Stabilization control of a bumblebee in hovering and forward flight
Our previous study shows that the hovering and forward flight of a bumblebee do not have inherent stability (passive stability). But the bumblebees are observed to fly stably. Stabilization control must have been applied. In this study, we investigate the longitudinal stabilization control of the bumblebee. The method of computational fluid dynamics is used to compute the control derivatives and the techniques of eigenvalue and eigenvector analysis and modal decomposition are used for solving the equations of motion. Controllability analysis shows that at all flight speeds considered, although inherently unstable, the flight is controllable. By feedbacking the state variables, i.e. vertical and horizontal velocities, pitching rate and pitch angle (which can be measured by the sensory system of the insect), to produce changes in stroke angle and angle of attack of the wings, the flight can be stabilized, explaining why the bumblebees can fly stably even if they are passively unstable.
KeywordsInsect Hovering and forward flight Stabilization control Navier–Stokes simulation Modal analysis
Unable to display preview. Download preview PDF.
- 4.Dudley R.: The Biomechanics of Insect Flight: Form, Function, Evolution. Princeton University Press, Princeton (2000)Google Scholar
- 7.Dudley R., Ellington C.P.: Mechanics of forward flight in bumblebees. I. Kinematics and morphology. J. Exp. Biol. 148, 19–52 (1990)Google Scholar
- 8.Etkin B.: Dynamics of Atmospheric Flight. Wiley, New York (1972)Google Scholar
- 9.Bryson A.E.: Control of Spacecraft and Aircraft. Princeton University Press, Princeton (1994)Google Scholar
- 11.Usherwood J.R., Ellington C.P.: The aerodynamics of revolving wings. II. Propeller force coefficients from mayfly to quail. J. Exp. Biol. 205, 1565–1576 (2002)Google Scholar
- 12.Brogan W.L.: Modern Control Theory. Quantum Publishers Inc., New York (1974)Google Scholar
- 13.Ennos A.R.: The kinematics and aerodynamics of the free flight of some diptera. J. Exp. Biol. 142, 49–85 (1989)Google Scholar