Dynamic Model of a Mobile Robot with Two Active Wheels and the Desing an Optimal Control for Stabilization

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.