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I would like to mention that Fuzzy logic is still an active control system used in many industry applications. In garbage fired power plants, concrete aggregate firing, hydraulics, and the control of flow of powdered 'fluids' in foundries to name a few. However, I will admit, I've only seen them used in 'one off' difficult to model projects, such as power ...


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Short answer: Fuzzy logic (FL) isn't applicable for robotics research, The long answer is, that in the 1980s as part of the fifth computer generation fuzzy logic was researched in Japan with the attempt to build intelligent advanced parallel computers, but the Japanese researchers have failed. Fuzzy logic isn't a technical idea but a philosophical ...


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Fuzzy logic is definitely used in many of the control systems including but not limited to robotics. See this paper for an example: https://pdfs.semanticscholar.org/b9a7/332b03d46b3ee08b9d113e64714e6b668601.pdf and this: https://ieeexplore.ieee.org/document/1678143 If we consider fuzzy logic as dubious then we should do the same to probabilities. Both ...


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This depends on how you want to quantify the uncertainty. For example, you can compute the sample covariance between all state variables i.e., $$ q_{jk} = \frac{1}{N-1} \sum_{i=1}^{N} (x_{ij} - \bar{x}_j) (x_{ik} - \bar{x}_k) $$ where the covariance matrix is $\mathbf{Q}$ with entries $q_{ji}$. This is straightforward; however, different approaches exist. ...


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You are correct. It's just a matter of interpretation. (1) is the guess on the location of the true value whereas (2) is simulating your sensor behavior. Your equation in (1) can be converted to N(z,sigma) = z + N(0,sigma) witch is eventually same as your second equation. Can we set Σ=Σ^, i.e. can we use the covariance learned in (2) in the setting described ...


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It may be worth noting that $\Sigma$ does not just describe "how far" the true value $\boldsymbol{x}$ is from $\boldsymbol{z}$ , but "where" in relation to it, the difference is apparent when the distribution is not 'circular' in the multidimensional case. Also, a Gaussian is a symmetric distribution, and only under that condition the ...


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Yes. This approach is commonly used when IMUs are present because they measure the rate of state change with some uncertainty.


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I have not seen any industry-grade application of fuzzy logic in space, flight, automotive control systems. Fuzzy logic came during mid-60s and it gradually faded away due to several reasons: It did not solve any control problem that cannot already be solved by the existing methods at that time. Bad news, no major advantage in terms of extending the ...


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Look for highly nonlinear problems where a single PID is not suitable to work at its best within the whole operational range thus requiring multiple controllers. Here's an example in Simulink. In your case, instead of having a repertoire of PID controllers already tuned up to operate in different points, you might consider sticking to a single PID whose ...


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