Abstract
In this work, a novel family of exact nonlinear control laws is developed for trajectory tracking of unmanned aerial vehicles. The proposed methodology exploits the cascade structure of the dynamic equations of most of these systems. In a first step, the vehicle position in Cartesian coordinates is controlled by means of fictitious inputs corresponding to the angular coordinates, which are fixed to a combination of computed torque and proportional-derivative elements. In a second step, the angular coordinates are controlled as to drive them to the desired fictitious inputs necessary for the first part, resulting in a double-integrator 3-input cascade control scheme. The proposal is put at test in two examples: 4-rotor and 8-rotor aircrafts. Numerical simulations of both plants illustrate the effectiveness of the proposed method, while real-time results of the first one confirm its applicability.
Highlights
Unmanned aerial vehicles (UAVs) have become a topic of interest in many works due to the fact that they are capable of operating in degraded environments which might be dangerous for humans. ese vehicles are designed to fly with high agility and rapid maneuvering, even under wind gusts
The UAVs have a wide variety of applications such as military [1], 3D mapping and aerial photography [2, 3], and inspection of places that are not accessible or are too dangerous for humans [4], among others [5, 6]
We will focus on plants with a cascade structure that allows for a family of novel cascade nonlinear control laws to be applied, e.g., the quadrotor and the 8-rotor aircrafts. ese plants consist in a structure of symmetrical links and 4 or 8 rotors at its ends, respectively
Summary
Unmanned aerial vehicles (UAVs) have become a topic of interest in many works due to the fact that they are capable of operating in degraded environments which might be dangerous for humans. ese vehicles are designed to fly with high agility and rapid maneuvering, even under wind gusts. E quadrotor is an underactuated and nonlinear coupled system with six degrees of freedom; its mathematical model will be obtained using the well-known Lagrangian method To this end, let us define q (η, ξ) ∈ R6 as the generalized coordinates vector for the quadrotor, where η (x, y, z) ∈ R3 is the position of the center of mass of the quadrotor relative to the frame Ro (Figure 1), and ξ (ψ, θ, φ) ∈ R3 are the Euler angles (yaw, pitch, and roll) that describe the orientation of the aircraft. A novel family of exact nonlinear control laws is developed for trajectory tracking of UAVs; it will exploit the cascade structure without recurring to backstepping and will be able to deal with the underactuated characteristics that the computed torque technique is unable to cope. Notation: in matrix expressions, 0 and I stand for a zero and identity matrix, respectively, whose dimensions can be inferred from the context; > and < stand for positive and negative-definiteness; the symbol ( ∗ ) denotes the transpose of the expression on the left, i.e., A + ( ∗ ) A + AT
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