A study on the modeling of a hexacopter Le, Dang-Khanh; Nam, Taek-Kun;
The purpose of this paper is to present the basic mathematical modeling of a hexacopter, which could be used to develop proper methods for stabilization and trajectory control. A hexacopter consists of six rotors with three pairs of counter-rotating fixed-pitch blades. This mechanism is an under-actuated, dynamically unstable, six-degrees-of-freedom system. The whole motion of this object consists of translational and rotational motion in three dimensions, where the translational motion is created by changing the direction and magnitude of the upward propeller thrust. The hexacopter is controlled by adjusting the angular velocities of the rotors, which are spun by electric motors. It is assumed to be a rigid body; thus, the differential equation of the hexacopter dynamics can be derived from the Newton-Euler equation. The Euler-angle parametrization of the three-dimensional rotations contains singular points in the coordinate space that can cause failure of both the dynamical model and control. In order to avoid singularities, the rotations of the hexacopter are parametrized in terms of quaternions. This choice has been made considering the linearity of the quaternion formulation and their stability and efficiency. Further, control simulation of a hexacopter applying cascaded-PID control is also presented in this paper.
J. Fogelberg Navigation and Autonomous Control of a Hexacopter in Indoor Environments, Lund University, ISSN 0280-5316, 2013.
J. M. Rico-Martinez and J. Gallardo-Alvarado, "A simple method for the determination of angular velocity and acceleration of a spherical motion through quaternions," Meccanica 35, pp. 111-118, 2000.
A. P. Yefremov, Quaternions: Algebra, Geometry and Physical Theories, Hypercomplex Numbers in Geometry and Physics 1, 2004.
N. Ohlsson and M. Stahl, A Model-Based Approach to Computer Vision and Automatic Control using Matlab Simulink for an Autonomous Indoor Multirotor UAV, Department of Signals and Systems, CHALMERS UNIVERSITY OF TECHNOLOGY, Sweden, 2013.
T. Luukkonen, Modelling and control of quadcopter, Aalto University, School of Science, 2011.
B. W. McCormick, Aerodynamics, Aeronautics, and Flight Mechanics, John Wiley & Sons, 1995.
S. S. Shin, J. H. Noh, and J. H. Park, "A study on the optimal tuning of the hydraulic motion driver parameter by using RCGA," Journal of the Korean Society of Marine Engineering, vol. 38, no. 1, pp. 39-47, 2014.
Y. H. Lee, G. G. Jin, and M. O. So, "Level control of single water tank system using fuzzy-PID technique," Journal of the Korean Society of Marine Engineering, vol. 38, no. 5, pp. 550-556, 2014.
S. S. Shin, J. H. Noh, and J. H. Park, "A study on the stabilization and controller design for directional Pan-tilt system," Journal of the Korean Society of Marine Engineering, vol. 37, no. 2, pp. 192-198, 2013.