The concept of making a two-wheeled self-stabilizing vehicle can be a possibility soon. These vehicles use control moment gyroscopes (CMGs) to provide enough torque for the vehicle to prevent it from rolling and falling to the ground. CMGs can be used with different numbers and configurations. In this article, the aim is to offer a design procedure for a double gyroscope system, which can be used for any two-wheel vehicle to be self-stabilized. The procedure is based on using optimization algorithms in reaching the optimum double gyroscope configuration for a certain two-wheel vehicle to reach a zero-degree roll angle in the least time possible, which is the novel part of the procedure. A design procedure for a double gyroscope with the yaw axis as a spinning axis for a two-wheel vehicle is offered. This procedure has been tested for both a small two-wheel robot and a two-wheel enclosed vehicle. The research method started with a presentation of motion equations, followed by a discussion of the use of the PID cascade controller and its tuning process. Also setting up the simulation and finally using the gradient descent method of optimization with both the sequential quadratic programming (SQP) and the interior point algorithms to optimize the simulation results to achieve the optimum design. The simulations were carried out using an initial roll angle of 15°. Before optimization, the small two-wheel robot reached 0° roll angle in nearly 5 seconds at 2000 RPM flywheel spinning velocity and the two-wheel enclosed vehicle reached 0° roll angle in nearly 2.5 seconds at 4000 RPM flywheel spinning velocity. After optimization for the same spinning velocities the small two-wheel robot reached 0° in nearly 2 seconds but the enclosed two-wheel vehicle did not show a significant improvement with the results due to the good performance of the initial design of the vehicle.