Oscillatory signals with nonlinear frequencies for control of nonholonomic systems

This paper considers the construction of amplitude-modulated oscillatory controls with nonlinear frequency for the purposes of trajectory tracking in second order nonholonomic systems. Solutions of an optimization problem show that, for a class of second order nonholonomic systems, this choice results in a lower quadratic control cost while producing the same net system motion as linear frequencies. Motivated by these results, we will consider the choice where the frequency of oscillation is quadratic in time. The optimization and trajectory tracking results are demonstrated in simulation.