This paper introduces a Transformer-Enhanced Physics-Informed Neural Network (TE-PINN) designed for accurate quaternion-based orientation estimation in high-dynamic environments, particularly within the field of robotics. By integrating transformer networks with physics-informed learning, our approach innovatively captures temporal dependencies in sensor data while enforcing the fundamental physical laws governing rotational motion. TE-PINN leverages a multi-head attention mechanism to handle sequential data from inertial sensors, such as accelerometers and gyroscopes, ensuring temporal consistency. Simultaneously, the model embeds quaternion kinematics and rigid body dynamics into the learning process, aligning the network's predictions with mechanical principles like Euler's laws of motion. The physics-informed loss function incorporates the dynamics of angular velocity and external forces, enhancing the network's ability to generalize in complex scenarios. Our experimental evaluation demonstrates that TE-PINN consistently outperforms traditional methods such as Extended Kalman Filters (EKF) and LSTM-based estimators, particularly in scenarios characterized by high angular velocities and noisy sensor data. The results show a significant reduction in mean quaternion error and improved gyroscope bias estimation compared to the state-of-the-art. An ablation study further isolates the contributions of both the transformer architecture and the physics-informed constraints, highlighting the synergistic effect of both components in improving model performance. The proposed model achieves real-time performance on embedded systems typical of mobile robots, offering a scalable and efficient solution for orientation estimation in autonomous systems.