This paper focuses on the problem of controlling the relative position between a moving target and an autonomous nonholonomic vehicle. This problem represents a meaningful case study belonging to the class of multirate nonlinear control systems. A multi-level stabilizing control system is synthesized in continuous-time, based on a detailed analytic model of the vehicle, including the robot kinematics and nonholonomic dynamics, and actuators transfer functions. The discrete-time implementation provides a multirate nonlinear digital controller. Simulations in both continuous and discrete-time domain highlights interesting performance variations effects arising from different choices of the sampling frequencies