Tau Coupling Investigation Using Positive Wavelet Analysis

Abstract

Investigation into motion guidance using τ theory primarily relies on the accurate calculation of the coupling term between the tau (time-to-contact) of the motion, τ, and its relevant so-called tau guide. However, the traditional approach is numerically unstable, requiring experience and skill, and has limited application when information is incomplete. A new approach based on positive wavelet analysis, combined with the new concept of a guidance element, has been proposed to deal with these issues. The desired τ-guide shapes form the mother wavelet and its scale is considered to be the manoeuvre period. The scale and positions of interest are found by searching the best local correlation with the whitened original signal. An inverse de-whitening process is used to approximately reconstruct the original signal. The adequacy of the proposed approach has been demonstrated on data from piloted simulation. Results show that the proposed approach is feasible, has better numerical stability and reliability, enhanced performance and wider application.

Design and Evaluation of a Constraint-Based Head-Up Display for Helicopter Obstacle Avoidance

“…with the normalized maneuver time 0 ≤t ≤ 1:t = t − t st art t end − t st art (10) To estimate k, a least-square fit is applied to subsets of the maneuver data. Work by Lu et al [29] has shown that this approach has a number of downsides, e.g., a sensitivity to maneuver length, boundary conditions causing instability, and sensitivity to incomplete or oscillatory data. In this experiment, however, the analyzed flight path angles show little to no oscillatory behavior, and the employed methodology seems to provide reasonable results.…”

Development of Occupant-Preferred Landing Profiles for Personal Aerial Vehicles

“…Compared to the actual inputs, the derived input profile is generally smoother. Notably absent are the oscillations observable on the actual input signals, which are primarily a characteristic of the pilot's higher-frequency stabilization control activities [32]. The guidance activity only consists of low-frequency control inputs.…”

“…The motion gap profile can be compared to the motion of the appropriate tau guide. The coupling constant k and total maneuver time T that define the motion can then be computed using the method shown in [32].…”