Modeling, attitude estimation, and control of Hexarotor micro aerial vehicle (MAV)

Mathematical Modeling With Parameter Identification for Hexarotor System: A Hamiltonian Approach

“…T denotes the thrust generates by each rotor and d is the distance from center of rotor to center of mass. A rotation matrix R in the special orthogonal group SO(3) can define the orientation of the rigid body frame {B} relative to the inertial frame {G} [6,11].…”

“…Let denote the generalized momentum, 𝒑𝒑 = [ 𝑝𝑝 𝑥𝑥 𝑝𝑝 𝑦𝑦 𝑝𝑝 𝑧𝑧 𝑝𝑝 𝜙𝜙 𝑝𝑝 𝜃𝜃 𝑝𝑝 𝜓𝜓] 𝑇𝑇 ∈ ℝ 6 . The Hamiltonian mechanics approach explain that the Hamiltonian as the summation of the total kinetic energy, 𝑇𝑇(𝒒𝒒, 𝒑𝒑) with total potential energy, 𝑉𝑉(𝒒𝒒) and focus on generalized position, 𝒒𝒒 and generalized momenta, 𝒑𝒑 variables.…”

“…The translational force in the body-fixed frame is 𝑭𝑭 𝒃𝒃 = [0 0 𝑇𝑇 𝑡𝑡 ] 𝑇𝑇 and 𝑇𝑇 𝑡𝑡 is the main thrust and 𝑇𝑇 𝑖𝑖 is the thrust moment generated by each motor. The total thrust force, 𝑇𝑇 𝑡𝑡 in hovering is the summation of the individual thrust of each rotor and can be expressed as, [6], [13], [14].…”

“…In addition, research on multirotor previously focus mainly on the multirotor control issue. Due to the two extra rotors, the torque of the hexarotor around each axis differs from the quadrotors, and consequently affects the dynamical reaction differently [6,7]. As a result, multirotor mathematical modeling is critical for both mechanical and electronic systems to address its stability analysis and controller design issues.…”

Modeling and experimental parameter identification of a multicopter via a compound pendulum test rig

“…In order to describe the dynamics of the hexacopter assumed to be a rigid body, the Newton-Euler equations [16] are taken into account. Different nonlinear models for hexacopters are introduced in [17], [18]. Nine equations of motion are here considered: (i) three equations for the translational velocity with components (u, v, w) T , (ii) three equations for angular velocities (p, q, r) T and (iii) three angles (φ, ϑ, ψ)…”