This paper proposes a method to reduce the error on the position given by the global position system (GPS), using a back-propagation arti cial neural network (ANN) focused on a known linear path employed as target, which is used on the creation of path planning for an Unmanded Aereal Vehicle (UAV) tested on real time. This document shows the step by step development of the equations used and the algorithm for trigonometric functions and then to a lineal path made by a path planning code. The implementation of this project was made on Python for real time ight in which the GPS data are acquired and graphed to analyse results.
Programming control of autonomous paths for UAVs, nowadays, has been
difcult for the inaccuracy of the received signal from the global position system
(GPS); [
Jha, Chattopadhyay, [
Nieuwenhuisen, M [
An arti cial neural network is used to reduce the error given by the global
position system [
During the tests that were carried out to feed the arti cial neural network
and establish knowledge, a linear path followed by a thread was conducted; the
data acquired by the GPS of the UAV is stored in real time On this project the
GPS device is used [
The mathematical method developed here, proposed by Aguado [
We used the back-propagation arti cial neural network shown on Fig. 1; to use this, we must make a standard data input and output in the range 0-1. To declare "bias" as random numbers, the input given to the network are values di erent to zero. A sigmoid function is used as activation function, then the output of the neuron | of the hidden layer is expressed as: Excitation of the neuron k of the output layer is calculated analogously by the expression: and nally, the output of the neuron k of the output layer is expressed as: n Sjp = X Wipj xip + Wnp+1;j
i=1 hjp = f (Sjp) =
1 1 + exp( Sjp) rkp =
l X vjpkhjp + vl+1;k
p j=1 Okp = f (rkp) =
1 1 + exp( rjp) (1) (2) (3) (4) We now de ne the output error k, for sample p as: The criterion to be minimized in the sample | is de ned by: epk = ykp
Okp m m Ep = 21 X(epk)2 = 21 X(ykp
p 2
Ok) k=1 k=1 (5) (6)
The training process of the neural network consisted in presenting the inputs
sequentially, calculate the outputs on the network, the error and the citerion
E, and to apply the procedure to minimize the function error; the procedure
is to always move in the direction of the negative gradient of the function with
respect to the coe cients w and v, this is called "steepest descent", [
The mathematical method was implemented with MATLAB R2014a. In this tool the equations are written and adapted to the language to estimate any given function, for number of samples on the network, for number of periods, for learn coe cient between 0 and 0.9 and for any neuron number |. This is represented on the algorithm shown below: Algorithm 1: 1. Compute number of samples 2. Compute function 3. Convert sigmoid function data 4. Compute periods, learn coe cient and neuron number 5. While: ep Number of periods 6. ! For i = 1: neuron number 7. ! ! hjp = f (Sjp) = 1+exp( Sjp)
1 8. ! For i = 1:neuron number 9. ! ! rkp = Plj=1 vjpkhjp + vlp+1;k 10. ! Error = (T arget
Okp = f (rkp) = 1+exp( rjp) ) 1 11. ! For i = 1:neuron number 12. ! ! using vjpk = vjpk 1 + kphjp 13. ! For i = 1:neuron number 14. ! ! using wipk = wipj 1 + jpxip 15. ! For i = 1:neuron number 16. ! ! using hjp = f (Sjp) = 1+exp1( Sjp) 17. ! For i = 1:neuron number 18. ! ! using rkp = Plj=1 vjpkhjp + vlp+1;k 19. ! using Okp = f (rkp) = 1+exp1( rjp)
Okp 20. ! using epk = ykp 21. ! ep = ep + 1 22. mse = mean((N sal 23. Plot
T arget):2) You can nd this MATLAB code on: https://drive.google.com/open?id= 0B6xtNWuLHIRMT2U0c0gtbG1MNDg 4
For any trigonometric or lineal function with one variable, we can use the last algorithm, in which the number of tests corresponds to the amplitude of the graph or the number of tests to be estimated in the ANN. Trigonometric functions such as sine and tangent were tested in order to verify the behaviour and the mean squared error (mse).
To match what we have done at the time, for path planning using global positioning data it is necessary to know the starting point and end point of the desired path. Once obtained these data, we can create our lineal function full of points to match with the quantity of inputs as Target, with the input data obtained from the global position system. After knowing our target input data and our data target we can create our arti cial neural network.
The path planning works like a multithread algorithm. The rst thread named "data acquisition" is responsible for sending a command to update the UAV and to perform the most frequent calculations updating these data with global variables.
The second thread named "acquisition and writing sample", performs veri cation of existence of strong GPS signal and checks the level of battery charge, and once all data is correct, it starts the storage of the sampling information such as latitude, longitude and height above ground. The third thread named "Commands sender" is the UAV control; it generates a virtual barrier between the current point and the next point, checks that the angle is physically relative to the angle generated against the GPS point and it sends the UAV motion commands to perform the route.
In tests to feed the neural network and establish knowledge, took just by
walking in a straight line followed by a thread ensuring that is kept as straight
as possible, while advancing, the data acquired by the GPS device are saved,
on this project a only the GPS devise is used [
For testing was used the UAV from Parrot company the Bebop 1, the
programming language was Python, to establish communication and commands sending
was used the library of Martin[
After feeding the ANN we can see the behaviour (Fig.4) taken by the estimation of the back-propagation arti cial neural network who is very similar to the established straight as target with an mse = 7:651903681967e 05.
Once the ANN was trained, we took the synaptic weights and implemented them in the path planning algorithm modifying the original data given by the GPS, as shown in Fig. 3. To test physically this algorithm three ights were tested as shown in Fig. 5, with the same GPS points to reach for all(Table 1) and with uncontrolled weather conditions using a ight algorithm of path planning by GPS; we can compare the improvement in accuracy with respect to the data given by the GPS (left side without feedback of the ANN and right side with feedback). The sample data is acquired by generating a le in real time by saving the current global position of the UAV every second elapsed to be interpreted and plotted later.
The same algorithm for path planning was used in all tests. In Fig. 5 red circles represent points target of the path planning algorithm. On the left side we have an error in circumference of about 10m (32.8ft); on the contrary, on the right side (which uses the estimate of the ANN), an error to the circumference of 1.5m (4.6ft) was obtained. During the ight, this was measured by placing ags on the testing ground in the points shown in Table 1.
In this document we studied a method of reducing the error given by the GPS using path planning algorithm for UAVs. The ANN back-propagation algorithm predicts the location of the UAV giving a start point and an end point to generate a straight line that breaks down into the number of data provided by the GPS. As the UAV moves, the algorithm predicts its location with respect to the learned error and the point at which it encounters respect to the line, thus giving a smooth and accurate point to point travel. It is noteworthy that the tests were taken on a eld without climate controlled conditions and without obstacles in the path of UAVs. A sampling time of one second is considered, as the calculated processing time for this algorithm (in a conventional system) is greater than 0.5 and less than 0.8 seconds.
Our future task is to compare this method and implement a Kalman lter [