# Generic Component-Based Mission-Centric Energy Model for Micro-Scale Unmanned Aerial Vehicles
## 3 Model
### An Energy Model for the FINken Quadcopters  
To evaluate the generic energy model, we decided to use the FINken [4] quadcopters, which were developed in our lab. These copters are designed to be a modular research platform for indoor quadcopter and swarm robotics research. The main benefit of this platform in comparison to commercial ones is the option to easily adapt the sensory equipment. For these experiments we added an analogue current sensor to the internal power distribution of the copter to enable live current measurement. Another benefit is the option to log the measurement with high-speed to an on-board SD-Card, which enables fine-grained analysis of the behaviour of the copter. Consequently, we implemented the presented energy model for the FINken3 [4] robot. To this end, we decomposed the quadcopter into several components. As the FINken3 (see Figure 1) is a modular quadcopter where each module can be plugged in, the decomposition was based on these modules. The modules where measured individually as far as possible. Some modules where combined to fit the component definition of the energy model (Definition 2). The current draw of the motors cannot be measured directly. Consequently, we compute the power of the motors by measuring the overall power of the quadcopter and subtract the power draw of the other components. The decomposition of the FINken3 quadcopter showed the following individual components. Motorsare modelled through a _Discrete Power Function_ transitioning between deactivated, idle and flying using five parameters: arming \(a\in 0,1\), height above ground \(z\in\mathbb{R}^{+}\) and three axes accelerations \(\bar{x},\bar{y},z\in\mathbb{R}\)\(p_{motor}=(a,z,\bar{x},\bar{y},\bar{z})\). Three cases are distinguished: _Off_ (not armed), _Idle_ (armed and not flying) and _Flying_ (armed and flying). The first two cases are modelled as _Constant Power Functions_ with coefficients \(k_{off}\) and \(k_{idle}\). The third case as a _Continuous Power Function_ in form of a multivariate polynomial of order three with the coefficient vector \(\vec{a}_{motor}\). \[P_{motor}(\vec{p}_{motor})=\left\{ \begin{array}{ll}k_{off},&a=0\\ k_{idle},&a=1,z<z_{idle}\\ \vec{a}_{motor}\left(\vec{p}_{motor},\vec{p}_{motor}^{2},\vec{p}_{motor}^{3 }\right)^{T},&a=1,z\geq z_{idle}\end{array} \right. \tag{8}\]  
Motor Driver and Height Sensorare modelled through a _Constant Power Function_, because these  
Figure 1: Illustrations of the FINken Swarm of Quadcopters Platform. The left figure (**a**) shows a closeup picture of an example FINken3 quadcopter. The right figure (**b**) shows a schematic of the connections of components within the quadcopter. sub-assemblies cannot be switched off:  
\[P_{driver}=k_{driver} \tag{9}\]  
Embedded Autopilot Boardis modelled through a _Constant Power Function_, because the autopilot as the central unit of control cannot be switched off:  
\[P_{ap}=k_{ap} \tag{10}\]  
Sensor Interface Board with attached LEDs is modelled as a _Discrete Power Function_ containing multiple _Constant Power Functions_, because the board itself cannot be switched off, but the eight attached LEDs draw current based on the selected colour and illumination. In the case of the FINken, only specific configurations are used for the LEDs. Four LEDs are used for camera tracking and have static colours, whereas 4 LEDs are used as an identification pattern:  
\[P_{id}(id)=\left\{ \begin{array}{ll}k_{id_{0}},&id=id_{0}\\ k_{id_{1}},&id=id_{1}\\ k_{id_{2}},&id=id_{2}\\ \vdots&\vdots\end{array} \right.