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This paper proposes fine and fast discretization, which is based on the Finite Difference Time Domain (FDTD) method without a matrix exponential function. The proposed method is more accurate than the conventional discretization based on the first-order Pade approximation. Moreover, compared with that of the conventional method, the computational cost of the proposed method is very small. Although the Pade approximation is impossible to realize broadband real-time control, the FDTD method achieves the broadband real-time control. The proposed method and the conventional Pade approximation are analyzed by the Taylor expansion in a symbolic expression. According to the theorical analysis, the error of the FDTD discretization method is smaller than that of the conventional method. Numerical simulations also compare the errors and computational cost associated with the proposed and conventional methods. The FDTD discretization method is applied in admittance control for rendering the time-variant haptic sensation. In the case of the conventional method, owing to the limitation due to computation cost, the parameter update is not completed within the sampling period. On the other hand, the FDTD method completes the discretization within the sampling period. The gain and phase characteristics of the proposed method are close to the ideal responses. The validity of the method is verified by an experiment involving linear motor systems.

Time-Variant Haptic Simulator Based on Fine and Fast Real-Time Discretization Using FDTD Method