Multirate output estimation for real-time haptic rendering

This paper presents MIMO output estimation with reduced multirate sampling for real-time haptic rendering. The graphic models of the haptic systems are required to deal with complex geometries, material properties, and the dynamics of the virtual objects to display realistic deformation. Accurate graphic models often incur heavy computational burden, and the reflective force cannot be computed at 1 kHz. This problem is resolved by employing a multirate output estimation method. The dynamics of the graphic model is represented by a discrete input-output model. The parameters of the discrete input-output model are estimated on-line by the proposed multirate output estimation algorithm. The reflective force is computed from the estimated input-output model at a high rate, and traces the force computed from the graphic model as the estimation error quickly approaches zero. The convergence of the proposed estimation algorithm is proved, and the performance is evaluated with simulation