A Robot Scorpion Using Ground Vibrations for

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Anders Wallander

A Robot Scorpion Using Ground Vibrations for

Navigation

2000:316

MASTER'S THESIS

Civilingenjörsprogrammet Elektroteknik Institutionen för Systemteknik Avdelningen för Industriell elektronik

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A Robot Scorpion Using A Robot Scorpion Using A Robot Scorpion Using A Robot Scorpion Using

Ground Vibrations for Ground Vibrations for Ground Vibrations for Ground Vibrations for

Navigation Navigation Navigation Navigation

Anders Wallander

Civilingenjörsprogrammet Institutionen for systemteknik

Avdelning for Industrell elektronik och robotik

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Abstract

Robotics can learn a lot by investigating simple and effective techniques

evolved in biology. The sand scorpion that lives in the Mojave Desert uses

ground vibrations when locating its prey. This thesis work shows that a robot

can be made to navigate using similar techniques as the sand scorpion. A six-

legged robot was constructed and fitted with vibration sensors to try the

concept. A robot navigating with the help of ground vibrations could be used

in applications such as the search for victims after natural disasters. This

report presents the hardware design, algorithms for direction and location

finding of a vibration source, simulation results and the performance of the

direction finding system fitted on the robot.

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Preface

This Master Thesis work was conducted at the Intelligent Robotics Research Centre at Monash University in Melbourne, Australia. The thesis concludes the M.Sc. study in Electrical Engineering at Luleå University of Technology.

The main goal with this thesis was to design and build a small robot which will be able to detect and react intelligently to ground vibrations caused by footsteps of surrounding humans or animals.

The Intelligent Robotics Research Centre, within the Department of Electrical and Computer Systems Engineering at Monash University, is Australia’s foremost centre for research in sensory based robot control including robotic “hand/eye” coordination and autonomous mobile robot navigation in unstructured environments. The machine perception aspects of this research includes vision, tactile, force/torque, ultrasonic, olfactory and thermal sensing in an intelligent robotics application context. The research efforts are largely driven from a sensory instrumentation, computer systems and artificial intelligence perspective but with some mechatronics expertise as well.

Acknowledgements

I wish to address my acknowledgements to Andrew R. Russell, my

supervisor at Monash University, and Kalevi Hyyppä, my examiner at Luleå University of Technology, who both gave me advice and encouragement during this thesis work.

I am grateful to all the people in the electronic and the mechanical workshop at Monash University for their invaluable help during the construction of the robot.

Finally I would like to thank Sven Molin, at Luleå University of Technology, who encouraged me and worked hard to make it possible for me to do my thesis work at Monash.

Anders Wallander

Melbourne, July 2000

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1 Introduction

Several animals use substrate vibrations for navigation, for example the sand scorpion, the trapdoor spider, the lion ant and the fiddler crab [5]. After a closer look at the sand scorpion, which lives in the Mojave Desert, USA, it was decided to investigate if it would be possible for a robot to use ground vibrations to help locate a source of vibration. Possible missions for such a robot could be helping in the search for avalanche and earthquake victims.

The sensors on the robot could pick up substrate vibrations created by taps in the ground made by the victim and help direct the robot towards the victim.

Another application would be to act as a watchdog to detect intruders.

1.1 Goal

The main goal with this thesis was to design and build a small legged robot which should be able to detect and react intelligently to ground vibrations caused by footsteps of surrounding humans or animals.

1.2 Outline

The following chapter presents the literature survey, which investigates if similar robotic projects have been made. It also discusses the behaviour of the sand scorpion and finally describes the nature of seismic waves. Chapter 3 is concerned with the research and design of the vibration detectors.

Chapter 4 presents two navigation algorithms, one detecting the bearing of

the source of vibration and the other the exact location, given that the

vibration source is in the vicinity of the robot. Simulation results are also

presented in this chapter. The design of the robot is described in chapter 5. In

chapter 6 the software design is described and in chapter 7 the performance

results are presented. Finally chapter 8 presents conclusions and a discussion

of possible future work.

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2 Background

This chapter presents an investigation on similar robotic projects. It also discusses the behaviour of the sand scorpion and finally describes the nature of seismic waves

2.1 Similar Robotics Projects

When robots interpret their environment, senses such as vision, touch, smell and hearing are commonly exploited. However, robots are not restricted to use only human senses and can therefore be given sensors such as radar.

There exists many robotics projects where features from insects have been exploited, but no other robotics projects, where ground vibrations have been used for guiding a robot, were found.

The Swedish military has done research on direction finding using ground vibrations. By using vibration sensors, the direction of an approaching tank could be detected [17].

During the Vietnam War, seismic sensors were introduced to detect humans walking on trails. One of the sensors was the Platoon Early Warning System AN/TRS-2, which incorporated both seismic and magnetic sensors. When one of the sensors was trigged, a RF signal was sent to a receiver unit. The AN/PSR-1 Model X-150A sensor used wires between the geophones and the receiver box. It translated the sub sonic signals into the audio spectrum so that you could hear them. It was easy to distinguish a woman walking, a man walking or children playing without any training [6].

2.2 The Nature of Seismic Waves

A handclap in the air sends sound waves outward as the air compresses and rarefies. The mechanical energy originally in the moving hands is

transformed into air vibrations. A stone thrown into the water sends waves spreading across its surface in the form of ripples. The substrates of the Earth have similar elastic properties that cause them to deform and vibrate when pushed and pulled by forces applied to them. These substrate movements are called seismic waves. There are two basic classes of seismic waves: the faster body waves and the slower surface waves.

2.2.1 Body Waves

Body waves propagate through the earth and can be split up into the two

types shown in Figure 2.1: P (primary) and S (secondary ). The P wave is

faster and is similar to a sound wave because it alternately compresses and

dilates the ground. The slower of the body waves is the S wave, which shears

the rock sideways perpendicular to the direction of travel. This type of wave

cannot propagate through liquid parts of the Earth, because the liquid will not

spring back [3]. Body waves spread spherically, therefore their amplitude

falls off as 1/r, where r is the distance to the source [15].

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Figure 2.1. The two types of body waves. The primary wave (1) is faster than the secondary wave (2) (figures from [3]).

2.2.2 Surface Waves

The second basic class of seismic waves, the surface waves, can also be of two types, as shown in Figure 2.2. The first is called a Love wave. Its motion is essentially the same as for the S wave. It moves the ground from side to side in a horizontal plane perpendicular to the direction of the travel. The second type is the Rayleigh wave, which reassembles a rolling ocean wave, it moves both in a vertical and horizontal direction [3]. Surface waves are spreading in a circular pattern, therefore their amplitude falls off as 1/r

^1/2

, where r is the distance to the source [15].

Rayleigh waves are used in this project because they travel further than

compressional waves, and are therefore easier to detect.

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Figure 2.2. The two types of surface waves. The Love wave (1) is moving from side to side as it propagates. The Rayleigh wave (2) moves both in a vertical and horizontal direction (figures from [3]).

2.3 The Sand Scorpion

The sand scorpion, Paruroctonus mesaensis, shown in Figure 2.3, uses ground vibrations to locate its prey. It responds to substrate vibrations by detecting surface waves of low velocities [5].

Figure 2.3. The sand scorpion, Paruroctonus mesaensis (figure from [5]).

At night it leaves its burrow to hunt. It waits in ambush until a prey passes

within range. When a prey enters the scorpion's territory, the pedipalps (the

prey-capturing pincers) open and extend forward as the scorpion raises its

body off the sand. For each movement of the prey, the scorpion will turn and

move closer. If it fails to grab the prey with its pedipalps it waits motionless

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until the prey moves again. This sequence lasts for only a few seconds with one to five orientation movements.

Figure 2.4. The tarsal leg segment of the scorpion has two different types of

mechanoreceptors. The slit sensillum reacts to Rayleigh waves and the tarsal hairs respond to compressional waves (figure from [5]).

The sand scorpion uses two different mechanoreceptors on its tarsal leg segments, its “feet”, to detect substrate vibration (see Figure 2.4). By inserting fine wires into the terminal segments and record the bioelectric signals, Brownell [5] could show that the tarsal hairs reacted to

compressional waves while the slit sensillum responded to Rayleigh waves, as shown in Figure 2.5. The slit sensillum is similar to the lyriform organ in spiders, which is highly sensitive to web vibrations [5].

Figure 2.5. The tarsal hairs react on compressional waves (1) while the slit sensillum reacts to Rayleigh waves (2) (figures from [5]).

Brownell shows that the sand scorpion could locate the direction and the distance of a prey up to 10 cm away. If the distance was greater, up to 30 cm, only the direction was sensed. By experiments, where he covered the

animal’s eight eyes with opaque paint and inserted sound-absorbent tiles

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between the stimulation source, he showed that the sand scorpion reacts to vibrations conducted through the ground. Figure 2.6 shows the air-gap experiments that proved that the sand scorpion respond to substrate vibrations rather than visual or aural cues when locating their prey.

He also showed that the scorpion is using relative arrival time, and not relative intensity, to find the direction of its prey.

Figure 2.6. When locating its prey, air-gap experiments showed that the sand scorpion respond to substrate vibrations rather than visual or aural cues. The scorpion did not react when the surface, with which the scorpion’s leg did not have contact, was tapped (1). When the scorpion’s leg were in contact with the tapped surface, it reacted by turning against the source (2) (figures from [5]).

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3 Vibration Detectors

In this chapter, four different methods for detecting vibrations are evaluated.

The vibration sensors investigated were commercial accelerometer, electret microphone, piezoelectrical coaxial cable and piezoelectrical film.

3.1 Test of Suitable Sensors

A test bench was defined to make the comparison of the different sensors possible:

• Each sensor was mounted in a clamp standing on a wooden table. It is obvious that the clamp would absorb some vibrations, but as it was the same for all sensors, the attenuation could be neglected.

• Each test was conducted by dropping a 1.25 g ball-bearing from 15 cm height at a distance of 20 cm from the centre of the sensors.

• The signal generated by the impact was monitored on an oscilloscope.

3.1.1 Commercial Accelerometer

The ADXL05, from Analog Devices, is a complete acceleration

measurement system on a single monolithic IC. It contains both the micro- machined sensor as well as the signal conditioning and amplifying circuitry.

Figure 3.1 shows a functional block diagram of the sensor. Two ADXL05 sensors were available in the department and they were tested to try the concept of using commercial accelerometer for this project. This type of accelerometers is made for automotive air bags, and is therefore relatively inexpensive (~$A30).

Figure 3.1. Functional block diagram of the ADXL05 sensor (figure from [2]).

3.1.1.1 Theory of Operation

The ADXL05 is a force balanced capacitive accelerometer, fitted in a TO-

100 metal can. The sensor consists of 46 unit cells and a common beam.

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Figure 3.2 shows a simplified view of the actual sensor responding to an applied acceleration. The sensor’s fixed capacitor plates are driven

differentially by two 1 MHz square waves, each 180 ° out of phase from one another. At rest, the voltage output at their electrical centre (i.e. at the centre plate) is zero, due to same values of the two capacitors. When there is an applied acceleration, the common central plate moves closer to one of the fixed plates while moving further from the other. This alters the capacitance values, resulting in an output signal at the central plate. The output amplitude of the signal is proportional to the amount of acceleration experienced by the sensor.

Figure 3.2. The ADXL05 sensor responding to acceleration (figure from [2]).

The signal from the centre plate of the sensor is buffered and applied to a synchronous demodulator which is clocked, in phase, with the same

oscillator that drives the fixed plates. After the demodulator, a preamplifier levels the signal at 1.8 V ± 200 mV/g. The IC also includes an uncommitted buffer amplifier, which can be used to adjust the scale and 0 g offset over a wide range.

3.1.1.2 Performance Test

As only measurement of vibration and not tilt, was the subject of interest, the ADXL05 was configured for AC coupled response. The buffer amplifier was set up to give a full scale range of ±2 g with a bandpass filter, band-limited between 3 Hz and 10 kHz. The sensor was tested using the test bench described in section 3.1. The sensor’s response, when the ball bearing was dropped on the table, was around 2 V

pp

with a low noise floor. The high sensitiveness makes the accelerometer interesting for this application.

3.1.2 Electret Microphone

An omni-directional electret microphone was examined to investigate if it could be used as a vibration detector. It would provide an inexpensive

vibration sensor if the experiment was successful. A proof mass was glued to the membrane of the microphone to enhance its sensitiveness to vibrations, as seen in Figure 3.3. The signal, generated when the modified microphone was subject to vibrations in the test bench, was monitored on an oscilloscope.

The signal generated by the impact was very small, less than 0.1 mV

pp

, and

was not much higher than the noise floor. Because of the low resolution of

the signal, the microphone could not be used in this application.

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Membrane Proof mass

Figure 3.3. The modified electret microphone.

3.1.3 Piezoelectrical Coaxial Cabel

The piezoelectrical property of a coaxial cable changes when it is subject to vibrations. With normal coaxial cables this is seen as a problem and therefore their piezoelectrical property is minimised. While with the piezoelectrical coaxial cable this property is desired and therefore enhanced by using a highly piezoelectrical dielectric. This property makes it interesting to investigate for possible use as a vibration sensor in this project.

Piezoelectrical coaxial cables are mainly used to detect vibrations. An example is a British pedestrian detection system, called PUFFIN (Pedestrian User Friendly Intelligent Crossing) [7]. The system can detect a human or an animal, standing in the waiting area to cross a street, by their breathing and heartbeat.

The piezoelectrical coaxial cable tested here had a dielectric made of PVDF, a material which is explained in the next section. A proof mass was added to the end of the flexible piezoelectrical coaxial cable, as seen in Figure 3.4.

Electrical wires were connected to the centre conductor and the shielding of the cable. The signal generated from the bending of the coaxial cable, when it was subject to vibrations in the test bench, was monitored on an oscilloscope.

The signal generated was very small. It could not be distinguished from the noise floor with the eye on the oscilloscope. The piezoelectrical coaxial cable had to be dismissed as a suitable vibration sensor for this project, due to its insufficient resolution. In the British pedestrian crossing system it was necessary to use sophisticated signal processing to make sense of the signal.

Flexible coax-cable

Proof mass Figure 3.4. The piezoelectrical coaxial cable.

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3.1.4 Piezo Film

Piezo film has a wide range of applications. A few examples are

hydrophones, switches, tactile sensors, fluid level, liquid flow, vibration sensors and microphones [11]. The piezo film’s vibration measurement property makes it interesting to this project.

3.1.4.1 Piezo Film Theory

Pennwalt manufactures a piezo film under the tradename Kynar. It is made of polyvinylidene flouride (PVDF) which is a piezoelectric polymer with

groups of molecules (H2C=CF2) linked as orderly crystallites. The

crystallites form an amorphous matrix of chemically similar but differently structured material. The relative population of crystallites strongly effects the piezoelectric behaviour of the material. This synthetic material has far greater piezo activity than any other material [11].

Both surfaces of the piezo film are metallised to provide two electrodes.

When a voltage is applied to the electrodes of the piezo film, the film will elongate or contract, depending on the field’s polarity, as shown in Figure 3.5. The reverse is also true; when an external force is applied, the film experience a compressive or tensile strain and the film develops an open circuit voltage that is directly proportional to the applied force. Exposure to an alternating force results in a corresponding alternating electrical signal with a frequency response range from 0.005 Hz to several gigahertz [11].

A simplified model of a piezo film is shown in Figure 3.5. Here the dipoles with their respective polarities represent the net dipole within a unit volume of piezo film. The net film volume increases when the unit volume is placed in tension, resulting in a lower charge density at the positive and negative electrode surfaces. Electrons will now flow, through the wire connecting the film’s metallised surfaces, out of the top electrode and into the bottom electrode to achieve electrical neutrality. When the unit volume is subject to compression the reverse occurs.

+ _ + _

+ _ +

_

1. 2.

F

F Metallised

surface PVDF

Metallised surface

Figure 3.5. When a working voltage is applied to the electrodes of the piezo film, it will elongate or contract. Conversely, tension or compression change the piezo film volume (2) resulting in a change of the net charge distribution within the film, producing a voltage difference between the electrodes.

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3.1.4.2 Piezo Film with Brass

Piezo film was glued to a thin piece of brass, as suggested in [11], using highly flexible silicone, Silicagel, as adhesive. To improve sensitivity, a proof mass was added to the end of the brass, as shown in Figure 3.6. In the test bench, spikes with 0.5 V amplitude were generated from the impact of the ball bearing. As the noise floor was low, the piezo film could be considered sufficiently sensitive to be used in this application.

Proof mass Brass

Amplifier

Piezo film 10 mm

Figure 3.6. A vibration sensor using piezo film glued to a sheet of brass.

3.1.5 Conclusions

Commercial accelerometers are the best choice for measuring vibrations for this application, as they are sensitive, relatively cheap and are very similar to each other due to the micro machined sensor. Unfortunately the

accelerometers were made available in the end of the project and there was not enough time to include them in the sensory system. At an early stage in the project it was decided to use piezo film sensors as vibration detectors.

The next section describes their design.

3.2 Building the Vibration Detectors

To find the best configuration of brass thickness and proof mass, a multi variable performance test was conducted, see Table 3.1. The table shows that the best performance is achieved using a brass thickness of 70 µm and a proof mass of 2.9 g. This configuration generated a spike with 0.5 V

amplitude when a 1.25 g ball-bearing was dropped on a wooden table, from a height of 15 cm at a distance of 20 cm from the sensor.

3.2.1 Interfacing the sensor

The signal from the piezoelectrical film was buffered with a FET. Valid

vibrations are around 100 Hz on wooden surface. To avoid the detection of

invalid vibrations, the signal was filtered with a bandpass filter, band-limited

between 40 Hz and 500 Hz. An operational amplifier was used to further

amplify the signal before a comparator was used to threshold the signal. The

resulting logic transition triggered a pulse catcher in the microcontroller and

therefore the Time of Arrival (TOA) could be measured very accurately.

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Brass

thickness Proof

mass Amplitude

50 µm 1.7160 g 0.05 V

50 µm 2.9033 g 0.25 V

50 µm 3.7755 g 0.2 V

70 µm 1.7160 g 0.25 V

70 µm 2.9033 g 0.5 V

70 µm 3.7755 g 0.2 V

100 µm 1.7160 g 0.01 V

100 µm 2.9033 g 0.05 V

100 µm 3.7755 g 0.05 V

Table 3.1. Test of sensor sensitivity by dropping a 1.25 g ball bearing at a distance of 20 cm and a height of 15 cm

3.2.1.1 The JFET Amplifier

The piezoelectrical film is high impedance and therefore interfaced with a high impedance JFET amplifier, J2N5485, as shown in Figure 3.7. With a V

CC

at 9 V the JFET has 1 mA drain current. The amplifier circuit has a pass band between 40Hz and 500Hz, as shown in Figure 3.8.

x

Figure 3.7. The JFET amplifier.

dB

Figure 3.8. The frequency response of the JFET amplifier.

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3.2.1.2 The Operational Amplifier

To minimise the use of components, the second amplifying stage is using a single supply voltage operational amplifier, the LM358. This makes it possible to only use one comparator per channel and it removes the need of a voltage inverter to get a negative voltage from the battery pack. The single supply causes the negative part of the signal to be clipped. This is feasible because all vibration sensors are mounted with the same electrode pointing up. Figure 3.9 shows the amplifier configuration where the R2 potentiometer enables trimming of the gain. To achieve the same amplification for all operational amplifier circuits, they were trimmed with the help of a function generator.

x x

Figure 3.9. The operational amplifier.

3.2.1.3 The Comparator

The comparator, LM339, is used to generate a logic transition when the signal reaches a threshold. The logic transition is detected as the TOA in the microcontroller. The LM339 is designed to operate from a single power supply, but can also be used with dual supplies. Since the operational amplifier circuit rectifies the signal, single supply is used. The output of the comparator is open-collector and hence the built-in pull-up resistors in the microcontroller must be used on the inputs. All six comparators use the same threshold, V

thres

, which is set by the voltage-dividing potentiometer R1.

Figure 3.10 shows one of the comparators and the voltage-dividing potentiometer that generates the threshold.

x x

Figure 3.10. The comparator.

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3.2.2 Sensor response

This section presents the characteristic of the vibration sensor response at different stages in the amplifier circuit. Figure 3.11 shows the response, after the JFET buffer amplifier, when a ball bearing was dropped from a height of 15 cm at a distance of 20 cm from the sensor. The signal has a relatively large 50 Hz noise component. This component could be reduced by using a notch (band stop) filter and by proper shielding. This was not done due to limitation of time, but is recommended for further work. Due to the impact of the ball bearing, the signal also contains two dominant frequency

components at 20 Hz and 240 Hz. The high frequency component at 240 Hz is present due to the relative fast impact between wood and steel. It is not present in the next test, where a finger tap was used as a signal source.

However, the 20 Hz component is present in both tests, and could possibly indicate the resonance frequency of the wooden table.

T 1 >

1 >1 >

1 >

1) Ch 1: 100 mVolt 25 ms

Figure 3.11. Sensor response, after JFET buffer at JFx, when dropping a 1.25 g ball bearing at a distance of 20 cm and a height of 15 cm.

After the operation amplifier stage, at OPx, the signal is rectified, as shown in Figure 3.12. This is due to the single supplied operational amplifier, which neglect negative signals.

T

1 >

1 >1 >

1 >

1) Ch 2: 1 Volt 25 ms

Figure 3.12. Sensor response, after operational amplifier at OPx, when dropping a 1.25 g ball bearing at a distance of 20 cm and a height of 15 cm.

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It is interesting to note the different signal characteristic when a light finger tap was used as signal source instead of a ball bearing, as shown in Figure 3.13. The 50 Hz noise component is still present, but the signal has less high frequency components. The impact between wood and skin is slower than the impact between wood and steel and generates frequency components of 100 Hz and 20 Hz. The 20 Hz frequency component is, as mentioned above, probably due to the resonance frequency of the table.

1 > T 1 >

1 >

1) Ch 1: 100 mVolt 25 ms

Figure 3.13. Sensor response, after JFET buffer at JFx, for a light finger tap at a distance of 20 cm from the sensor.

Figure 3.14 shows the signal after the operation amplifier stage, at OPx, from a light finger tap.

T

1 >

1 >1 >

1 >

1) Ch 2: 1 Volt 25 ms

Figure 3.14. Sensor response, after operational amplifier at OPx, for a light finger tap at a distance of 20 cm from the sensor.

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4 Navigation

Difference in TOA, of a vibration wave front, between the six vibration sensors enables the calculation of the direction and the location of the source of vibration. The precision of the detected direction and location increases as the distance to the source of vibration decreases.

4.1 Direction Finding

Assuming a plane vibration wave front, generated by a vibration source at a great distance, the difference in TOAs can be used to calculate the direction of the source, as shown in Figure 4.1. The direction α is found by:

) arccos(

d δ l

α = (4.1)

Where d is the distance between the sensors and δl is the difference of TOA, δt, multiplied by the estimated propagation speed, c

est

.

d α δl

Sensor 2 Sensor 1

Vibration wave

Figure 4.1. Trigonometry of direction finding. The vibration wave is assumed to have a plane wavefront.

With only one sensor-pair it is not possible to distinguish if the source of vibration is in front or behind the sensor-pair. By using two sensor-pairs the problem can be solved. Only three sensors are actually needed, where one is common to both sets of sensor-pairs. The solution presented here minimises the direction error by using six sensors, which results in 15 sensor-pairs, which produce 30 detected directions. Some of the 15 possible directions may be invalid due to erroneous data, but the high degree of redundancy can be exploited to eliminate erroneous data and produce an accurate result.

4.1.1 Data Validation

The sensor system must overcome problems involving invalid sensor data. A

sensor could detect a vibration with an indirect path, caused for example by

discontinuities in the ground. The sensor system has three levels at which

invalid data can be rejected: (1) interrupt level data validation (2) first low-

level data validation and (3) second low-level data validation. Level 1, the

interrupt level data validation, is done in the 5 ms timer interrupt service

routine. If less than 4 sensors have been trigged during the past 5 ms all

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sensors are reset. Level 2, the first low-level data validation, is done in the direction finding algorithm. If the difference of TOA of a vibration wave front between two sensors is greater than 4 ms, the data from the sensor-pair is considered invalid and is therefore discarded. Level 3, the second low- level data validation, prevents invalid data by validating the data using the triangular inequality [10]. The 3

^rd

level data validation is described in this section, while the 1

^st

and 2

^nd

level are described in the chapter discussing the software design.

The triangular inequality states that the sum of the distance on two sides of a triangle must exceed the third [9]. Let P be the location of the source of vibration and S

1

and S

2

the locations of the two receiving sensors. The triangle inequality gives:

2 1 2

1

PS S S

PS < + (4.2)

Which can be rewritten as:

2 1 2

1

PS S S

PS − < (4.3)

When the distance to the source is great

2

1

PS

PS −

 =

 

 

 → ∞

= vibration source the to distance

δ l (4.4)

In Figure 2.1 the following relation is given:

2 1

S

= S

d (4.5)

Combining equation (4.3), (4.4) and (4.5) gives:

d l <

δ (4.6)

which accomplishes the data validation if the distance to the vibration source is large.

4.1.2 The Sliding Window Algorithm

The robot must be able to measure the wave propagation speed to be able to solve the direction finding problem accurately. An algorithm using a sliding window was developed.

The algorithm finds both the direction and the wave propagation speed by performing a two-dimensional search. The first dimension is the direction and it is found by sliding a fixed sized window over a set of detected

directions. The direction having the maximum number of detected directions

within the window is found, as shown in Figure 4.2. The second dimension is

the wave propagation speed and it is found by changing the estimated

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propagating speed and repeat the sliding window procedure until the propagation speed generating the maximum density has been found.

Results of a simulation are presented in Table 4.1. Six sensors were used, placed on a 0.3 m diameter circle. The source of vibration was placed at a bearing of 225°, 1 meter away from the centre of the sensors. The wave propagation speed was set to 100 m/s and Gaussian noise with a 100 µs standard deviation was added to the simulated TOA from the sensors.

0 50 100 150 200 250 300 350

0 1

Degrees

Sliding window

Figure 4.2. The plot shows all detected directions that are valid at a propagation speed of 100 m/s. The highest density of detected directions is found at 225°. The outliers are the directions detected at the opposite direction of the sensor-pair.

Estimated

speed Detected

direction Density

25 180 ° 4

50 240 ° 5

75 225 ° 7

100 225 °°°° 14

125 220 ° 6

150 250 ° 5

175 85 ° 2

200 90 ° 2

225 200 ° 2

250 10 ° 1

275 5 ° 1

Table 4.1. Result from the sliding window algorithm. By performing a two-dimensional search it is possible to find both the direction and the wave propagation speed as indicated by a maximum of density. Window size was 22.5° and the window step size was 5°.

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4.2 Location Finding

By using pairs of radio beacons it is possible to find the exact location of a moving vehicle at a given moment [16].

4.2.1 Location Finding Using Hyperbolic Lines

The LORAN (LOng RAnge Navigation) system is a radio based navigation system developed by the United States Army in the early 1940’s [16]. It enables navigation of a vessel without visible landmarks.

The ship located at P receives two radio signals that were broadcasted at the same time from radio stations located at F

1

and F

2

. The navigator measures the difference of TOA:

1 2

- t t t =

δ (4.7)

The difference between the distance from the ship to F

1

and the distance from the ship to F

2

is:

t c δ

1

=

2

- PF

PF (4.8)

where c is the propagation speed of the radio signals. Equation (4.8) indicates that the ship is on the hyperbola whose equation is:

t c δ

1

=

2

- PF

PF (4.9)

The exact location of the ship may be determined by using two pairs of radio stations and by finding the intersection of the two hyperbolic lines.

The same principles apply for the reversed condition, as in our case, where two or more receivers detect a signal from one source. The intersection is found using Newton-Raphson's method for non-linear systems of equation [12]. This method is only useful when the source of vibration is close to the robot, as the error grows large when the distance increases.

It is important to have a good initial guess in order to find the solution of the non-linear equation system. The initial guess, x , is set 10 cm from the centre of the robot, in the direction found by the direction finding algorithm.

Figure 4.3 shows the simulation results using 4 sensors. The source of

vibration was located at (-20,5) cm and was found by the algorithm after 90

iterations.

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-40 -30 -20 -10 0 10 -40

-30 -20 -10 0 10 20 30 40

Horizontal position [cm]

Source

Sensors used

Figure 4.3. Simulated location finding using two pairs of sensors.

4.2.2 The Newton-Raphson Method in Higher Dimensions Let

^x⁼

[

^x ^y

]

^T

be the location, in a two-dimensional Cartesian coordinate system, where the source of vibration is located. Let x also be the root of the two-dimensional non-linear system

0 ) ( x =

f (4.10)

The system is described by

 

 



= 

) , (

) , ) (

( h x y

y x

f x g (4.11)

where ) g ( y x , and h ( y x , ) are the functions of two hyperbolas derived from the differences of TOA between two pairs of vibration sensors. By expanding the functions to their first order Taylor series expansion about x ,

x x x x

x ∆

∂ + ∂

=

∆

+ f

f

f ( ) ( ) (4.12)

the Newton-Raphson method seeks a common root that solves equation (4.10) close to an initial guess. If x + ∆ x is the root of equation (4.10), the right hand side of equation (4.12) is zero, and the following set of linear equations is obtained:

) (x x x f

f ∆ = −

∂

∂ (4.13)

Solving equation (4.13) for ∆ gives x

Vertical position [cm]

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) (

1

x x

x f

⁻

f

 

 





∂

− ∂

=

∆ (4.14)

Suppose x

k

is the current approximation of x, then the improved guess x

k+1

can be found by

x x

x

_k₊₁

=

_k

+ ∆ (4.15)

Given a good initial guess of x , iteration of equation (4.14) and (4.15) gives the root of equation (4.10).

4.2.3 Location Finding in Reality

Simulations showed that the acquired sensor data was not sufficiently

accurate to permit location finding. When radio based navigation is used,

with pairs of antennas, the resolution decreases as the vessel moves out of an

area enclosed by the antennas [16]. In this application, the source of vibration

will almost always be outside the area enclosed by the sensors. Even if

sensor data with a much higher resolution was available, only close vibration

sources can be located.

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5 The Robot

This chapter describes the design and construction of the six-legged robot base. The robot that was built, shown in Figure 5.1, was based on a robot developed by Rodney Brooks [4].

Indicator LED

Vibration sensors Batteries

Microcontroller (underneath)

Servos

Figure 5.1. The six-legged scorpion robot.

5.1 Body

As it was important to keep the weight down, a lot of thought was given to

building the body. A sandwich material was created, using PVC-foam and

aluminium foil. The 8 mm PVC-foam, from Fibreglass International in

Melbourne, which is normally used in boat manufacturing, was coated on

both sides with 60 µm aluminium foil. Kwikgrip contact adhesive was used

to fix the aluminium foil to the PVC-foam. The PVC-foam is normally quite

flexible, but strengthened with the aluminium foil, the composite became

rigid enough to be used in this application. The body was then carved out

from the composite in an oval shape to make the legs cover an oval area, just

as the sand scorpion’s legs do. To further reduce the weight, holes were

punched in the body, where the rigidity could be decreased, i.e. between the

mountings for the servos. This resulted in a body weight of a mere 40g.

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5.2 Legs

The legs were constructed from 0.5 mm sheet aluminium to keep the weight down. An embossed ridge was added to the middle of each leg to increase the stiffness.

Figure 5.2 shows a leg mounted on the robot. Each leg is connected to a shoulder joint with two degrees of freedom, controlled by two orthogonally placed model airplane servos. The first servo is attached directly to the body and controls the swinging motion of the leg. The second servo is attached to the first servo and controls leg elevation.

One vibration sensor is fixed horizontal with the ground on each leg to pick up Rayleigh waves. An aluminium box encapsulate each sensor to prevent them from damages.

Rubber bumps from eyedroppers were put on the feet to add friction to the ground. The servos generate plenty of vibrations and must therefore be switched off during vibration sensing. During the switched off period the friction between the rubber bumps and the ground is enough to keep the robot standing.

Rubber bump

Protective box Amplifier

Sensor Swing servo

Elevation servo

Servo holder

Figure 5.2. A leg mounted on the robot. The servo that swings the leg is attached directly to the body of the robot. The servo that elevates the leg is attached to the servo holder that joins the two servos. The vibration sensor is encapsulated inside a protective aluminium box, on which the JFET buffer amplifier is attached.

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5.3 Locomotion

There are many ways of achieving leg locomotion, including various motors, pneumatic cylinders, electro-magnets, etc. The driving mechanism must be powerful, as a substantial torque is required to carry the load of the robot.

5.3.1 Servo control

It was decided to use model airplane servos, as they are inexpensive, light and easy to use. A servo is essentially a small DC motor with positional feedback. The servo has three inputs: V

cc

, ground and signal. The servo is controlled by a Pulse Width Modulation (PWM) signal. The angle of the output shaft is directly proportional to the duty cycle of the PWM signal.

These pulses must be updated at a frequency of at least 50 Hz. At 50 Hz, pulse widths generally range from 0.50 ms (extreme counter-clockwise) to 2.5 ms (extreme clockwise), see Figure 5.3.

tw

20 ms Vdd

GND

Figure 5.3. Servos are controlled with Pulse Width Modulation (PWM).

The servos used are made by HITEC, a large manufacturer of remote

controlled devices. Six servos (HS-425BB) are used to swing the legs and six high-torque servos (HS-605BB) are used to lift the legs. Both versions feature a ball bearing shaft, have the same dimensions and weight 45.5 g and 49 g respectively [8]. When driven at 6 V, the output torques are rated 0.36 Nm and 0.67 Nm respectively. However the servos can accept voltages up to 7.2 V, which increases the torque [8]. Figure 5.4 shows the HS-425BB servo.

20 mm

51 mm

35 mm

Figure 5.4. Picture of the HITEC HS-425BB servo.

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Using a multiplexer three PWM outputs from the microcontroller could be used to control twelve servos. A 5 ms timer interrupt service routine (ISR) is used to select which servo bank to control, as shown in Figure 5.5. Each interrupt call switches servo bank by setting four output port pins (PP4-PP7), which control the multiplexer, as shown in Figure 5.6, and sets new duty cycle values for the PWMs. Each servo responded differently to the same duty cycle. To correct this an individual duty cycle compensation was added to each servo.

0 5 10 15 20 [ms]

1A

5A

2A

6A

3B

4B

3A

1B

5B

4A

2B

6B

1A

5A

3B

Time

Activated servos

Figure 5.5. Servo control scheme. “A”-servos are used for swinging the legs, “B”-servos are used for elevating the legs. The number denotes the servo’s position on the robot viewed from the top. Starting with 1 in the one o’clock position, counting clockwise.

Figure 5.6. The servo control multiplexer.

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5.3.2 Leg motion

The legs are moved using a tri-pod gait, which means that at all time at least three legs are in contact with the ground. This was possible to achieve due to the high-torque servos (HS-605BB), which control the elevation of the robot.

Once the motion of one leg was established it could be used for all six legs.

The walking algorithm has six modes of operation:

Forced stop The robot stops and all legs are positioned to their centres, one at a time. This mode is used when preparing to detect vibrations.

Stop The robot stops.

Forward The robot walks forward.

Backward The robot walks backward.

Left The robot turns left by moving right side legs forward and left side legs backwards.

Right The robot turns right by moving left side legs forward and right side legs backwards.

5.4 The Microcontroller

It was chosen to use an on-board microcontroller to acquire sensory

information, compute algorithms and control the robot. The microcontroller used was the 16-bit Motorola M68HC12.

5.4.1 The MC68HC12 Microcontroller

The MC68HC912B32 microcontroller is the first in a family of the next generation of the very widely used M68HC11 microcontroller. It features both on-chip memory and peripheral functions. The CPU, CPU12, is a high- speed, 16-bit processing unit. The programming model is identical to the standard M68HC11 CPU and the CPU12 instruction set is a proper superset of the M68HC11 instruction set.

The MCU is capable of a bus-operation of 8 MHz. It contains an 8-channel timer, a 16-bit pulse accumulator, an 8-bit analog-to-digital converter and a four-channel pulse-width modulator (PWM). It also contains an

asynchronous serial communications interface and a serial peripheral interface.

The B32 model of the MC68HC12 comes with 32 kbyte Flash EEPROM, 1

kbyte RAM and 768 byte of byte-erasable EEPROM [14].

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5.4.2 The Evaluation Board

The microcontroller is mounted on an evaluation board (M68EVB912B32) from Motorola. In a prototype environment, an evaluation board (EVB) can simplify the hardware and software design, by providing essential MCU timing and I/O circuitry. The EVB has a 16 MHz crystal for 8 MHz bus operation and an RS-232 interface. It has header footprints for access to all MCU pins and a prototype area for customised interfacing with the CPU.

There are four jumper-selectable operation modes:

EVB Code in Flash EEPROM executes.

JUMP-EEPROM Code in byte-erasable EEPROM executes.

POD The EVB serves as a BDM probe.

BOOTLOAD The EEPROM may be reprogrammed.

The EVB mode is used in this project where the code is stored in the 32 kbyte Flash EEPROM. The RS-232 interface enables download of firmware from a host computer into the Flash EEPROM when the BOOTLOAD mode is selected [13].

5.5 Indicator LED

A red LED is mounted as a blinking “eye” on the front of the robot. The state of the led signals the current state of the robot:

Off The robot is turned off.

On The robot is walking/turning.

Blinking The robot is listening for vibrations.

Fast blinking The robot is calculating bearing to a vibration source.

The LED is driven by one of the configurable ports of the microcontroller and consumes about 10 mA.

5.6 Power

The microcontroller, the servo multiplexers and the sensor electronics

requires about 100 mA at 9 V. When the robot walks, the 12 servos consume about 2 A at 6 V. A single 9 V alkaline battery is used to supply the

electronics. The servos are supplied with a rechargeable 6 V NiCd

accumulator.

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6 Software Design

This chapter discusses general software design as well as implementation of the algorithms presented in chapter 4. The software was written in ANSI C and was compiled for the M68HC12 microcontroller using the ImageCraft ICC12 compiler.

6.1 Overview of Software

The software has two main tasks, namely vibration direction finding and leg motion control. The vibration detection system uses six timers, configured for input capture, to measure the TOA of the vibration wave front. Input capture resolution is 4 µs. Leg motion control is achieved with a 5 ms timer interrupt service routine, which updates the duty cycles of the servos. The timer interrupt is also used to validate the vibration sensor data, as discussed in section 4.1.1.

The start up of the system consists of several steps: hardware and software are initialised, the legs are positioned to the centre, and the interrupts are enabled.

The software then operates via interrupts and a background high-level task of data processing. The robot legs are forced to a listening position, i.e. they are moved to their centres and the servos are switched off to prevent generation of vibrations. When the system has collected enough sensory data, the

direction finding algorithm is executed. If a valid direction is found, the robot is turned towards that direction. As the resolution of the TOA data is

insufficient for calculating distance, the robot always walks approximately 0.4 meters towards the vibration source. Then the listening procedure is repeated.

Figure 6.1 on next page shows a flow chart of the robot’s behaviour.

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Init hardware and software

Centre legs

Initiate listening

≥ 4 sensors trigged

Calculate direction to vibration source

Valid direction?

Switch on servos, turn towards vibration source and walk 40 cm Switch off servos and wait 2 seconds

to eliminate vibrations.

No

Yes

No Delay 500 ms

Figure 6.1. Flow chart of the robot’s behaviour.

6.2 findBearing Function

This section describes the implementation of the sliding window algorithm

discussed in section 4.1.2. The findBearing function takes a set of TOA data

from the vibration sensors and calculates the direction towards the vibration

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source. A set of valid directions is obtained by executing the getDirection function for each sensor-pair that passes the level 2 data validation, i.e. if the difference of TOA between two sensors is less than 4 ms. The set of valid directions is then passed into the sliding window function, which returns the direction yielding the highest density of directions from the set. By repeating this procedure for all wave propagation speeds of interest, the direction of the source of vibration is found.

6.3 getDirection Function

The getDirection function returns two possible bearings from one pair of sensor data.

The triangular inequality, as discussed in section 4.1.1, is checked by evaluating equation (4.6). Invalid sensory data are ignored in the direction calculation. To speed up the calculation, the distances between all sensor- pairs are calculated only once during the software initialisation.

As discussed in section 4.1, two directions are detected for each sensor-pair.

One is the true direction while the other is a false direction, pointing in the opposite direction. The true direction and the false direction to the vibration source are determined by extending equation (4.1) with:

 







 







= −

) arccos(

2 ) arccos(

d d l

l π δ

δ

α (6.1)

All directions acquired must be relative to the same axis, hence the angle β must be calculated to compensate for the location of the sensor-pair, see Figure 6.2. The angle β is obtained by:

 

 



≤

− −

−

>

− −

=

0 ),

arccos(

2 0 ),

arccos(

1 1 2

2

1 1 2

2

y d y

x x

y d y

x x

β π (6.2)

where (x

1,

y

1

) is the position of sensor 1 and (x

2

,y

2

) is the position of sensor

2.

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d

Sensor 1

Sensor 2

α

Vibration wave

δl

β

x y

Figure 6.2. Trigonometry of direction finding that accepts arbitrary positions of sensors.

The two directions to the vibration source are obtained by adding equation (6.1) and equation (6.2) with a modulus of 2 π:

( ^α ^β ) ^π

θ = + ⊕ 2 (6.3)

6.4 slidingWindow function

Given a set of directions the slidingWindow function returns the bearing where the highest density of directions is found. A fixed sized window is moved over the data set. For each position of the window, the number of directions in the data set, that resides within the boundaries of the window, is calculated. By repeating this procedure the direction giving the maximum density is found.

6.5 Pulse Receiving Software

The pulse receiving part of the software utilises the input capture function of the microcontroller. There are six pins configured as Input Compare controls.

Each of these pins is associated with a 16-bit register, named TICx, where x is a value from 0 to 5. These registers are used to latch the value of the free- running timer counter when a logic transition occurs on the input pins. Since the outputs from the vibration sensing circuitry is connected to the inputs, an incoming vibration wave front will generate a latch of a timer value. This value indicates the TOA of the vibration pulse.

Because of what is probably a flaw in the microcontroller design, each Input

Capture needs to be serviced by an interrupt. The Input Capture registers are

always latched when a transition occurs on one of the inputs, no matter if the

corresponding Interrupt Flag is set or not. By servicing the Input Capture

with an interrupt service routine (ISR) false readings are minimised. The ISR

saves the contents of the corresponding Input Capture register in a global

variable for later processing.

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6.6 Leg Motion Software

The leg motion software controls the twelve servos by utilising the

microcontroller’s built in PWMs, as explained in section 5.3.1. Each leg’s motion is controlled by two servos, one for elevating the leg and one for swinging the leg. Two general patterns of duty cycles are used to control the leg motion. The empirically found patterns each contain eight points along the path of motion for the legs. The servos are updated once every 20 ms by the timer ISR. For every update, two new duty cycles are found by

interpolating between the duty cycles in the pattern.

Not all servos have the same duty cycle response. Therefore each servo is

compensated with an individually empirically found constant.

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7 Performance of the Direction Finding System

The results are divided into two sections. The first section presents how well the direction finding systems performed when the vibration sensors were mounted directly onto a wooden table with blue tack. In the second section the performance of the direction finding system, when the vibration sensors were mounted on the legs of the robot, is presented.

7.1 Sensors Mounted on a Table

Five sensors were positioned on a circle, with a radius of 15 cm, on a wooden table. A performance test was conducted by tapping the table at two different radiuses around the circle, as shown in Figure 7.1. To generate statistically valid data, each direction was tapped ten times. The results are shown in Figure 7.2 and Figure 7.3. The standard deviation of the detected directions was 10.5 degrees at 25 cm from the origin of the sensors and 22.8 degrees at 45 cm. The apparent errors are due to:

• Different sensitivities of the sensors.

• Discontinuities in the surface.

• Measurement errors when deciding where to tap.

The bias median error was 0 degrees at 25 cm from the origin of the sensors and 2.5 degrees at 45 cm, hence systematic errors were negligible.

15 cm 10 cm 20 cm

25 cm radius circle

45 cm radius circle Sensors

Figure 7.1. The five vibration sensors were placed on a circle with a radius of 15 cm. Two performance tests were conducted by tapping the table at a radius of 25 cm respectively 45 cm around the circle.

At the time the test was conducted, only five accurate sensors had been

produced. It is most likely that the performance would have increased with

six sensors. The resolution of the direction finding system decreases with

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distance (about 117% between 25 cm and 45 cm). This is due to the attenuation of the vibration waves traveling through the substrate.

-150 -100 -50 0 50 100 150

Target direction [degrees]

Figure 7.2. Detected directions versus target directions using the direction finding algorithm with five sensors mounted directly to the table. The distance to the source of vibration was 25 cm from the origin of the sensors. The standard deviation was 10.5 degrees and the median bias error was 0 degrees.

-150 -100 -50 0 50 100 150

Figure 7.3. Detected directions versus target directions using the direction finding algorithm with five sensors mounted directly to the table.. The distance to the source of vibration was 45 cm from the origin of the sensors. The standard deviation was 22.8 degrees and the median bias error was 5 degrees.

7.2 Sensors Mounted on the Robot

The performance test with the sensors mounted on the robot utilised six sensors. The wooden table was tapped at two different radiuses around the robot, as shown in Figure 7.4, just like in the first test. To generate

statistically valid data, each direction was tapped ten times. The results are shown in Figure 7.5 and Figure 7.6. The standard deviation of the detected directions was 46.7 degrees at 25 cm from the origin of the sensors and 60.9 degrees at 45 cm. The errors are much larger than in the previous test when the sensors were mounted directly to the table. Besides the errors listed in the

Detected direction [degrees]Detected direction [degrees]

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previous test, some errors were introduced due to the mounting of the sensors:

• The rubber bump on each leg absorbs vibrations.

• The mounting of each sensor absorbs vibrations.

• The sensors are linked to each other through the robot.

The bias median error was 5 degrees at 25 cm from the origin of the sensors and 2.5 degrees at 45 cm. The systematic error at 25 cm could be due to incorrect positioning of the robot. The systematic error at 45 cm can be considered negligible.

25 cm radius circle

45 cm radius circle Sensors

Figure 7.4. The robot with its six vibration sensors was placed on a wooden table. Two performance tests were conducted by tapping the table at a radius of 25 cm respectively 45 cm around the circle.

The resolution of the direction finding system decreases with distance as in the previous test. Now the resolution decreased with 30% between 25 cm and 45 cm, compared to 117% in the previous test. This indicates that most of the errors are due to the mounting of the sensors and not from the attenuation of the vibration waves travelling through the substrate.

7.3 Conclusions

The resolution of the direction finding system decreased remarkably when

the sensors were mounted on the legs of the robot. The errors, that were

introduced when the sensors were mounted on the robot, originate from the

rubber bumps, the mounting of the sensors and the fact that all sensors are

linked together by the body of the robot. To improve the performance,

double adhesive tape might be used instead of rubber bumps at the end of the

legs. The tape would not absorb as much vibrations as the rubber bumps,

whilst it would give sufficient friction with the ground. Sturdier mounting of

(41)

the sensors would also improve performance. However, using highly sensitive commercial accelerometers is probably the best way to achieve a reliable direction finding system.

To illustrate how well the robot performs the direction finding one can say that approximately three times of four the correct direction (within ±20°) is found. This is true when the robot is placed on a wooden table and the vibration source is a finger tap within 25 cm of the centre of the robot.

-150 -100 -50 0 50 100 150

Detected direction [degrees]

Figure 7.5. Detected directions versus target directions using the direction finding algorithm with six senors mounted on the robot. The distance to the source of vibration was 25 cm from the origin of the sensors. The standard deviation was 46.7 degrees and the median bias error was 5 degrees.

-150 -100 -50 0 50 100 150

Detected direction [degrees]

Figure 7.6. Detected directions versus target directions using the direction finding algorithm with six sensors mounted on the robot. The distance to the source of vibration was 45 cm from the origin of the sensors. The standard deviation was 60.9 degrees and the median bias error was 2.5 degrees.

A Robot Scorpion Using Ground Vibrations for

Anders Wallander