Non-holonomic constraints impose restrictions on the allowable velocities or motions of the system. These constraints may arise from physical interactions or mechanical limitations. Stabilizing constraints in a non-holonomic multibody system often involves employing numerical methods due to the complexity of the constraints and the dynamic nature of the system. Moreover, for self-balancing robots, driving constraints may be introduced to the system in the velocity level, and proper management of these constraints is crucial in the design and analysis of mechanisms, vehicles, robotics, and other complex systems. In this paper, we present an approach for stabilizing the driving velocity constraints, along with other holonomic and non-holonomic constraints, of a self-balanced robot. The proposed approach is intended for use in the numerical integration process of the Differential Algebraic Equations of multibody system dynamics, and not for real-time control. Successful numerical integration enables the calculation of driving forces in an open-loop manner. The paper proves that fuzzy logic control can be utilized effectively for driving constraints stabilization at the velocity level.