Artículos

 

Optimización de trayectorias para sistemas sujetos a restricciones no holónomas

 

Trajectory Optimization for Systems Under Nonholonomic Constraints

 

Gustavo Arechavaleta

 

Robótica y Manufactura Avanzada, CINVESTAV – Unidad Saltillo Carretera Saltillo–Monterrey Km. 13.5, C.P. 25900, Ramos Arizpe, Coah. México garechav@cinvestav.edu.mx

 

Artículo recibido en Enero 15, 2010
Aceptado en Junio 11, 2010

 

Resumen

Presentamos una estrategia numérica para calcular trayectorias válidas para sistemas sin deriva con restricciones diferenciales no integrables que minimicen el consumo de energía expresado como la norma L₂ del control. Utilizamos herramientas de la teoría del control óptimo y la programación no lineal para formular y resolver el problema de optimización. Primero analizamos las condiciones necesarias que debe satisfacer el control óptimo. Posteriormente convertimos el problema de dimensión infinita a un problema de optimización no lineal de dimensión finita. Esta formulación nos permite generar las trayectorias deseadas utilizando una estrategia simple y eficiente basada en la Programación Cuadrática Secuencial (PCS).

Comparamos la estrategia propuesta con el algoritmo desarrollado por [Fernandes, et al., 1994], en términos de convergencia y tiempo de cálculo, utilizando varios modelos cinemáticos de robots móviles con ruedas y remolques y también un modelo dinámico de robot espacial.

Palabras clave: sistemas no holónomos, control óptimo, optimización numérica, robótica móvil.

 

Abstract

This paper presents a numerical strategy to compute feasible trajectories for driftless systems under nonintegrable differential constraints that minimize the norm of the control. We made use of optimal control tools and nonlinear programming to formulate and solve the optimization problem. First, we analyze the necessary conditions to be satisfied by the optimal control. Then, we transform the infinite–dimensional problem into a finite–dimensional nonlinear optimization problem. This formulation allows us to generate the desired trajectories by using a simple and efficient strategy based on the Sequential Quadratic Programming (SQP).

We compare the proposed strategy with the algorithm developed by [Fernandes, et al., 1994], in terms of convergence and computational time, by using various kinematic models of mobile robots with wheels, chained systems and a dynamic model of space robot.

Keywords: Nonholonomic systems, optimal control, numerical optimization, mobile robotics.

 

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Agradecimientos

Agradecemos el soporte financiero del CONACyT por medio del proyecto No. 84855 para desarrollar este trabajo.

 

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