Cubic Hermite Spline Interpolation Research Articles

Field‐programmable gate array‐based design for real‐time computation of ensemble empirical mode decomposition

SummaryEmpirical mode decomposition (EMD) is considered as a suitable method when the signal to be analyzed is nonlinear or nonstationary in nature. But, EMD suffers from a problem known as mode mixing. To, reduce this problem, ensemble EMD (EEMD) was proposed. In this paper, we have presented a fast field‐programmable gate array (FPGA)‐based design for EEMD. Where calculation of output can be done in a parallel manner for different realizations. The design has a comparatively less execution time, and the execution time of the proposed EEMD design is even less than some state‐of‐the‐art EMD‐based design, although the architecture of EEMD is more complex, when compared with the EMD design. In this work, we have also performed an FPGA implementation of the EMD algorithm. The root mean square error (RMSE) and the correlation values of the intrinsic mode function (IMFs) obtained from the proposed EMD and EEMD designs are compared. The proposed FPGA‐based architecture of the EEMD algorithm is designed using Verilog‐hardware description language (HDL) and implemented on a Kintex‐7 FPGA. The EEMD architecture consists of cubic Hermite spline interpolation (CHSI) and cubic spline interpolation (CSI) for the envelope generation.

Integral LOS Path Following for Curved Paths Based on a Monotone Cubic Hermite Spline Parametrization

This paper addresses two interrelated problems concerning the planar three degree-of-freedom motion of a vehicle, namely, the path planning problem and the guidance problem. The monotone cubic Hermite spline interpolation (CHSI) technique by Fritsch and Carlson is employed to design paths that provide the user with better shape control and avoid wiggles and zigzags between the two successive waypoints. The conventional line-of-sight (LOS) guidance law is modified by proposing a time-varying equation for the lookahead distance, which is a function of the cross-track error. This results in a more flexible maneuvering behavior that can contribute to reaching the desired path faster as well as obtaining a diminished oscillatory behavior around the desired path. The guidance system along with a heading controller form a cascaded structure, which is shown to be κ-exponentially stable when the control task is to converge to the path produced by the aforementioned CHSI method. In addition, the issue of compensating for the sideslip angle β is discussed and a new κ-exponentially stable integral LOS guidance law, capable of eliminating the effect of constant external disturbances for straight-line path following, is derived.