The dynamics of inverted pendulum systems have an inherit property of instability, nonlinearity and underactuation. Therefore, the inverted pendulum systems have been recognized as a benchmark problem to validate emerging controllers. In addition, the dynamics of many real-world system resembles the inverted pendulum systems. To broaden the diversity of this classical system, this work focuses on a new type of inverted pendulum i.e., spatial inverted pendulum. In contrast to classical inverted pendulum systems, this system is highly complex to model and control due to its large degrees of freedom as well as underactuation. This paper proposes the bond graph model of this complex system to derive its dynamic equations. The bond graph technique only requires kinematics of the model and derives the complex dynamics by itself. Furthermore, the robust neuro-fuzzy controller based on linear quadratic regulator (LQR) controller is designed and simulated for the stabilization of the system. The proposed controller provides an advantage of improved robustness compared to classical LQR controller. The robustness of the proposed controller is verified by simulation results for various pendulum masses. The results demonstrate that when the mass variation is significant, proposed controller outperforms the LQR controller by achieving superior performance and robustness to parameter uncertainties.