On-line time-scaling control of a kinematic car with one input

This paper reports a time-scaling scheme to realize a tracking controller for the non-differentially flat model of the kinematic car with one input which is the steering angle or the angular velocity of the steering angle. The longitudinal velocity of the car is a measurable external signal and cannot be influenced by the controller. Using an on-line time-scaling, driven by the longitudinal velocity of the car, by a scaling output of the tracking controller, and by their time derivatives up to the second order, one can achieve exponential tracking of any sufficiently smooth reference trajectory, similar to the differentially flat case with two control inputs. The price to pay is the modification of the finite traveling time of the reference trajectory according to the time-scaling.