Verification of reduced-order models for real-time applications with haptic feedback

Real-time simulation systems equipped with haptic peripherals, like those employed in virtual surgery or industry lay-out design, require feedback rates on the order of 1kHz. Such an impressive requirement for a simulation code, usually including non-linear approaches, has recently been accomplished by model order reduction techniques [1] within the framework of the so-called computational vademecums [2]. These vademecums are in fact a pre-computed solution of a high dimensional parametric problem. This solution is obtained in a very efficient manner through the use of Proper Generalized Decomposition (PGD) and then evaluated (rather that simulated) in real time very efficiently. In this work a verification strategy has been developed towards an effective use in health and industry of such systems. Error estimation [3] has been accomplished with especial emphasis in one particular quantity of interest, namely, the force transmitted to the haptic peripheral. This force is crucial to provide the user with a realistic sensation in the operation of the simulation system