Version vom 25. März 2015, 19:49 Uhr

Abstract

A perimeter wire (or buried wire fence, BWF) is like a 'virtual fence': it stopps the robot when it reaches its boundaries. A perimeter is not always necessary for all surroundings (a lawn sensor might be an alternative).

Principle idea: You will install a perimeter loop (a wire) in your garden through which a signal is sent and this signal is detected by the robot. So, you'll need: a sender (to transmit the on the wire) and a receiver (to detect the signal in the robot).

How is the signal detected? The signal is detected by one (or two) receiver coils. The closer the distance between coil and perimeter loop, the higher the signal strength. Also, something interesting happens when the robot crosses the perimeter loop: the signal changes its polarity, that means positive and negative voltages reverse each other. So, there are two basic principles to detect the perimeter loop. We have implemented both methods (perimeter v1 and v2) which are described below.

Perimeter wire
Components
Signal strength
Perimeter gradient
Perimeter magnetic field

Magnetic field calculator

Videos: Magnetic field demonstration video

Perimeter v1 (for old v0.9.3 code, not recommended)

This was the first version of our perimeter sender and receiver. It has some drawbacks (orientation issues, no sender-off detection, no inside/outside state detection), so it's not recommended to build it anymore. Use the second version (v2) of our perimeter sender and receiver further below.

Sender

You can use the sender of a commercial lawn robot (the sender shown here is compatible with Tianchen or Rotenbach robot mowers), or you build one yourself.

So, here's the sender:

An Arduino (e.g. Nano) generates a square signal that is used to switch the direction of a motor driver (L298N) at 7.8 Khz. Thereby, the motor driver will switch the output between VCC and GND. A resonator circuit amplifies the signal spikes as it's dimensioned so that its resonation frequency is the same as the switching frequency (7.8 Khz). That way, the motor drive only needs to be operated at 5V (instead of 12V). The power supply should be able to supply 2W (400mA at 5V). One part of the signal is captured by the Arduino (ADC) through a diode and a voltage divider. This allows to detect if the perimeter loop is connected or not. A 150 mA current will flow through in the perimeter wire (wire cross section 2-3 mm^2) - the wire should not be longer than 500m.

Because it's sometimes difficult to find a specific coil, here are possible combinations (coil / capacitor) you can use (all will have a resonation frequency of 7.8 Khz):

Combination 1: Coil: 160µH, Capacitor: 3,3µF/50V (tested)
Combination 2: Coil 33mH, Capacitor: 12nF (not tested)

Power supply

It is recommended to use a voltage step-down converter (e.g. module using LM2596) to generate the 5V voltage. Before connecting, set the voltage of the converter to 5V.

Warning : never connect more than 5V on the Arduino 5V pins, or you will damage the Arduino. Therefore, always measure the 5V voltage before connecting it to the Arduino 5V pin!

Functional test

1. After uploading the code and connecting the perimeter wire, the Arduino LED should be ON. Now remove the perimeter wire - the Arduino LED should go OFF. 2. If that doesn't work: Using a voltmeter, measure once at Arduino pin D9 and once at motor driver output pin (OUT_1) against ground - both should have a DC voltage of 2.5 Volt. 3. If you have an oscilloscope, replace the perimeter wire by the oscilloscope. The measured signal look like below:

The output signal shows a higher amplitude (high spikes) as the input signal:

signal on the sender output
resonator circuit basic principle

For a simple receiver test, you can simply connect the receiver coil to an oscilloscope. The measured oscilloscope signal should look like below:

This signal can be detected easily with a coil:

coil signal at receiver coil
signal in frequency spectrum, superposed by motor noise
frequency spectrum via pfodApp

Receiver

The receiver uses 2 coils mounted left and right in the robot. The signal strenght of left and right coils is evaluated to be able to compare them.

Principle:

Amplification of alternating signal using OPAMP
Optional: Bandpass-filtering to filter-out noise caused by motors etc.
Evaluation of signal strength of left and right coil

Advantage of this version: analog controlling works great. Disadvantage: You cannot detect, where you are (inside/outside) if your missed the perimter crossing. Also, you cannot detect if you drive clockwise or anti-clockwise on the perimeter wire.

A coil receives the sender's signal. A resonator circuit (LC) amplifies the received signal at resonation frequency (7.8 kHz). Then the signal is amplified using an LM386 (here: Arduino sound sensor using coil instead of microphone). A bandpass-filter (digital filter, FFT) on the Arduino filters the desired frequency (7.8 Khz) and outputs a PWM signal (pulse width is proportional to signal strength). A lowpass-filter converts it to a DC voltage. Note: Wiring between Nano and Mega has been simplified - see schematics for exact wiring.

We have tested the following combinations of amplifier und coils:

'Arduino sound sensor'

Amplifying signal using LM386 - Arduino Sound Sensor using coil instead microphone
Arduino Sound Sensor using LM386
Arduino Sound Sensor schematics
85 mH coils

LM386 amplifier

LM386 amplifier (200x amplification)
LM386 amplifier modified
LM386 circuit
104 mH coil

Important: When using this amplifier, capacitor C3 should be bypassed (will give a VCC/2 offset required for Arduino) and the coil will be connected to "IN" and "GND".

NOTE: It's recommended to directly mount the coil on the amplifier module. This ensures the 'small signal' of the coil is not distorted by other components (motors etc.)

Functional test

Make sure that the sender works correctly (see further above).
Increase the Arduino Sound Sensor potentiometer to maximum (rotate counter-clock-wise).
After uploading the code, move one coil towards the perimeter wire. The Arduino LED should start to blink. Now, hold both coils at same distance over the perimeter wire. The Arduino LED should be always ON now.
If that doesn't work, open the serial console (19200 baud), and verify the signal values.

Choice for coil

Induction math, only approximation:

L = 1nH x n² x ((D² / mm² ) / (l / mm))
l = coil length
D = coil diameter

Example: An inductance of 85 mH, and diamter of 10 mm, and length of 40 mm require about 5830 windings.

This inductance of 85 mH and a capacity of 4.7 nF results in a resonation frequency of 7963 Hz.

f0 = 1 / (2 * PI * sqrt(L * C)) = 1 / (2 * PI * sqrt(0.085 H * 0.0000000047 F)) =  7963 Hz

Because it's sometimes difficult to find a specific coil, here are possible combinations (coil / capacitor) you can use (all will have a resonation frequency of 7.8 Khz):

Combination 1: Coil: 85mH, Capacitor: 4.7nF  (tested)
Combination 2: Coil 104mH, Capacitor: 4nF (tested)

Arrangement of coils

The coils are arranged at the bottom of the robot, about 90 degress to each other, both turned 45 degress.

Arrangement of coils
Example (Ambrogio L50)
Test parcours

Measurements of signal strength

To compare measurements, the signal strength has been determined at several distances. The signal strength (i.e. the calculated ADC value) is shown in the Android pfodApp. The distance (cm) is the length calculated from the perimeter loop until the coil (coil built-in the robot).

Layout of the wire

It's important that the wire layout is round and does not have corners! Let's assume that the wire has a corner, and the robots drives exactly over the corner, it will not be able to detect the wire as both wire and coils are aligned.

Not recommened: robot cannot detect sharp edges!
How does the signal change when rotating the coil?

Videos

Perimeter v2 (for SVN version, recommended)

https://www.youtube.com/watch?v=NIer_kITelc&feature=youtu.be

This is the new version of the perimeter sender and receiver (that can be purchased via the shop ).

While crossing the perimeter loop, something interesting happens: the signal changes its polarity, that means negative and positive voltages reverse each other. By using this principle, crossing the perimeter wire as well as the current state (robot is inside/outside) can be detected. As with perimeter v1, we will again use a motor driver to amplify the signal and an operational amplifier to amplify the received signal. The perimeter sender outputs a digital code sequence (aka 'pseudo-noise' code), and the receiver will detect that code using a software-based digital matched filter. Depending on wheter the match result peak is positive or negative, the robot is inside or outside of the perimeter wire.

Principle:

Generate output signal by Arduino Nano
Amplify output signal by motor driver (MC33926), motor driver output connected to the perimeter wire (instead of a motor)
Receive input signal with perimeter coil
Amplify input signal with an operational amplifier (aka opamp - LM386)
ADC sampling using Arduino Mega
Signal filterung and signal detection using a digital filter (software-based matched filter algorithmn)
Evaluation of matched filter output (for perimeter inside/ouside detection, tracking etc.)

The images below explain why the polarity of the received coil signal changes between inside and outside of the perimeter wire. The image shows the direction of the electric flux lines sent out from the perimeter wire and how they hit the coil for both inside and outside position.

Inside/outside detection using polarity change
Flux directions

Signal

To receive the perimeter signal everywhere on the lawn, the key is to maximize signal-to-noise ratio (SNR=signal/noise). There are two approaches to maximize SNR:

increase signal strength (power) or
increase the signal length

We use a combination of both. The sender sends a repeating sequence of a digital code ('pseudonoise4_pw') at 9615 Hz :

1,1,-1,-1,1,-1,1,-1,-1,1,-1,1,1,-1,-1,1,-1,-1,1,-1,-1,1,1,-1

'1' means signal a positive pulse, '-1' a negative pulse. Because the shortest signal change generated is '-1,1', the lowest generated 'tone' (if you would make this hearable) is 2404 Hz. The longest signal change generated is '1,1,-1,-1', and so the highest generated 'tone' is 4808 Hz.

The coil only sees 'changes' of the sender signal - so (without using a capacitor in series with the coil) the received signal would be:

1,0,-1, 0,1,-1,1,-1, 0,1,-1,1,0,-1, 0,1,-1, 0,1,-1, 0,1,0,-1

However, using a capacitor in series with the coil, the received signal looks like the sender signal again.

The Arduino ADC samples the receiving signal at 9615 Hz.

Filter

The signal chosen has specific characteristic: it does not correlate in parts with itself - only as a whole sequence (because it looks 'random'). Because of this characteristic, the starts of the signal can be detected by a matched filter (aka 'correlation' with the search signal) and they generate a high peak in the matched filter result, even when high noise was added (due to motors etc.). The polarity of the peak (positive or negative) determines if the coil is inside or outside of the perimeter wire.

You can see how it works: For a better understanding of the perimeter signal and the filter, the matched filter is simulated here: Matched filter simulation

Choose the perimeter signal at the right side (Set slider 'example signals': pseudonoise4_pw).
Increase the noise a little bit (Set slider 'noise' to 2).
At the left bottom plot ('Matched filter') you can see that the repeated signal was detected 3 times.
Now simulate moving the coil outside of the perimeter wire. Click on 'Invert' to set amplifcation to '-1'. The matched filter results a negative match.

Matched filter
What makes a good/bad signal

Sender

Sender circuit
Sender box (example)
Sender signal (open perimeter)
Sender signal (open perimeter)
Sender signal (closed perimeter)

We use a motor driver as output amplifier and an Arduino Nano to generate the signal. The motor driver is driven by 3.2 Khz (two pulse widths 4808 Hz and 2404 Hz). The circuit draws max. 20W (12V, 1.7A). We use a motor driver with integrated current limiting and thermal switch-off (e.g. MC33926). The perimeter wire length should be in the range 20m - 450m.

sender circuit:

 motor driver M1OUT1     o---------- perimeter loop (20-450 meters)--+
                                                                     |
 motor driver M1OUT2     o---------- perimeter loop -----------------+
 motor driver Vin        o-- 12V
 motor driver M1IN1      o-- Arduino Nano pinIN1
 motor driver M1IN2      o-- Arduino Nano pinIN2
 motor driver M1PWM_nD2  o-- Arduino Nano pinPWM
 motor driver M1nSF      o-- Arduino Nano pinFault
 motor driver M1FB       o-- Arduino Nano pinFeedback
 motor driver EN         o-- Arduino Nano pinEnable
 motor driver VDD        o-- Arduino +5V
 motor driver M1D1       o-- GND (via Jumper)
 motor driver SLEW       o-- VDD (via Jumper)
 
               |---------o-- GND
 Potentiometer 100k -----o-- Arduino Nano pinPot
               |---------o-- Arduino +5V
 
 ACS712-05 OUT ------o-- Arduino Nano pinChargeCurrent    
 ACS712-05 A   ------o-- charging pin (+)
 ACS712-05 B   ------o-- battery charger +24V
 battery charger GND-o-- charging pin (-)

Example of sender implementation on a dot matrix board: [1] [2] [3]

Sender perimeter lawn size

At an operating voltage of 12V, the perimeter wire length should not exceed 450m.

Assuming an ideal lawn shape (circle shape), we get a lawn radius:

radius = length / (2*PI) = 450m / (2*PI) = 70 meter

Assuming there is no maximum perimeter radius for good signal quality, the maximum lawn area size (ideal circle shape) would be:

area = PI * (r*r) = PI * (70m * 70m) = 15000 m2

However, assuming there is a maximum perimeter radius for good signal quality of 18m, the maximum lawn area size (ideal circle shape) would be:

area = PI * (*r) = PI * (18m * 18m) = 1000 m2

Sender current control

To increase/decrease the current, the motor driver supply voltage can be changed (e.g. you could use 5V supply voltage for the motor driver instead of 12V). That's one way to do it.

Another way to control the current is to 'PWM' the generated signal which means the signal is switched on and off very quickly resulting in an effective current change. The duty cycle controls how long the on/off ratio is. Duty cycle 100% (duty=1.0 or dutyPWM=255) means no off-time, and duty cycle 50% (duty=0.5 or dutyPWM=127) means 50% off time, 50% on time.

So you have two ways to control the current. For a 50m perimeter wire, I would start with 5V and duty=100%. For my 120m perimeter, I'm using 12V and duty=100%. For my indoor 5m test perimeter wire, I'm using 5V and duty=3%. The duty can be set via the potentimeter connected to Arduino pin 'pinPot' shown above.

You can find the optimum current like this: First set IMAX pot to zero (0), and place robot in the center of the garden. Now, slowly increase IMAX pot, until 'sig' in the pfodApp plot ("Plot->Perimeter") increases (wait 10 seconds). Where 'sig' reaches its maximum, keep IMAX pot setting.

Sender automatic standby

The sender can be switched off during the time the robot is in the charging station. To detect the robot, a current sensor (ACS712) is connected between the charger and the charging pins.

Sender software

NOTE: If you have never worked with Arduino before, read our 'Arduino first steps' introduction.

Note: Always verify that the pin configuration in your Arduino code (sender.ino) matches your actual circuit!

In the sender.ino you have two options:

Define if you have connected a potentiometer for current control: #define USE_POT 1 (or 0)
Define if you have connected a charging current sensor for automatic sender standby: #define USE_CHG_CURRENT 1 (or 0)

Sender diagnostics

The perimeter sender status is indicated by the sender LED (Arduino Nano LED):

ON: perimeter wire loop is closed and working
OFF: perimeter wire loop is opened and not working
blinking: robot is charging and perimeter will be switched OFF (energy saving)

Test sender with your PC's sound card

You can use your sound card to try out the sender with just a coil:

Connect a coil (100 mH) to your sound card microphone/line input (max 1V)
Launch the web oscilloscope, and choose Filter 'Matched', Frequency '9615' Hz, Visualization Math 'MinMax'
The output signal should reflect the distance to your perimeter loop - the polarity (negative/positive) should indicate the side of the loop (inside/outside)

Try to move the coil as close as possible to the perimeter loop (for both inside/outside case) (Keep in mind that this is without pre-amplifier, so the signal will be only valid close to the loop - the microphone input cannot be higher than 1V, so we cannot use the pre-amplifier here).

Actual received time signal (Filter Off, Time scale: x5)
Ideal time signal, generated by sender (Filter Off, Time scale: x5)
Matched filter signal (Frequency: 9615 Hz, Math: MinMax)
What makes a good/bad signal

Video explaining all steps

Receiver

For receiving the signal, we use a coil (100 mH or 150 mH) in upright position (centered at front in robot), connected through a capacitor (4.7nF) to an LM386 operational amplifier (to amplify the received signal). When using the LM386 module, capacitor C3 on the LM386 module should be bypassed (which is needed so that the LM386 generates a signal between 0..5V and not the default range -5V..+5V). The LM386 output pin should be connected to an analog Arduino pin ('pinPerimeterLeft').

The signal output of LM386 should look like this. For more details, see section signal.

Receiver circuit and shortened capacitor C3
One centered, upright coil
Receiver signal
Pulse modulated perimeter signal

receiver circuit:

                                      LM386 IN  o------- capacitor 4.7nF ----------- coil 100 mH  (or 150 mH)
 Arduino pinPerimeterLeft   o------o  LM386 OUT
                                      LM386 GND o----------------------------------- coil

NOTE: It's recommended to directly mount the coil on the amplifier module. This ensures the 'small signal' of the coil is not distorted by other components (motors, DC/DC converters etc.)

Coil

The inductance of 100 mH and capacity of 4.7 nF results in a resonation frequency of 7341 Hz.
The inductance of 150 mH and capacity of 4.7 nF results in a resonation frequency of 5994 Hz.

f0 = 1 / (2 * PI * sqrt(L * C)) = 1 / (2 * PI * sqrt(0.15 H * 0,0000000047 F)) =  5994 Hz

Bandwidth = R / L = 155 Ohm / 0.15 H = 1033 Hz

Receiver ADC calibration

The ADC calibration ensures that the zero point (silence) is detected correctly, and so later the received signal is symmetric around zero.

The perimeter sender and robot motors must be switched off during calibration!
If you cannot avoid that another sender is disturbing during calibration, remove the coil during calibration (connect LM386 input line to GND)
Run the ADC calibration once ("pfodApp->ADC Calibration")

When calibrated correctly, the signal in the pfodApp plot ('sig') should be around zero (0) when the perimeter sender is switched off. When the perimeter sender is switched on, the plotted signal ('sig') should have the same maximum amplitude for both positive and negative axis (is 'symmetric around zero').

symmetric signal when sender is on (after ADC calibration)
zero signal when sender is off (after ADC calibration)

Receiver diagnostics/troubleshooting

The receiver signal, filter result and signal quality can be monitored via Android phone (pfodApp->Plot->Perimeter):

NOTE: Keep away coil/pre-amplifier from DC/DC converters and motors!

Plot signal description:

sig:  coil signal (raw pulse sequence after ADC)
mag:  filter result: inside (negative) or outside (positive), magnitude: distance to perimeter wire/magnetic signal strength (RSSI)
      - this is used for perimeter tracking
smag: filter result, low-pass filtered, without sign (smooth mag) - this is used for 'sender-off' detection
in:   binary result, low-pass filtered: inside (1) oder outside (0) - this is used for perimeter boundary detection
cnt:  number of "inside-outside" transitions (counter)
on:   perimeter sender active (1) or inactive (0), evaluation based on smag result
qty:  filter quality (filter min/max ratio - how distinguisable inside and outside were in filter result - 1.0 means poor quality)

The 'mag' plot should be clear: Inside the perimeter loop, the signal should be a negative curve, outside it should be a positive curve. If your 'mag' curve is not clear, try to troubleshoot/optimize:

Always test using long perimeter wire (20m or longer)
Verify, your coil is connected correctly at 'pinPerimeterLeft'
Minimize cable length between coil and LM386-amplifier (omit cables)
Increase distance between coil and mower motor/DC converter
Add some magnetic shield (e.g. your battery) between coil and motors/DC converter
Adjust sender potentiometer (IMAX): for longer perimeter (>80m) increase, for shorter perimeter (>25m) decrease IMAX
Use 12V sender voltage, if 'mag' values are too low

Videos

Tracking of perimeter

The tracking of the perimeter wire is performed using a (software) digital PID controller. The controller's parameters (P,I,D) can be configured via the phone (pfodApp).

You can find more information about PID controllers here: Forum.

Sensor fusion

The perimeter magnetic field could be used as input for a robot position estimation.

@@ Zeile 373: / Zeile 373: @@
 <gallery>
+ File: Dcdc_noise.jpg | NOTE: Keep away coil/pre-amplifier from DC/DC converters and motors!
   File: PerimeterV2screenshot.png
   File: Perimeter_v2_plot.png

Perimeter wire: Unterschied zwischen den Versionen

Version vom 25. März 2015, 19:49 Uhr

Inhaltsverzeichnis

Abstract

Perimeter v1 (for old v0.9.3 code, not recommended)

Sender

Power supply

Functional test

Receiver

Functional test

Choice for coil

Arrangement of coils

Measurements of signal strength

Layout of the wire

Videos

Perimeter v2 (for SVN version, recommended)

Signal

Filter

Sender

Sender perimeter lawn size

Sender current control

Sender automatic standby

Sender software

Sender diagnostics

Test sender with your PC's sound card

Receiver

Coil

Receiver ADC calibration

Receiver diagnostics/troubleshooting

Videos

Tracking of perimeter

Sensor fusion

Further links

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