A Robot Scorpion Using Ground Vibrations for Navigation*

* The work was conducted at Monash University, Melbourne, Australia

Anders WallanderDivision of Industrial Electronics and Robotics

Luleå University of TechnologyS-971 87 Luleå

Sweden

A/Prof R. Andrew RussellIntelligent Robotics Research Center

Monash UniversityClayton, VIC 3800

Australia

Abstract

Robotics can learn a lot by investigating simpleand effective techniques evolved in biology. TheSand Scorpion that lives in the Mojave Desertuses ground vibrations when locating its prey. Inthis paper it is shown that a robot can be made tonavigate using similar techniques. A six-leggedrobot was constructed and fitted with vibrationsensors to try the concept. Such a robot could beused in the search for victims after naturaldisasters. This paper presents the hardwaredesign, algorithms for direction and locationfinding of a vibration source, and the results ofsimulations.

1 IntroductionSeveral animals use substrate vibrations for navigation,for example the sand scorpion, the trapdoor spider, the antlion and the fiddler crab [Brownell, 1984]. After a closerlook at the sand scorpion, which lives in the MojaveDesert in the USA, it was decided to investigate if itwould be possible to use ground vibrations to help locatea source of vibration. Possible missions for such a robotcould be helping in the search for avalanches andearthquake victims. The sensors on the robot could pickup substrate vibrations created by taps in the ground madeby the victim and help direct the robot towards the victim.It could also be used as a watchdog to detect intruders.

The organisation of the paper is as follows: Insection 2 the behaviour of the sand scorpion is brieflydiscussed. Section 3 describes the nature of seismic wavesand in section 4 the design of the vibration detectors isdescribed. The design of the robot is described in section5. In section 6, two navigation algorithms are presented,one detecting the bearing of the source of vibration andthe other the exact location, given that the vibrationsource is in the vicinity of the robot. Simulation resultsare also presented. Finally future work and conclusionsare presented in section 7.

2 The Sand ScorpionThe sand scorpion Paruroctonus mesaensis uses groundvibrations to locate its prey. It responds to substratevibrations by detecting surface waves of low velocities

[Brownell, 1984].At night it leaves its burrow to hunt. It waits in

ambush until a prey passes within range. When a preyenters the scorpion's territory the pedipalps (the prey-capturing pincers) open and extend forward as thescorpion raises its body off the sand. For each movementof the prey, the scorpion will turn and move closer. If itfails to grab the prey with its pedipalps it waits motionlessuntil the prey moves again. This sequence lasts for only afew seconds with one to five orientation movements.

Brownell shows that the sand scorpion couldlocate the direction and the distance of a prey up to 10 cmaway. If the distance was greater, up to 30 cm, only thedirection was sensed. By experiments, where he coveredthe animal’s eight eyes with opaque paint and insertedsound-absorbent tiles between the stimulation source, heshowed that the sand scorpion reacts to vibrationsconducted through the ground. He also showed that thescorpion is using relative arrival time, and not relativeintensity, to find the direction of the prey.

3 The Nature of Seismic WavesThere are two basic classes of seismic waves: the fasterbody waves and the slower surface waves.

Body waves propagate through the earth and canbe of two types: primary (P) and secondary (S). The Pwave is the fastest and is similar to a sound wave becauseit alternately compresses and dilates the ground. Theslower of the body waves is the S wave, which shear therock sideways perpendicular to the direction of the travel.This type of wave cannot propagate through liquid partsof the Earth, because the liquid will not spring back [Bolt,1978]. Compressional waves spread spherically, thereforetheir amplitude falls off as 1/r, where r is the distance tothe source [Narins, 1990].

Figure 1. The four types of seismic waves.

Figure describing the four differentseismic waves.

The second basic class of seismic waves, thesurface waves, can also be of two types. The first is calleda Love wave. Its motion is essentially the same as S wave,it moves the ground from side to side in a horizontal planeperpendicular to the direction of the travel. The secondtype is the Rayleigh wave, which reassembles a rollingocean wave, it moves both in a vertical and horizontaldirection [Bolt, 1978]. Surface waves are spreading in acircular pattern, therefor their amplitude falls off as 1/r1/2,where r is the distance to the source [Narins, 1990].

Rayleigh waves are used for navigating the robotbecause they travel further than compressional waves.

4 Vibration DetectorsInstead of using expensive commercial accelerometers,vibration detectors were manufactured by the author.Kynar piezoelectrical film, made of polyvinylideneflouride (PVDF), was glued to thin pieces of brass with aproof weight on one end. The size of the detectors is 15 x40 mm. They are highly sensitive. A spike of 0.5V wasgenerated when a 1.5g ball was dropped on a woodentable, from a height of 0.15m at a distance of 0.2m fromthe sensor.

The piezoelectrical film was interfaced with a fieldeffect transistor. After filtering the signal, with a bandpassfilter with poles at 10Hz and 200Hz, it was furtheramplified with an operational amplifier. A comparatorwas then used to threshold the signal. The resulting logictransition triggered a pulse catcher in the microcontrollerand therefore the time of arrival could be measured veryaccurately.

Different materials damp vibrations differently.Wood is a good conductor while concrete is damping alot.

Figure 2. A vibration sensor.

Figure 3. The vibration detector picks up Rayleigh wavesconducted through the ground.

5 The Robot DesignThe six-legged robot, Figure 4, is based on a robotdeveloped by Rodney Brooks [1989]. The body has anoval shape to make the legs cover a circular area. As itwas important to keep the weight down, great concernwas taken building the body. The author created asandwich material with a PVC-foam coated on both sideswith aluminium foil. The 8 mm PVC-foam, ClickGel,from Fibreglass International in Melbourne and the 60 µmaluminium foil, from a pie dish manufacturer, resulted abody weight of 50 g.

Each leg is connected to a shoulder joint withtwo degrees of freedom, controlled by two orthogonallyplaced model airplane servos. One vibration sensor isgoing to be fixed to each leg. The servos generates plentyof vibrations and must therefor be switched off duringvibration sensing. During that time a spring supports eachleg.

The servos are controlled by an 8MHzMC68CH12 microcontroller with 1Kbytes of RAM and32Kbytes of FLASH EEPROM. A 7.2V NiCdaccumulator makes the robot totally self-contained.

Figure 4. The six-legged robot scorpion.

6 NavigationDifference in Time of Arrival (TOA) between the sixvibration sensors enables the calculation of the directionand the location of the source of vibration. The precisionof the detected location increases as the distance to thesource of vibration decreases.

6.1 Direction FindingAssuming a plane vibration wave, generated by avibration source at a great distance, the difference in Timeof Arrivals can be used to calculate the direction of thesource, as shown in Figure 5.

The direction α is found by:

l

d

) arccos(

δα = (1)

Where d is the distance between the sensors and δl is thedifference of Time of Arrival, δt, multiplied by theestimated propagation speed, cest.

With only one sensor-pair it is not possible todistinguish if the source of vibration is in front or behind

Figure describing how the sensor reactsto ground vibrations.

the sensor pair. By using two sensor-pairs the problemcan be solved. Only three sensors are actually needed,where one is common to both sets of sensor-pairs. Thesolution presented here minimises the direction error byusing six sensors, which results in 15 sensor-pairs, whichproduce 30 detected directions.

dSensor 1 Sensor 2

α

Vibration wave

δl

Figure 5. Trigonometry of direction finding

Data ValidationA sensor could detect a vibration with an indirect path,caused for example by discontinuities in the ground. Thiscan be prevented by validating the data using thetriangular inequality [Kleeman, 1989]. The sum of thedistance on two sides of a triangle must exceed the third[Jennings, 1994]. Let P be the location of the source ofvibration and S1 and S2 the locations of the two receivingsensors. The triangle inequality gives:

2121 SSPSPS +< (2)

Which can be rewritten as:

2121 SSPSPS <− (3)

When the distance to the source is great

21 PSPS −∞→

=distance

lim lδ(4)

Combining equation (3) and (4) gives:

dl < δ (5)

which accomplish the data validation if the distance to thevibration source is large.

The Sliding Window AlgorithmThe robot must be able to measure the wave propagationspeed to be able to solve the direction finding problemaccurately. An algorithm using a sliding window wasdeveloped.

When rolling a fixed sized window over thedetected directions, the direction generating the maximumdensity within the window is detected. Both direction andthe wave propagation speed are found by changing theestimated propagating speed until the speed generating themaximum density has been found. A simulation ispresented in Table 1. Six sensors were used, placed on a0.3m diameter circle. The source of vibration was placedin a direction of 225°, 3 meters away from the centre of

the sensors. The wave propagation speed was set to 3500m/s and a Gaussian noise with a 100µs standard deviationwas added to the simulated Time of Arrival from thesensors. Figure 6 shows all detected directions that arevalid at a propagation speed of 3500 m/s. The outliers arethe directions detected at the opposite direction of thesensor pair.

Estimated speed Detected direction Density500 90° 3

1000 200° 41500 190° 52000 215° 52500 220° 73000 225° 103500 225°° 144000 225° 94500 220° 65000 225° 55500 225° 36000 245° 3

Table 1. By using a sliding window it is possible to find thedirection and the wave propagation speed as indicated by amaximum of density. Window size was 22.5° and the windowstep size was 5°.

0 50 100 150 200 250 300 3500

1

Degrees

Figure 6. The plot shows all detected directions that are valid ata propagation speed of 3500 m/s. The highest density of detecteddirections is found at 225°.

6.2 Location FindingBy using pairs of radio beacons it is possible to find theexact location of a moving vehicle at a given moment[Pierce et. al, 1948].

Location Finding Using Hyperbolic LinesThe LORAN (LOng RAnge Navigation) system is a radiobased navigation system developed by the United StatesArmy in the early 1940’s [Pierce et. al, 1948]. It enablesnavigation of a vessel without visible landmarks.

The ship located at P receives two radio signalsthat were broadcasted at the same time from radio stationslocated at F1 and F2. The navigator measures thedifference of Time of Arrival:

12 - t tt =δ (6)

The difference between the distance from the ship to F1and the distance from the ship to F2 is:

tc δ=12 PF-PF (7)

where c is the propagation speed of the radio signals.Equation (7) indicates that the ship must be on thehyperbola whose equation is:

tc δ=12 PF-PF (8)

The exact location of the ship may be determined by

using two pairs of radio stations and by finding theintersection of the two hyperbolic lines.

The same principles apply for the reversedcondition, as in our case, where two or more receiversreceive a signal from one source. The intersection isfound using Newton-Raphson method for non-linearsystems of equation [Maron and Lopez, 1991]. Thismethod is only useful when the source of vibration isclose to the robot, as the error grows large when thedistance grows large.

Figure 7 shows a simulation using 4 sensors. Thesource of vibration was located at (-20,5) cm and wasfound by the algorithm after 90 iterations.

-40 -30 -20 -10 0 10

-40

-30

-20

-10

0

10

20

30

40

Horizontal position [cm]

Source

Sensorsused

Figure 7. Simulated location finding using two pairs of sensors.

The Newton-Raphson Method in Higher Dimensions

Let [ ]Tyx=x be the location, in a two-dimensionalCartesian coordinate system, where the source ofvibration is located and the root of the two-dimensionalnon-linear system

0)( =xf (9)

The system is described by

=

),(

),()(

yxh

yxgf x (10)

where ),( yxg and ),( yxh are the functions of twohyperbolas derived from the differences of Time ofArrival between two pairs of vibration sensors. Byexpanding the functions to their first order Taylor seriesexpansion about x ,

xx

xxx ∆∂∂

+=∆+f

ff )()( (11)

the Newton-Raphson method seeks a common root thatsolves equation (9) close to an initial guess. If xx ∆+ isthe root of equation (9), the right hand side of equation(11) is zero, and the following set of linear equations isobtained:

)(xxx

ff

−=∆∂∂

(12)

Solving equation (12) for x∆ gives

)(1

xx

x ff

−

∂∂

−=∆ (13)

Suppose xk is the current approximation of x, then theimproved guess xk+1 can be found by

xxx k1k ∆+=+ (14)

Given a good initial guess of x , iteration of equation (13)and (14) gives the root of equation (9).

7 Further work and conclusionsThe result of the simulations shows that ground vibrationscan be used to navigate a robot. A vibration sensor systemwas developed and was successfully tested on woodensurfaces.

Further improvements to the vibration detectors,for example by using highly sensitive commercialaccelerometers, would make system more accurate. Bydoing so vibrations conducted through highly dampingmaterials such as concrete and sand could be used fornavigation. Enhancements could also be done to thelocation finding algorithm by using Bab-Hahiashar [1995]modified Newton-Raphson method for solving non-linearsystems of equations. The modified method is reported toconverge faster.

References

[Bab-Hadiashar, 1995] Alireza Bab-Hadiashar, "ModifiedNewton-Raphson Method for Solving Non-linearSystems of Equations" Technical Reports MECSE 95-2, Monash University, Australia, 1995.

[Bolt, 1978] Bruce A. Bolt, Earthquakes. ISBN 0-7167-0094-8

[Brooks, 1989] Rodney A. Brooks, "A Robot That Walks;Emergent Behaviors from a Carefully EvolvedNetwork,", MIT AI Lab Memo 1091, February 1989.

[Brownell, 1984] Philip H. Brownell, Prey detection bythe sand scorpion. Scientific American v251 p94, Dec1984.

[Jennings, 1994] George A. Jennings, Modern Geometrywith Applications, p 173-174. ISBN 0-387-94222-X.

[Narins, 1990] Peter M. Narinsm, Seismic communicationin Anuran amphibians. (white-lipped frogs), BioSciencev40 n4 p268, April 1990.

[Kleeman, 1989] Lindsay Kleeman, "Ultrasonicautonomous robot localisation system", IEEEinternational conference Intelligent Robots and Systems'89 Tsukuba, Japan, pp.212-219 September 1989.

[Maron and Lopez, 1991] Melvin J. Maron and Robert J.Lopez, Numerical Analysis, p 205-213, ISBN 0-534-12372-4, 1991.

[Pierce et. al, 1948] J.A Pierce, A.A McKenzie, R.H.Woodward, LORAN, McGraw-Hill Book Company,Inc, 1948.