# Modeling and Control of an Articulated Multibody Aircraft
## 1 Introduction
### Related Work
#### 1.1.1 Moving Masses in Insect Flight  
In recent years, there has been an increased interest in the development of insect-inspired micro-aerial vehicles (MAVs), but biological research into insect flight has a long history. The development of bioinspired systems requires the understanding of the physics of biological systems and behaviors, not just copying the external shape [9].  
Prior research on the importance of body appendages for force and moment generation in actively flying animals was largely done on insects, including fruit flies [10; 11; 12], house flies [13], orchid bees [14], moths [15; 16], honeybees [17] and butterflies [18]. Several videos by [PERSON] show dragonfly abdominal movements during flight [19]. The study conducted by [PERSON] [20] also found some abdominal movement from kinematic analysis of dragonfly flight. This theory was tested using visual stimulation that mimicked yaw rotations, in which flying tethered flies bent their rear legs and abdomen horizontally to the inside of the intended turn [10; 11; 13; 21]. In contrast, visual stimulation that mimicked body-pitching caused the abdomen to bend upward during upward motion of the visual pattern [22; 23; 24]. Abdominal steering is adequate for maintenance of body posture in the hawkmoth, according to mathematical models [15; 16; 22; 25]. Some insects, such as desert locusts, flex their abdomens in response to changing air flow conditions in addition to the visual stimulus [26]. This behavior is said to resemble an aerodynamic rudder that aids the animal in orienting itself into the direction of the wind during flight [27; 28]. In the flight of monarch butterflies, abdomen undulation has been shown to improve stability, and reduce energy and power consumption [29; 30].  
Many flight dynamics models used in studies rely upon a conventional single-body approach [31; 32; 33] to explore limited aspects of insect flight. Yet, to adequately capture the effects of movement of anatomical parts, the multibody modeling approach provides the necessary insight to insect flight [34]. Various methods have been used to derive multibody equations of motion for air vehicles including Newton-Euler [35; 36; 37; 38], [PERSON]'s energy-based methods [29; 30; 39; 40], [PERSON] principle [41; 42], and [PERSON]'s method [43; 44]. Regarding insect-inspired aircraft, most of the multibody flight dynamics models in the literature focus on the degrees of freedom associated with wing motion. Although some strictly only consider the relative movement of the wings [35; 43; 45; 46; 47; 48; 49], a few consider the effects of wing mass and inertia [38; 50]. Fewer studies have considered the effect or role of abdominal articulation. A nonlinear model of a dragonfly-like flapping-wing MAV was developed by [PERSON] [51]. The study considered the effect of the head and abdomen in developing the equations of motion of a dragonfly-like MAV; however, their movements were not investigated with regard to their effects on flight, stabilization or control of the model. [PERSON] et al. [22] developed a model to examine the active role of the abdomen in the hawkmoth. However, the model was obtained using a system identification approach. Another study by [PERSON] et al. [29; 30] developed a model of the dynamics of a flapping-wing flyer, inspired by monarch butterfly. The model was, however, developed using Euler-Lagrange equations to examine the use of abdomen undulation to improve stability, and reduce energy and power consumption.  
Dynamic moving masses in insects are typically a relatively large part of the aircraft mass, or have quite high moment due to length, or both. Actuation is generally in rotation about a joint with at least two degrees of rotational freedom, or involve controlled flexibility, or might have multiple joints along its length. Actuation can often be rapid, such that reaction torques are also significant. The mass is generally multifunctional, serving both anatomical and flight control functions.