Armando Carlos de Pina Filho

Modeling of a bipedal locomotor using coupled nonlinear oscillators of Van der Pol

Abstract. Research to date points to an understanding of human biped locomotion that has been primarily experimental in nature largely due to the complexity of the process. In view of the new, exciting possibilities of programmed electrostimulation of artificial muscles to generate motion (locomotion), a critical study at the theoretical level is greatly warranted. There is strong evidence that many biological clocks consist of a population of mutually coupled oscillators [Pavlidis T (1973) Biological oscillators, Academic; Johnsson A (1978) Zur Biophysik biologischer Oszillatoren. In: Biophisik, Springer]. In this work, a form of bipedal locomotion is simulated by using mutually coupled nonlinear oscillators. A planar model, which includes three out of the six determinants of gait that characterize the human locomotion, was adopted.

Modeling of a bipedal robot using mutually coupled Rayleigh oscillators

Abstract.The objective of the work presented here was the modeling of a bipedal robot using a central pattern generator (CPG) formed by a set of mutually coupled Rayleigh oscillators. We analyzed a 2D model, with the three most important determinants of gait, that performs only motions parallel to the sagittal plane. Using oscillators with integer relation of frequency, we determined the transient motion and the stable limit cycles of the network formed by the three oscillators, showing the behavior of the knee angles and the hip angle. A comparison of the plotted graphs revealed that the system provided excellent results when compared to experimental analysis. Based on the results of the study, we come to the conclusion that the use of mutually coupled Rayleigh oscillators can represent an excellent method of signal generation, allowing their application for feedback control of a walking machine.

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

Simulating the Hip and Knee Behavior of a Biped by Means of Nonlinear Oscillators

Nervous networks in the spinal marrow are capable to produce rhythmic movements, such as: swimming, jumping, and walking. These specialised nervous systems are known as central pattern generators (CPGs). Nonlinear os- cillators 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 objective of this work is to present the simulation of the biped gait using a cen- tral pattern generator formed by coupled nonlinear oscillators. Using nonlinear oscillators with integer relation of fre- quency, the transient motion and stable limit cycles of the network formed by oscillators were determined, showing the behavior of the hip and knee angles. Modification of the step length and gait frequency can be obtained by means of the change of few parameters in the oscillators.

Study and Modeling of an Underwater Cleaning Robot

The development of new technologies in urban automation has increasingly intensified in recent decades. Among the research initiatives, there is the study and design of service robots for home tasks, such as: cleaning floors, windows, and pools. The technology used in these robots depends on specific resources and great investments, and consequently, the price is expensive, restricting the use for people with high purchasing power. Thus, it is important to study means to manufacture robots with better cost-benefit, looking for to develop mechanisms that can reduce the production costs, and then a greater number of people can use such technology. Therefore, the objective of this work is to develop an underwater cleaning robot, which can be used for cleaning pools. Several aspects of the project, a model created by means of computational methods, and some analyses of the robot structure will be presented.

Dynamical Analysis of a Biped Locomotion CPG Modelled by Means of Oscillators

The study of mechanisms like mechanical members intends not only to build autonomous robots, but also to help in the rehabilitation of human being. The study of locomotion to take part in this context, and has been intensively studied since the second half of 20th century. An ample vision of the state of the technique up to 1990 can be found in works as Raibert (1986) and Vukobratovic et al. (1990). Year after year, from technological advances, based on theoretical and experimental researches, the man tries to copy or to imitate some systems of the human body. It is the case, for example, of the central pattern generator (CPG), responsible for the production of rhythmic movements. Modelling of this CPG can be made by means of coupled oscillators, and this system generates patterns similar to human CPG, becoming possible the human gait simulation. There are some significant works about the locomotion of vertebrates controlled by central pattern generators: Grillner (1985), and Pearson (1993). From a model of two-dimensional locomotor, oscillators with integer relation of frequency can be used for simulating the behaviour of the hip angle and of the knees angles. Each oscillator has its own parameters and the link to the other oscillators is made through coupling terms. We intend to evaluate a system with coupled van der Pol oscillators. Some previous works about CPGs using nonlinear oscillators, applied in the human gait simulation, can be seen in Bay & Hemami (1987), Zielinska (1996), Dutra et al. (2003), Pina Filho (2005), and Pina Filho (2008). The objective of this work is to analyze the dynamics of this coupled oscillators system by means of bifurcation diagrams and Poincare maps. From the analysis and graphs generated in MATLAB, it was possible to evaluate some characteristics of the system, such as: sensitivity to the initial conditions, presence of strange attractors and other phenomena of the chaos.