Genetic algorithm-based adaptive fuzzy logic systems for dynamic modeling of quadrotors Unconstrained Evolutionary and Gradient Descent-Based Tuning of Fuzzy-partitions for UAV Dynamic Modeling with Christoffel Symbols of the First Kind

This paper presents a novel fuzzy identification method for dynamic modelling of quadrotor UAVs. The method is based on a special parameterization of the antecedent part of fuzzy systems that results in fuzzy-partitions for antecedents. This antecedent parameter representation method of fuzzy rules ensures upholding of predefined linguistic value ordering and ensures that fuzzy-partitions remain intact throughout an unconstrained hybrid evolutionary and gradient descent based optimization process. In the Euler-Lagrange based equations of motion the first order derivative component is calculated based on Christoffel symbols, the derivatives of fuzzy systems are used for modelling the Coriolis effects, gyroscopic and centrifugal terms. All linear parameters are evaluated by the least squares method. The non-linear parameters are subjected to an initial global evolutionary optimization scheme and fine tuning with gradient descent based local search. Keywords—quadrotor UAV, dynamic model, fuzzy system, fuzzy-partition, unconstrained optimization, genetic algorithms, gradient descent search