This article investigates the trajectory tracking control of a differential-drive two-wheeled mobile robot (DDWMR) using its kinematic model, framed in the context of sustainability. A nonlinear-to-linear transformation based on differential flatness is employed to convert the original nonlinear system into two fully decoupled linear subsystems, enabling a simple and robust controller design. Unlike conventional flatness-based methods that rely on exact feedforward linearization around a reference trajectory, the proposed approach performs plant linearization, ensuring reliable tracking across a wide range of trajectories. The resulting two-loop architecture consists of an inner nonlinear loop implementing state prolongation and static feedback and an outer linear controller performing trajectory tracking of the linearized system. Simulation results on a circular reference trajectory demonstrate high tracking accuracy, with a maximum transient deviation of 0.28 m, a settling time of approximately 120 s, and a steady-state mean tracking error below 0.01 m. These results confirm that the plant-linearization-based framework provides accuracy, robustness, and practical applicability for DDWMR trajectory tracking, all within a responsible control environment.

The paper presents a trajectory control method for nonlinear differentially flat control systems, referred to as the generalized Computed Torque Control (CTC) method. It is shown that the classical Computed Torque Control, traditionally applied to serial manipulators, can be regarded as a special case of a general trajectory control method for a specific class of flat systems, denoted as class A systems. An approach to the linearization of such systems is proposed, based on class C coordinate transformations, which transform the original nonlinear control system into an equivalent trivial linear control system while preserving equivalence in the sense of control system theory. It is noted that class C transformations admit hardware implementation using physically realizable signal-processing elements. It is shown that flat systems of class A possess a flat output depending only on the current state of the system, which extends the applicability of the proposed method to other nonlinear control objects, including certain types of mobile robots. In addition, the analysis of the classical CTC method makes it possible to formulate a disturbance rejection criterion for the linear controller included in the trajectory control scheme.

This article investigates the trajectory-tracking control of a differential-drive two-wheeled mobile robot (DDWMR) using its kinematic model. A nonlinear-to-linear transformation based on differential flatness is employed to convert the original nonlinear system into two fully decoupled linear subsystems, enabling a simple and robust controller design. Unlike conventional flatness-based methods that rely on exact feedforward linearization around a reference trajectory, the proposed approach performs plant linearization, ensuring reliable tracking across a wide range of trajectories. The resulting two-loop architecture consists of an inner nonlinear loop implementing state prolongation and static feedback, and an outer linear controller performing trajectory tracking of the linearized system. Simulation results on a circular reference trajectory demonstrate high tracking accuracy, with a maximum transient deviation of 0.28 m, a settling time of approximately 120 s, and a steady-state mean tracking error below 0.01 m. These results confirm that the plant-linearization-based framework provides superior accuracy, robustness, and practical applicability for DDWMR trajectory tracking.