J. La Favre Calibrating Sharp Distance Sensors July 18, 2018

Transcription

1 GEAR has a number of Sharp brand IR distance sensors that can be used to determine distance to a target object. This type of sensor can be useful for maze robot projects as well as others. Sharp offers two types of IR distance sensors: analog and digital. This lesson covers the analog type. The analog type sensor outputs a voltage that varies depending on the distance to the target. Figure 1 is a graph of distance vs. voltage output by a Sharp analog sensor that is designed to measure distances between 10 and 80 cm. You will notice that the data points of the graph form a curve. We need to find the equation for this curve so that we can use the equation in our code to convert voltages to distances. This process involves some mathematics you may not be familiar with, depending on your grade in school. Happily, there is an easy solution. You can use computer software to calculate the equation. Figure 1 Sharp 10 to 80 cm distance sensor This lesson covers the use of three spreadsheet programs to graph data and obtain a line equation for a sensor: LibreOffice Calc, Microsoft Excel and Google Sheets. LibreOffice is packaged with the Raspbian operating system of the Raspberry Pi and will be convenient to use. Alternatively, you could use Excel or Sheets. You must have a GMail account to use Google Sheets. In order to calibrate a sensor, you will need to record the voltage output of the sensor at various distances to a target. To obtain the best results, you should take multiple readings at each test distance and average the readings (I would suggest 15 to 20 readings at each test distance). I have also found that best results will be obtained if you power the sensor by a separate battery supply (4 rechargeable batteries in series will provide about 5.3 volts, which is ideal - the sensor must be powered by a voltage between 4.5 and 5.5 volts DC). You can use an Arduino Uno or Arduino Leonardo to control the sensor and collect the voltage readings. Connect the signal line of the sensor (white or yellow wire) to pin A0 of the Arduino. If you are using a separate battery supply, connect it to the power wires of the sensor (positive to red wire and negative to black wire). You should also connect the negative side of the battery to a ground pin of the Arduino so that all grounds in your system share a connection. You will need to upload some code to the Arduino to make your measurements. An example code is provided on the next page. You can use a Raspberry Pi to write the code and upload it. Page 1 of 18

2 Arduino code for recording voltage output from Sharp IR sensor void setup() { Serial.begin(9600); //be sure the S in serial is upper case while(!serial) { // loop stops when serial connection is made ; } // end of while loop } // end of setup() void loop() { String datastring = ""; // this variable stores data to print float value = analogread(0); // read sensor signal on pin A0 float volts = (value / ) * 5.0; // convert to voltage datastring += String(volts); // write voltage to datastring Serial.println(dataString); // print the voltage to serial monitor delay(1000); // wait one second, then repeat } After you have uploaded the code to the Arduino, and with the sensor connected to the Arduino, you are ready to take measurements. In the Arduino IDE software running on Raspberry Pi, select Serial Monitor in the Tools menu. If all goes well, numbers will begin to appear in the Serial Monitor. These are the voltage readings, one reading done every second. Remove the checkmark for Autoscroll in the Serial Monitor. Drag the mouse over the numbers in the Serial Monitor and then press Ctrl + C on keyboard to copy the numbers. Paste the numbers into a text file. Make sure to include a note with the numbers to indicate the distance to the target for the set of voltages. Then close the Serial Monitor. Adjust the distance to your target and repeat the procedure to collect another set of measurements. Repeat until you have measurements for a set of distances to the target in the range of the sensor. For the Sharp 10 to 80 cm sensor I took measurments at the following target distances: 8, 10, 12, 14, 16, 18, 20, 25, 30, 35, 40, 50, 60, 70, 80 and 100 centimeters. You will need to take the average of all voltage readings for each distance. A convenient way to do this is with a spreadsheet program. Here is how it is done with LibreOffice Calc (see next page). Page 2 of 18

3 Copy the voltage readings to the spreadsheet, making sure that each set of readings includes the distance to target at the top of the column (see Figure 2). Figure 2 Click the mouse in the cell just below the first column of data (see Figure 3). Figure 3 Click the fx button (see Figure 4). Figure 4 Page 3 of 18

4 Figure 5 In the Function Wizard box (Figure 5) select AVERAGE. Then click the Next button. Drag the mouse down the first column of data to select all voltage readings. Page 4 of 18

5 Figure 6 The Function Wizard box should now be similar to Figure 6 (there should be a range of data cells listed after AVERAGE. Click the OK button. The average value should now appear at the bottom of the data column as in Figure 7. Carefully position the mouse cursor over the small square at the bottom-right corner of the selected cell. Figure 7 When the mouse cursor changes to a + symbol, click and drag the mouse to the right to highlight all cells underneath the columns of data. This will result in averages computed for each column of data (see Figure 8 on next page). Page 5 of 18

6 Figure 8 Now that you have computed the average voltage of the sensor at several target distances, you are ready to graph the data and find the equation that fits the data. Let's start with LibreOffice Calc. If you would rather use one of the other spreadsheet programs, skip down to the section that describes the software you wish to use. Graphing the Data with LibreOffice Calc Open LibreOffice Calc (click the Raspberry, click Office, click LibreOffice Calc). Enter the data into the spreadsheet. You can use the data in Figure 9 for practice if you like. After you have completed entering the data, drag the mouse to select (highlight) all of the data table cells as seen in Figure 9. Figure 9 Open the Insert menu and click on Chart. The Chart Wizard will open (Figure 10) Page 6 of 18

7 Figure 10 In the Choose a Chart Type list, click on XY (Scatter) to select it as the chart type. Then click the Finish button. A graph should now appear in your spreadsheet. With the right mouse button, click on one of the data points in the graph. A menu will open. Select Insert Trend Line. In the Trend Line box (Figure 11), select Power as the Regression Type. Then click the check box for Show Equation. Then click the OK button. Figure 11 Page 7 of 18

8 Figure 12 Now you should have a graph that looks similar to Figure 12 above. Notice that an equation for the curved line is included on the graph. You will need to copy this equation down so that you can use it in your code. In this case, f(x) is the same as the distance in centimeters. The equation can be expressed as follows in a more compact form: distance in cm = * voltage Here I am using the asterisk character (*) as a symbol for multiplication. The (^) symbol is used in the graph to indicate an exponent or power. For example, 2^3 would be the same as 2 cubed or 2 3. Two raised to the third power is 2 x 2 x 2 = 8. You may not be familiar with numbers raised to a negative power, as you see in the above equation. This will be explained in the Using the line equation section. You can now skip down to the Using the line equation section on page 18 to learn how to use this equation. Page 8 of 18

9 Graphing the Data with Google Sheets Log in to your Google account and click on the menu button (arrow 1) then click on Sheets (arrow 2). Figure 13 Click on Blank to start a new spreadsheet. Figure 14 A blank spreadsheet will appear on the screen. Click on Untitled spreadsheet and give your spreadsheet a name (for example: Sensor # 6 calibration) Figure 15 Page 9 of 18

10 You will now need to enter the data to graph. Below is an example you can use for practice. volts cm Drag your mouse to select all of the cells of the data table as illustrated in Figure 16. Figure 16 Page 10 of 18

11 Open the Insert menu and click on Chart. Figure 17 A graph should now appear on the page, but it may be covering some of your data table. If so, drag the graph to a blank portion of the spreadsheet. In the Chart editor box, click on the drop-down for Line chart (black arrow, Figure 18). Figure 18 Page 11 of 18

12 Click on the chart type labeled cm vs volts (the one marked with black arrow in Figure 19). Figure 19 Now close the Chart editor box. Then double-click on one of the data points in the graph, which should open up the Chart editor again. The Chart editor should now appear as in Figure 20. Click in the Trendline checkbox to select it. Figure 20 Page 12 of 18

13 Open the Type drop-down and select Power Series (Figure 21). The curves for the Sharp analog sensors are of the power type. Figure 21 Open the Label drop-down and select Use Equation. Figure 22 Now the equation of the line will appear as part of the graph legend (black arrow in Figure 23). The software has calculated the equation of the line for you! [skip the MS Excel section and go to the Using the line equation Figure 23 section on page 18 ] Page 13 of 18

14 Graphing the Data with Microsoft Excel Open Excel and save the spreadsheet with a descriptive name (for example calibration_sensor_6). You will now need to enter the data to graph. Below is an example you can use for practice. volts cm Page 14 of 18

15 Drag the mouse to highlight all cells of the data table in Excel (Figure 24). Figure 24 Figure 25 Select the Insert tab (Figure 25). Then select the Scatter graph type (black arrow, Figure 25). A graph of the data will now appear on your spreadsheet (see Figure 26 on next page). Page 15 of 18

16 Figure 26 Click the Add Chart Element button. In the menu that opens, select Trendline. In the sub menu that opens, select More Trendline Options. Figure 27 Page 16 of 18

17 In the Format Trendline box, select Power as the Trendline Option. You should now notice that a line has been drawn between the data points on the graph. Figure 28 Figure 29 Near the bottom of the Format Trendline box, click in the check box for Display Equation on Chart. The equation for the line will now appear on the chart. You may need to drag the equation to a clear portion of the chart. The equation font size may be small. If it is hard to read, you can copy the text and paste it into a cell below the chart. Then change the font size so that it can be read easily. Using the example data, Excel provided the following equation: y = x Compare this to equation from Google Sheets: y = 25.3x And LibreOffice Calc: y = x All three spreadsheets found the same equation, although the equations provided by Excel and Calc have more significant figures. For our purposes, any of the three software solutions will work just fine. Page 17 of 18

18 Using the line equation Okay, you may be wondering how to use this equation. Let's express the equation like this: distance in centimeters = (25.3) (volts ) You may not understand the meaning of volts raised to a negative power if you have not covered this in math class yet. Raising the volts to a negative power is the same as creating a fraction with one over the voltage to the positive power. Let us take the example of 2.25 volts, which is the signal measured from the sensor when the target is 10 cm distant. If the target distance is unknown, how do we calculate the distance from the voltage? 1. raise the voltage to a power of You can do this with a Windows calculator or other calculator that has a function of X Y (you may need to set the calculator to scientific mode). Suppose we want to calculate enter the number 2.25 press the X Y key enter 1.15 press the equal key. The answer is [I used a Windows calculator] 2. to convert to a negative power, just place a one over the answer: 1/2.541 = distance = (25.3) (0.3935) = 9.96 cm In the data table on page 6 note that a voltage of 2.25 was developed by the sensor when the target was at a distance of 10 cm. Now notice that the calculated distance from the equation worked out above is 9.96 cm, very close to the value of 10 cm. This demonstrates the utility of calculating distance from an equation. Example Arduino Code using the equation (see lesson on using Sharp distance sensors for more details) float value = analogread(0); // sensor connected to analog input pin 0 float volts = (value/1023.0) * 5.0; //convert 10-bit A/D value to volts by dividing by then multiply by 5.0 float distance = (25.3) * pow(volts, -1.15); // apply the line equation to convert to distance Page 18 of 18