vertebrates controlled by central pattern generators. The human locomotion is controlled, in a way, by a CPG, which is evidenced in works as Calancie et al. (1994) and Dimitrijevic et al. (1998). Nonlinear oscillators can be used in control systems of locomotion as pattern generators, providing approximate trajectories for the legs. The CPG is formed by a set of oscillators, where each oscillator generates angular signals of reference for the movement of the legs. Each oscillator has its proper amplitude, frequency and parameters, and coupling terms makes the linking to the other oscillators. Bay and Hemami (1987), Dutra (1995), Zielinska (1996), and Pina Filho (2005) are some works about CPG formed by oscillators, applied in the locomotion. The objective of this work is to present the modeling of a central pattern generator formed by a set of coupled nonlinear oscillators, applying this system to a bipedal robot model. We present some concepts about the spinal marrow of human being, including its main structures and characteristics, as well as its relation with the motor functions. In the application, we consider a 2D model, with the three most important determinants of gait (the compass gait, the knee flexion, and the plantar flexion of stance ankle), that performs motions parallel to the sagittal plane. Using nonlinear oscillators with integer relation of frequency, we determine the transient motion and the stable limit cycles of the network formed by coupled oscillators, showing the behavior of the hip and knee angles. By changing a few parameters in the oscillators, modification of the step length and the frequency of the gait can be obtained. The study of the utilization of this system in the locomotion has great application in the project of autonomous robots and in the rehabilitation technology, not only in the project of prosthesis and orthesis, but also in the searching of procedures that help to recuperate motor functions of human beings. 2. SPINAL MARROW The spinal marrow is formed by nerves from the cerebral cortex or in some areas of the cerebral trunk, and prolonged, in great part, to the somatic motoneurons (which make connection with the muscles that performing the conscientious movements). The bones of the spinal column protect the spinal marrow, and its nervous fibers pass through small gaps between each vertebra. In the superior vertebrates, the spinal marrow is more strong subordinated to the cerebrum, executing its orders.