This paper presents a tracking dynamic model designed to smooth a primitive trajectory defines a wheeled robot’s motion path under first-order approximation. The model has a canonical input–output form and is adjusted by nested saturators with variable gains, which improves the primitive trajectory’s approximation accuracy on straight path sections relative to fixed-gain models. The setting algorithm automatically considers for the specified dynamic constraints of the mobile robot and features of the primitive trajectory. Numerical simulation results are presented, demonstrating the effectiveness of the developed dynamic model.