This seminar presents techniques and applications for rapidly developing computationally optimized models for HIL simulation of high-fidelity physical plant models. Using symbolic computation techniques, multibody models can be effectively preprocessed to select optimal coordinate frames, eliminate redundant calculations, simplify algebraic constraints, and generate computationally minimal code for real-time deployment. Furthermore, novel mathematical techniques can be deployed for efficient parameter optimization and other advanced analysis. Applications in robotics, including space and industrial robotics will be presented. The symbolic computation system Maple and the related modeling system MapleSim will be used to illustrate examples.