Insect Locomotion: Control, Stability, and Optimization

In complex dynamical systems consisting of many interacting degrees of freedom it can be impossible to predict how any single one will behave. Yet, usually, out of the chaos emerge simple laws that guide the behavior of the system as a whole. Many examples exist in Nature, from the ideal gas law to superconductivity, and it can be expected that the same principle holds in the study of insect locomotion. This thesis examines three aspects of insect locomotion and attempts to provide simple laws that guide them. First, the focus is on the steering control of a tiger beetle while it chases its prey. The steering is governed by a proportional controller with a distance dependent gain. Moreover, the same control law can be seen in the position that the front leg is placed at each individual step. Next, this thesis provides insight into the principles that guide evolution as it drives morphological adaptations in flying insects. Using computer simulations of 3D flight, we find that the wing hinge position relative to the center of mass of a model fly has a significant effect on the lift production and only marginally affects flight stability. Most intriguing is the result that the nominal hinge position of a fruit fly optimizes its lift production and maximizes ascending speed, irrespective of stroke amplitude. This can be understood by looking at the coupling between the body and wing motions. We construct a new model, which shows that the maximum speed, associated with the maximum vertical lift, is due to an antiresonance between the body and wing oscillations. In addition, the evolutionary process from four-winged to two-winged flight is investigated. The four-winged dragonfly, an example of one of the oldest flying insects, flies with the body horizontal during steady state flight. In contrast, two-winged insects, which developed later, fly with their body pitched up vertically. The simulations presented here will show that during the evolutionary transition the flight style naturally switches from horizontal to vertical. This change must be accompanied by a switch from an asymmetric to a symmetric wing stroke in order to maintain flight. The results indicate that small changes to the wing size of a four-winged flyer require simultaneous large adaptations to the front wing pitch if successful flight is to be maintained. Finally, the last chapter will report on the construction of an interactive insect flight simulator, where a human can control the insect flight by flapping a wing model in the lab. The system combines the previous insect flight simulations with real-time input of the wing beat. Initial results will be discussed, which indicate the setup and code are functioning properly. In addition, we show that a human can reproduce typical fruit fly flight and can control the longitudinal flight of a dragonfly. This setup allows for experiments that look at how control laws are developed and how they might change over time, but those experiments have yet to be performed