# A Node Placement Algorithm Utilizing Mobile Nodes in WSN and IoT Networks +
## 5 The Energy Node Placement Algorithm
### Energy Models
#### 5.4.2 Moving Energy Model 2  
In [26], [PERSON] et al. present a novel energy model for mobile robots that can be used to calculate and predict their energy consumption. The main idea is to provide an energy model to be used for energy-efficient strategies. The mobile robot used for the experimentation of this work is a Mecanum. A Mecanum [27] is a four-wheeled omni-directional mobile robot. An omni-directional characteristic describes the ability to move instantaneously in any direction without considering the configuration. This type of robot is able to move sideways, follow complex trajectories, and turn on the spot, as well as perform tasks with both static and dynamic obstacles. This mobile robot uses mecanum wheels, which are similar to the universal wheels except for their rollers being mounted on angles. The energy consumption of the robot is divided into three parts: (a) the sensor system, (b) the control system, and (c) the motion system. Each part defines its own energy consumption and all together defines the total energy consumption of the mobile robot. The energy consumed by the sensor part is almost stable and is defined by multiplying the electrical power (\(P_{sensor}\)) and time (\(\Delta t\)). The equation is given below:  
\[E_{sensor}=P_{sensor}\cdot\Delta t\]  
The energy consumption of the control system depends on the power of the control circuit board and is related to the robot's running state. A robot's running state can be divided into three states: the standby state, the start to move state, and the smoothly run state. Each state has its own energy consumption formula, which is given below and is used based on the current state of the robot. \[E_{control} \begin{cases}E_{standby}=P_{standby}\cdot\Delta t\\ E_{startp}=\int(\phi\cdot\Delta u+(\frac{t}{t0})+P_{standby})dt\\ E_{stable}=\int(P_{standby}+t^{2})dt.\end{cases} \]  
The energy consumption of the motion system can be divided into four parts: the traction energy consumption, the kinetic energy, the friction energy dissipation, and the energy dissipated in thermal form. The motion of a robot is divided into three stages: standby, startup, and stable. In the standby stage, the power is constant. In the startup stage, an instantaneous pulse is needed in order to send the signal to the electric motor. Additionally, when a robot is on the move, it enters the stable operation stage. The energy consumption of the motion system is given below:  
\[E_{motion}=\int P_{motion}dt=Ek+Ef+Ee+Em.\]  
Each energy used in the motion energy formula given above is further explained below:  
* \(Ek\) is the kinetic energy of the robot. To calculate the kinetic energy, the mass of the robot and its speed at the current moment are needed and is given by: \(Ek=M\cdot u^{2}/2\). * \(Ef\) is the friction dissipation during the robot's movement. To calculate this energy, it is needed to know the mass, the speed at the current moment, and the friction coefficient between the wheel and the ground, and is given by: \(Ef=\int(\mu\cdot M\cdot u)dt\). * \(Ee\) is the energy dissipation as heat in the armatures of motors. To calculate this energy, it is necessary to know the time-heat constant and the speed-heat constant of the robot, as well as the time and speed and is given by: \(Ee=\int(e\cdot t^{2}+\sigma\cdot u+\lambda\cdot t)dt\). * \(Em\) is the mechanical dissipation that is caused by overcoming the friction torque in the actuators. To calculate this energy, it is necessary to know the drag coefficient of the robot itself and the vibration velocity coefficient and is given by: \[Em=\int\Big{[}M\cdot e^{Qt}\cdot\cos\Big{(}\psi\cdot t+u+\Big{(}\frac{M}{2} \Big{)}\Big{)}+M\Big{]}dt.\]  
The results show that the proposed energy model can be used by mobile robots to predict the energy consumption of its movement processes. In general, this work presents a complete model that connects all parts of a mobile robot and provides a feasible and effective model.