^{1}

^{2}

^{3}

^{2}

^{2}

^{4}

Through the creation and construction of a curvature sensor of accelerometer type, using the spectral curvature concept or curvature energy that measures curvature in Volts/m
^{3}, an autonomous and mobile censorship of curvature sensing with reliable data transmission/reception in real time and remote position is designed and constructed considering the spectra of curvature of the measured curvature energy during the advance of the prototype as the normed measure by
with
β , a constant rationalized parameter according with the required advance of the mobile device in the control scale of their velocity. Likewise, the sensed curvature data are digitalized through wireless interconnectivity using a HC-05 Module with a programmable device that includes logic blocks whose interconnection and functionality can be configured according to the sensor measure
in situs. Also an application is planted to the obtaining of an energy plus due to the curvature that could be used in the displacement of a vehicle.

Along several researches and works on integral geometry theory to field observables as curvature and torsion of the space, we have constructed an adequate energy integrals theory obtaining important results to international level of curvature given as smooth embedding of a differential sub-manifold given in co-cycles [

[

tial energy of curvature (in this case voltages)^{1}; A, is the area of the surface and h, their mean curvature and the last integral corresponds to the curvature energy employed to measure the roundness in their displacement along a principal direction. Applying certain cycles as Gaussian pulses which are measured invariant of curvature, we obtain the corresponding energy co-cycles that are curvature information “in situs” of the curvature sensor designed to first prototype of this type.

In the development of the different prototypes of curvature sensors and their study [

The communication problem that arises is in the wireless interconnectivity which must be synchronized with the displacement of the mobile curvature sensor, furthermore considering the elimination of possible vibrations that can be transmitted to the mobile curvature sensor due to the proper ground, and that could be included as noise in the curvature data that are transmitted to their exploring. The autonomy and independence must be two characteristics necessary to the remote development of the prototype considering their stability, mechanical robustness which will be characterized by their traction as continuous function of displacement and of the direction change of the mobile curvature sensor. Our curvature sensor is obtaining a Gaussian curvature through electrical pulses (electrically gauged [

The wireless interconnectivity must obey a relation between the transmission/recep- tion of spectral curvature which must be a continuous transformation in a ^{2} of

where ^{3} [

The independence traction in the four tires to the mobile system of the curvature sensor reduces the vibrations offsetting the mass forces that are produced by the vibrations and that these can be transmitted to the sensor, that is to say, create an anisotropic elastically system, where the deforming and stress mechanisms in the inner as well as

outside the mobile system not have inherence in the field observable measure. The spectral curvature is not deformed or noise contaminated. For it, we can consider an equilibrium equations system that will be constructed starting from the structural equations of curvature through of the field of observation^{4} (field of reference systems).

Then we will focus our study to the velocity advance of our mobile prototype which will be conditioned to the data Wi-Fi-transmission or data Bluetooth transmission velocity of our curvature sensor. As we want a constant data transmission then the velocity of advanced will be constant too. One our problem will be design a control of velocity in the mobile prototype such that the velocity field created by the reference systems field, obeys the fundamental equation

As a second problem that we want to solve and improve is on the energy optimization, where at the same time be measured the curvature could be used their curvature energy for optimization and performance of own sensor system, and have the better functioning of this.

The regularity problem must to be normed by the transmission velocity problem, which from a point of view of functional analysis has that see with order of a constant that must bounded the norm of the derivative to certain order.

In a transmission problem of the mobile devise the velocity of feeding of reference system field data must be normed by the velocity of the displacement of the device such that this last velocity is constant.

Lemma (regularity) 2.1.

The velocity of response of the curvature sensor must be minor or equal to a constant^{5} (that is to say, a multiple factor of displacement).

Proof. We consider the spherical mapping over

with rule of correspondence

It’s necessary to prove that to the curvature signals detected by our curvature sensor their data transmission velocity must be bounded by a constant along of the space walked made by the sensor in movement, that is to say, their displacement velocity. First we must to prove that the process of transmission is given as continuous transformation of curvature energy data to the corresponding inverse problem. After, we use this to find the bound of velocity in this curvature context or geometrical context.

We consider the curvature integral operator as the spectral curvature in the direction^{6}:

But we need verify the transmission process mobile sensor system-micro-controller, that is to say, the convolution ^{7}. Then considering (5) we have:

But

All processes are bounded to the transmission velocity, which takes as reference the velocity of the shape operator where this last defines implicitly the curvature.

The scaled gravitational energy used in the process of gauging of sensor mobile advance corresponds to the measured and gauged by the proper universal gravitation and considered by the spherizer operator

Theorem (F. Bulnes) 2.1. (Scaled Gravitational Energy to Curvature Sensor advance^{8}).

Let be the Einstein equations:

Let be the spherizer operator ^{9}

Then the scaled gravitational energy of the curvature sensor advance certain length

Proof. The scaled gravitational constant is

which is the proportionality between space-time curvature and energy (see the

Due to the symmetry of sphere,

We consider the curvature signals (curvature energy) in real time ^{10}. We consider a curvature energy obtained in the spectra of energy constructed through Gaussian pulses [

Then the optimal signal in the transmission process will be the PWM resultant signal of plane ridge obtained in the sampling of the curvature energy signal (see the

Due to the equation

line exist slopes to upwards and downwards ensuring that the data transmission of the curvature sensor device to the wireless receptor device that is reliable.

Now to the control process of velocity to the vehicle of our mobile curvature sensor we have the diagram (

Likewise, if

where

where to simplify the compute of data, we can have square pulses in our sampling, considering the condition

Proposition 3.1. The curvature ^{11}:

where

(see the Figures 6-9).

We establish the bordering conditions. The velocity of the mobile servosystem that carries the sensor device (accelerometer) is considered minor much that the transmission velocity

where

Likewise, to norm the velocity of the mobile servo-system we use the linear displacement that arise in the theoretical analysis of our energy integrals given in Equation (7) and applying this to a displacement in one direction. Then the velocity servo-system must to comply the following system equations:

where

where ^{12}

where

We consider the following analysis of velocity and torque in motors. Let the equation system of motors:

Substituting the voltage expression from (16) in (14), and considering the velocity transference function of each motor:

to obtain the linear velocity with 0.06 m of radius of the wheels, (see

We obtain (see blue line in the (

Now the torque will be:

The dynamical analysis shows that the velocity is expressed in terms of the current through (19). The servo-system that is showed in the block diagram in Simulink is a CD motor of unique phase mechanically coupling to a rotational-traction system that finally as output variable is a velocity in constant straight line (see the

The automata being in their travel through a slope in ascent requires major traction force thus their feeding of the motors requires in their corresponding width modulation of pulse, major time in high voltage state that implicitly is available as electrical current necessary that demands the proper servo-systems in ascent (see the

For other way, the contrary case in the moment of decline is required the decreasing of the velocity because is reduced the pulse width in high voltage state, such that the motors to not receive constant voltage then their velocity decreases to compensate the velocity that the servo-system sums when for gravity tends to go down (see the

The modulation of pulse width PWM, whether in raising or lowering has variation, and exists a relation of this signal with the inertia of the servo-system in their constant movement and thus also with the variation of the electric field inside the sensor device due to their respective variable capacitance according the position that this has, which is translated in curvature measure (see the

In laboratory the before analysis is verified and proved (see the

Due to the covering of field energy the data transmission of curvature energy will be given in bluetooth transmission whose decoding module use the energy interval [

The Bluetooth HC-05 module, is the that offers a best relation of price and functioning characteristics since is a master-slave module, which want to say that furthermore of receive connections from a PC or tablet, also is able of generate connections to other Bluetooth devices. This permit us, for example to connect two Bluetooth modules and form a connection point to point to transmit data between two micro-controllers or devices, as could be the case in our mobile curvature sensor [^{13}.

Communication via Bluetooth from a cell to the FPGA to test obtaining bits sent. Android application is made, the application is installed cell and connects to the HC-05. Given the connection a program structured VHDL is made to connect with the Bluetooth module and therefore the information as programmed in the FPGA is processed. The data output ports of the FPGA are sent. Physically they show each bit by LEDS [

The serial data transmission allows the scope of the data is greater, since the form of higher performance parallel transmission system and transmission range is less demand. The RS-232 communication is made to review and store data processing on the computer, an interface defined chart in order to visualize the bits of information, which in turn are stored to be analyzed late [

The tests and rehearsals in laboratory show the binary encoding using the transmission optimization characterizes signed in the curve (

1) It requires two HC-05 Bluetooth modules for transmission and reception of data from the PLC (see the

2) FPGA is required for processing the data obtained. A USB-SERIAL wire is used for the connection the FPGA to computer (see the

3) A computer with a hyper-terminal program is required to achieve RS-232 connection of the FPGA and store the acquired data (see the

The transmission optimization will be normed by the energy coefficients to the digitalized signal of ^{14}:

which is the optimal way of data detection when the received signal could be corrupted for additive white noise. Here the coefficients (21) represent the digital data ready to be become them in binary codes [

The gravitational energy factor to design an accelerometer to a universal curvature sensor brings with it an “available” energy factor for the proper curvature in any curved space (included the Universe) bringing profit as “energy plus” to the proper mobile curvature sensor device. Likewise, due to the problem transmission optimization of curvature data we can enounce the following

The future work of this research will design other devices of solid state that realize this profit of energy using the curvature energy obtained in downs and ups, or due to the positioning of the mobile device in the space (see the prospective to an advanced design of energy curvature sensor in the Universe to measure their curvature installed in an aerospace ship).

As it has been said, in the Section 4, and through the modulation analysis of pulse width PWM, the variations in raising or lowering show a relation of the signal with the inertia of the servo-system in their constant movement (see the

We can conclude that the synchronization problem in the transmission process (movement of curvature sensor and the data transmission problem) stays normed by the lemma of regularity 2.1, which must establish as norm of the device displacement velocity such that this last velocity is constant.

Complete Energy System | |||
---|---|---|---|

Energy Amplitude | Wave Type | Band-width | |

1 | |||

2 | |||

3 | |||

4 |

The next research that will be realized is the adjustment of constant movement of the mobile curvature sensor device and will be used to realize a terrestrial relief exploring to data of their curvature and obtain a curvature map. Finally the circuital optimizing of the sensor will be searched to increase their profit or yield in energy, and likewise decrease their loss of energy due to the heat or their transmission efficiency due to the electromagnetic scattering or signal dissipation.

We are very grateful with Edgar Daniel Sánchez Balderas, Law B, Principal of TESCHA, Evaristo Vázquez, Hernández, LC, B, Financial Sub-principal, and Rene Rivera Roldán, Electronic Eng., Electronic Division Chief, by their material support and facilities to realize this research.

Bulnes, F., Martínez, I., Cayetano, R., Zamudio, O., Gutierrez, C. and Martínez, I. (2016) Autonomous and Mobile Prototype of Curvature Sensor with Remote Reliable Communication of Spectral Curvature. Journal of Sensor Technology, 6, 159-179. http://dx.doi.org/10.4236/jst.2016.64012

USB-SERIAL―Storage-connection cable to binary signal recollecting.

FPGA―Field Programmable Gate Array. This is a programmable device that include logic blocks whose interconnection and functionality can be configured “in situs” through a language of specialized description.

ASCII―American Standard Code for Information Interchange. Also named usually as “aski code”, which is a character code based in the Latin alphabet, such as is used in modern English

TTL―Technology model based in “logic from transistor to transistor”, (transistor-transistor logic).

PCL―Programmable Logic Controller.

Bluetooth HC-05 Module―It’s data transmission system of master-slave module, which has advantages in intercommunication in a closed electronic system.

GPIO―General Purpose Input/Output. It´s a generic pin in a chip, whose behavior (including, if is an input or output pin) can be controlled (programmed) by the user in time of execution.

Cyclone II―Electronic platform or board with low cost and optimized feature set of FPGAs make them ideal solutions for a wide array of automotive, consumer, communications, video processing, test and measurement, and other end-market solutions. Reference designs, system diagrams.

RS-232―Recommended Standard 232. Also known as EIA/TIA RS-232C, is an interphase that designs a norm to the interchange of a binary data series between a DTE (Data Terminal Equipment) and a DCE (Data Communication Equipment), although exist other in the that also is used the interphase RS-232. Also is known as V.24.

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