Efficient physics simulation has significantly accelerated research progress in robotics applications such as grasping and assembly. The advent of GPU-accelerated simulation frameworks like Isaac Sim has particularly empowered learning-based methods, enabling them to tackle increasingly complex tasks. The PAL Robotics TIAGo++ Omni is a versatile mobile manipulator equipped with a mecanum-wheeled base, allowing omnidirectional movement and a wide range of task capabilities. However, until now, no model of the robot has been available in Isaac Sim. In this paper, we introduce such a model, calibrated to approximate the behavior of the real robot, with a focus on its omnidirectional drive dynamics. We present two control models for the omnidirectional drive: a physically accurate model that replicates real-world wheel dynamics and a lightweight velocity-based model optimized for learning-based applications. With these models, we introduce a learning-based calibration approach to approximate the real robot's S-shaped velocity profile using minimal trajectory data recordings. This simulation should allow researchers to experiment with the robot and perform efficient learning-based control in diverse environments. We provide the integration publicly at https://github.com/AIS-Bonn/tiago_isaac.
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