Title :
Dynamic Model of a Mobile Robot with Two Active Wheels and the Desing an Optimal Control for Stabilization
Author :
Morales, M.C.G.C. ; Alexandrov, Vladimir V. ; Arias, J.E.M.G.
Author_Institution :
Fac. de Cienc. Fisico-Mat., Benemerita Univ. Autonoma de Puebla, Puebla, Mexico
Abstract :
In this paper is considered the problem of finding an optimal control for the stabilization of trajectories in a differential mobile robot, based on dynamic programming as synthesis tool. Nonlinear dynamic equations of the robot are obtained through Lagrange´s equation, and the multipliers involved in these equations are determined. DC motor equations are incorporated to the model, and by the application of Thikonov´s Theorem, a simplification for the model is derived. Considering a desired trajectory, the linear deviation equations are obtained. To synthesize the optimal control from this linear system, it is necessary to solve a Riccati type matrix differential equation, to obtain the stabilization solution.
Keywords :
DC motors; Riccati equations; control system synthesis; dynamic programming; matrix algebra; mobile robots; nonlinear differential equations; nonlinear dynamical systems; optimal control; stability; trajectory control; wheels; DC motor equations; Lagrange equation; Riccati type matrix differential equation; Thikonov theorem; active wheels; differential mobile robot; dynamic programming; linear deviation equations; linear system; mobile robot dynamic model; nonlinear dynamic equations; optimal control design; optimal control synthesis tool; trajectory stabilization; Movile robot; dynamic programming; equation matrix Riccati; optimal control; stabilization;
Conference_Titel :
Electronics, Robotics and Automotive Mechanics Conference (CERMA), 2012 IEEE Ninth
Conference_Location :
Cuernavaca
Print_ISBN :
978-1-4673-5096-9
DOI :
10.1109/CERMA.2012.42
