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This paper presents an output-estimation method with reduced multirate sampling for real-time multi-input-multi-output (MIMO) haptic rendering. Haptic systems employ physics-based deformation models such as finite-element models and mass-spring models. These physics-based deformation models for high fidelity have to deal with complex geometries, material properties, and realistic behavior of virtual objects. This incurs heavy computational burden and time delays so that the reflective force often cannot be computed at 1 kHz which is a safe frequency for stability of the haptic systems. Lower update rates of the haptic loop and the computational time delay also deteriorate the realism of the haptic system. This problem is resolved by the proposed MIMO output-estimation method. The haptic system is designed to have two sampling times, T and JT, for the haptic loop and the graphic loop, respectively. Dynamics of the physics-based deformation is captured in a discrete and deterministic input-output model. The MIMO output estimation method is developed drawing on a least-squares algorithm and an output-error estimation model. The P-matrix resetting algorithm is also designed to deal with the changing input-output relationship of the deformation model. The parameters of the discrete input-output model are adjusted online. Intersample outputs are computed from the estimated input-output model at a high rate, and traces the correct output computed from the deformation model. This method enables graphics rendering at a lower update rate, and haptic rendering at a higher update rate. Convergence of the proposed method is proved, and performance is demonstrated through simulation with both a linear tensor-mass and a linear mass-spring models.
Date of Publication: June 2007