A method is presented and tested for planning time optimal trajectories for a mobile robot with constraints by using an evolutionary technique with neural-networks components. The method establishes shortest time trajectories redefined to form a multi-constrained non-linear global optimization problem. The trajectory components such as the turning translational speeds of the mobile robot (i.e. the parameter vector of the problem) are found by using Differential Evolution Algorithm (DE) to obtain the time optimality. DE is a floating-point genetic algorithm. Kinematics structure and upper bound of the velocities on the trajectory are learned by Artifical Neural Networks. Experiments are successfully implemented on Nomad 200 Mobile Robot.