  Highly non-linear vehicle dynamics plays an important role in autonomous
driving systems, especially in congested traffic situations at very low speeds.
Due to this fact, accurate controllers are needed in order to ensure safety
during navigation. In this paper, based on a previous fractional order speed
control, an improved fractional order control is presented to control a
commercial Citro\"en C3 prototype -which has automatic driving capabilities- at
low speeds, which considers a hybrid model of the vehicle. Specifically, two
different fractional order PI{\alpha} controllers are designed to act over the
throttle and brake pedals, respectively. Concerning to the uncertain dynamics
of the system during the brake action parameters are tuned to design a robust
controller. In addition, the system is modeled as hybrid fractional order
differential inclusions. Experimental and simulation results, obtained in a
real circuit, are given to demonstrate the effectiveness of the proposed
strategies for cruise control at low speeds.
