The basic module for the solution of the minimum time optimal control of acar-like vehicle is herein presented. The vehicle is subject to the effect oflaminar (linear) and aerodynamic (quadratic) drag, taking into account theasymmetric bounded longitudinal accelerations. This module is studied anddesigned to be fast and robust in sight to be the fundamental building block ofa more extended optimal control problem that considers a given clothoid as thetrajectory and the presence of a constraint on the lateral acceleration of thevehicle. The nonlinear dynamics and the different possible boundary conditionsyield different analytical solutions of the differential equations, hence theyby themselves a particular attention. The study of the numeric stability of thecomputation for limit values of the parameters is essential as showed in thenumerical tests.
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