# A Node Placement Algorithm Utilizing Mobile Nodes in WSN and IoT Networks +
## 5 The Energy Node Placement Algorithm
### Energy Models
#### 5.4.3 Moving Energy Model 3  
Many research works on energy models focus on differential drive mobile robots. This type of robot uses a drive mechanism called differential drive. This mechanism consists of two independently actuated drive wheels that are mounted on a common axis. However, each wheel is able to be driven independently, either forward or backward. In order to perform a rolling motion the robot needs to vary the velocity of each wheel but at the same time rotate a point on the common wheel axis. We present two works that focus on different mobile robots, namely the P3-DX robot [28] and the Nomad Super Scout robot [29], respectively; these are popular mobile robots in the research community of energy consumption models. P3-DX is a mobile robot with two wheels driven by two DC motors and powered by a rechargeable battery. Nomad Super Scout robot is a two-wheel differential robot that has an embedded robot controller to control the motion commands and lower-level motors. In [28], [PERSON] et al. start by investigating various energy loss components of the differential drive robots and then present an energy model based on their findings. The experiments were performed with a robot that has four wheels, two that are driven from the DC motors and two that act as casters. The energy model is validated by moving the mobile robot with a specific velocity profile, where all losses have been measured and analyzed. In [29], [PERSON] et al. propose a power model for a two-wheel differential drive mobile robot. The model presented considers the dynamic parameters of the robot, as well as the motors, and it is able to predict the consumption of the robot's energy for trajectories using variable accelerations and payloads. The experimentation was done with the use of a Nomad Super Scout II mobile robot for straight and curved trajectories. The results show that the accuracies of the energy consumption for straight trajectories are 96.67% and for curved trajectories are 81.25%. Based on all of the above work, the following results have been obtained. The overall energy model is given by the equation below after the analysis of all loss components. \[E_{battery}=E_{dc}+E_{kinetic}+E_{friction}+E_{elect}.\]  
Each energy used in the overall energy model formula given above is further explained below. \(E_{dc}\) represents the energy produced by the DC motors of the robot. The DC motors are attached to the robot's wheels and are responsible for converting the electrical energy to mechanical energy. The conversation depends on the losses that occur, such as armature resistance loss, windage loss, and stray loss. As a result, the energy consumption of the DC motors is given by the sum of the armature energy and the energy of other losses that occur. The armature loss energy (\(E_{armature}\)) represents the consumed energy of the armature currents and resistances of the left and right DC motors of the robot. The energy of other losses (\(E_{other}\)) represents the energy of all other losses, such as friction, windage, and stray. It is worth mentioning that the energy of other losses can be disregardedm as shown by the experimental work of the authors. The equation is given below:  
\[E_{dc}=E_{armature}+E_{other}\]  
\(E_{kinetic}\) represents the energy loss where the output power is used in order to increase the kinetic energy and the acceleration of the robot. However, during the deceleration phase, the kinetic energy will be transformed back but, due to heating, a part of it will be lost. As a result, the kinetic energy consumption uses the linear (\(u(t)\)) and angular (\(w(t)\)) velocities of the robot, its mass (\(m\)), and the robot's moment of inertia (\(I\)). The equation is given below:  
\[E_{kinetic}=\frac{1}{2}(mu(t)^{2}+Iw(t)^{2}),\]  
where \(u\) is the linear velocity of the robot and is given by \(u=\frac{r(w^{R}+w^{L})}{2}\), \(w\) is the rotational velocity of the robot and is given by \(w=\frac{r(w^{R}+w^{L})}{2b}\), where \(r\) is the ratio of the robot's wheel and \(b\) is the axle length.