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Quadrotor modeling and model parameters identification

In order to perform valuable controller design in a simulation environtment, it is important to develop both: rich and worthy quadrotor models, and parameter identification methodologies for these models. Two quadrotor models are proposed: a simplified model that captures only the main dynamics of the quadrotor, and a second model based on the physical laws underlying the AR Drone behavior. For each model a general methodology for the model parameters identification is proposed.


Fig 1. (Left) Free body diagram of a quadrotor.The four propellers, and each of their performed thrust Ti and torque Mi are labeled 1-4. The euler angles are denoted {φ, roll}, {θ, pitch} and {ψ, yaw}

Fig 1. (Right) Quadrotor simplified model, only the pitch and roll inputs are kept, along with the main resulting quadrotor behavior.


Fig 2. Identification results. In both graphics: "experimental data" corresponds to data provided by the organizers of the international competicion CEA 2012, "simple model" corresponds to the model shown in Fig 1. (right), and the "phys. model"  corresponds to the complete quadrotor model which simulates the rigid body of the quadrotor shown in Fig 1 (left). In this figure, (left) response to two succesive step commands (right) response to a sequence of pseudo-random step commands


1. Complete quadrotor model:

This model consists of: the quadrotor rigid body dynamics, the propeller mechanical and time response, the aerodynamic friction (including wind and quadrotor speeds) and the low-level estimated control laws. The utilized identification methodology permits to estimate parameters for all these properties, obtaining a physical-based model that can be used to test the stability robustness of the designed controllers in simulation.


2. Quadrotor simplified model to the XY plany with fixed yaw orentiation:

A simplified model of the quadrotor has several advantages, among them that it is easier to identify and that provides good results for position estimation with lower computing requirements. Some interesting results, is that the Kalman Filter obtained by implementing these model can actually correctly estimate the position of the complete quadrotor model. This model is being improved to work with all the quadrotor position and speed coordinates.