Modelling of Bipedal Robots Using Coupled Nonlinear Oscillators

The first indications that the spinal marrow could contain the basic nervous system necessary to generate locomotion date back to the early 20th century. According to MackayLyons (2002), the existence of nets of nervous cells that produce specific rhythmic movements for a great number of vertebrates is something unquestionable. Nervous nets in the spinal marrow are capable of producing rhythmic movements, such as swimming, jumping, and walking, when isolated from the brain and sensorial entrances. These specialised nervous systems are known as nervous oscillators or central pattern generators (CPGs). Grillner (1985), Collins & Stewart (1993), Pearson (1993), and Collins & Richmond (1994) are some interesting works about the locomotion of vertebrates controlled by central pattern generators. According to Moraes (1999), the relation between spinal marrow and encephalus in the central nervous system of domestic animals is most significant than relation in human beings. This occurs because the most motor activities in the animals is performed by reflexes and not by the cerebral activity. In relation to the total activity of the central nervous system, it is estimate that exist approximately ten times more activity in the spinal marrow of dogs than in humans. However, the human locomotion is controlled, in part, by a central pattern generator, which is evidenced in the works as Calancie et al. (1994), Dimitrijevic et al. (1998) and Pinter & Dimitrijevic (1999). Coupled nonlinear oscillators can be used in control systems of locomotion as pattern generators similar to the pattern of human gait, providing the approach trajectories of the legs. The central pattern generator is composed of a set of mutually coupled nonlinear 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. Some previous works on central pattern generators formed by nonlinear oscillators, applied in the locomotion of bipedal robots, can be seen in Bay & Hemami (1987), Dutra (1995), Zielinska (1996), Dutra et al. (2003) and Pina Filho et al. (2005). The objective of this chapter is to present the modelling of a bipedal robot using a central pattern generator formed by a set of coupled nonlinear oscillators. We present some