acai

Computes the degree of controllability (DOC) based on the Availability Control Authority Index, namely ACAI, which is proposed by Guang-Xu Du in [1].

Syntax

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acai(bf, fmax, fmin, G)

Description

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doc = acai(bf, fmax, fmin, G)

Computes the DOC based on ACAI according to the theory and method that are introduced in the paper.

In mathematics, an enclosed space $U$$U$ is defined as

A new space $\mathrm{\Omega }$$\Omega$ is also enclosed, which is defined as

In mathematics, the ACAI is essentially the minimum of the nearest distances between the boundary of $\mathrm{\Omega }$$\Omega$ and the given point $\mathbf{G}$$\mathbf{G}$.

Examples

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>>> from OpenHA.assessment.attribute import acai, control_allocation
>>> import numpy as np

>>> bf = control_allocation(4, 0.28, 0.1)
>>> fmax, fmin = 6, 0
>>> G = np.array([15, 0, 0, 0]).reshape((-1, 1))
>>> acai(bf, fmax, fmin, G)

0.7299473938200366

Input Arguments

bf —— An n-by-m matrix, which refers to the linear map from $U$$U$ to $\mathrm{\Omega }$$\Omega$.

For the DOC assessment of the quancopter's propulsion system, it is just the 4-by-m control allocation matrix ${\mathbf{b}}_f$$\mathbf{b}_f$.

where $f_1,f_2,\cdots ,f_n$$f_1,f_2,\cdots,f_n$ are the propeller thrusts.

fmax —— The upper bound of each dimension of the space $U$$U$, specified as a numeric scalar or an array of length m.

When the upper bounds of all the dimensions of $U$$U$ are equal, specify it as a numeric scalar. Otherwise, specify it as an array of numeric scalars of length m.

fmin —— The lower bound of each dimension of the space $U$$U$, specified as a numeric scalar or an array of length m.

When the lower bounds of all the dimensions of $U$$U$ are equal, specify it as a numeric scalar. Otherwise, specify it as an array of numeric scalars of length m.

The values of fmin should be no more than fmax.

G —— An point in $\mathrm{\Omega }$$\Omega$, specified as a 1-D array of length n.

Properties of Arguments

References

[1] G.-X. Du, Q. Quan, B. Yang, and K.-Y. Cai, "Controllability Analysis for Multirotor Helicopter Rotor Degradation and Failure," Journal of Guidance, Control, and Dynamics, vol. 38, no. 5, pp. 978-984, 2015. DOI: 10.2514/1.G000731.