Estabilidad de Lyapunov del control visual PD en un robot plano paralelo
Resumen
En este trabajo se estudia la estabilidad de reguladores, con acciones proporcional y derivativa, que usan información visual para el control de posición de robots planos paralelos. Para esto, se hace una revisión bibliográfica breve de técnicas empleadas en esta clase de mecanismos, así como de técnicas empleadas en mecanismos de cadena cinemática abierta para asegurar estabilidad. Se presenta el análisis de estabilidad utilizando funciones de Lyapunov estrictas que junto con el empleo del segundo método de estabilidad de Lyapunov aseguran que los sistemas en lazo cerrado obtenidos sean asintóticamente estables en un punto de equilibrio, diferenciándose así de los análisis usuales donde se requieren funciones candidatas de Lyapunov especiales junto con teoremas de estabilidad global como el teorema de Barbashin-Krasovski o el principio de invariancia de La Salle. Los algoritmos de control visual propuestos, haciendo uso de estimación de velocidad a partir de mediciones de posición, calculan los pares necesarios en las articulaciones activas del robot paralelo para así poder mover el órgano terminal a la posición deseada. Finalmente, el desempeño del control propuesto se evalúa en un prototipo de laboratorio y se ilustran los correspondientes resultados experimentales.
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