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Experimental Analysis and Control of a Chaotic Pendubot

Centro de Investigación Científica y de Educación, Superior de Ensenada CICESE, Depto. de Electrónica y Telecomunicaciones, Km. 107 Carr., Tijuana-Ensenada, 22860 Ensenada, B.C., Méxicohgonz{at}cicese.mx

Joaquín Alvarez

Centro de Investigación Científica y de Educación, Superior de Ensenada CICESE, Depto. de Electrónica y Telecomunicaciones, Km. 107 Carr., Tijuana-Ensenada, 22860 Ensenada, B.C., México

Jaime Alvarez-Gallegos

Centro de Investigación y de Estudios Avanzados, CINVESTAV-I.P.N. Depto. de Ingeniería Eléctrica, Sección de Mecatrónica Ap. Postal 14-740. 07000, México, D.F. México

Applying attractor reconstruction techniques and other chaotic measurements, it is shown that the long-term dynamics of a vertical, underactuated, two-degrees-of-freedom robot called Pendubot may exhibit complex dynamics including chaotic behavior. These techniques use only the measurement of some available variable of the system, and the resulting reconstruction allows us to identify unstable periodic orbits embedded in the chaotic attractor. In this paper, we also propose a parameter-perturbation-like control algorithm to stabilize the behavior of the Pendubot to force its dynamics to be periodic. We control this device using only the measurement of one of its angular position coordinates and consider that the system may be seen as five-dimensional (a non-autonomous, four-dimensional system), taking the amplitude of a sinusoidal external torque as the perturbation parameter. We change this parameter to stabilize one of the equilibrium points in the so-called Lorenz map. The main advantage of the method proposed here is that it can be implemented directly from time series data, irrespective of the overall dimension of the phase space. Also, reconstructions of the attractor based on the measurements are shown, as well as some experimental results of the controlled system.

Key Words: Pendubot • chaos control • underactuated robot • delay coordinates

The International Journal of Robotics Research, Vol. 23, No. 9, 891-901 (2004)
DOI: 10.1177/0278364904044407


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