On time and in balance: a control strategy for self-balancing robots

Two-wheeled self-balancing systems exhibit an inherently unstable equilibrium, making them highly sensitive to disturbances and challenging to control. Therefore, the design of robust and fast-acting control strategies is essential to ensure stability and satisfactory performance. In this work, a predefined-time control scheme is proposed to drive the system states to the desired equilibrium within a user-defined finite time, independent of initial conditions. The proposed predefined-time framework is integrated with sliding mode and backstepping control. The effectiveness of the proposed approach is evaluated through numerical simulations. Results demonstrate that both controllers successfully drive the system to the desired equilibrium within the prescribed settling time. In addition, they maintain strong robustness against external disturbances, measurement noise, parametric uncertainties, and actuator saturation, ensuring reliable performance under challenging conditions. Compared with standard sliding mode control, the proposed approaches achieve lower total energy consumption, reduced control effort, improved tracking accuracy, and mitigated chattering.