Bichop R.H. (Ed.) Mechatronic Systems, Sensors, and Actuators: Fundamentals and Modeling

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20-94 Mechatronic Systems, Sensors, and Actuators

Worst-case range measurement accuracy is ±5 cm, with typical values of around ±2 cm. The pulsed near-

infrared laser is Class-1 eye-safe under all operating conditions.

Microwave Range Sensors

Microwave technology may be used to measure motion, velocity, range, and direction of motion

(Figure 20.68). The sensors are rugged since they have no moving parts. They can be operated safely in

explosive environments, because the level of energy used is very low (no risk for sparks). Their operating

temperatures range from −55°C to +125°C. They can work in environments with dust, smoke, poisonous

gases, and radioactivity (assuming the components are hardened for radiation). Typically microwave

sensors are used to measure ranges from 25 to 45,000 mm, but longer ranges are possible depending on

power and object size. The reflected power returning to the receiver decreases as the fourth power of the

distance to the object. Typical wavelength used ranges from 1 to 1000 mm.

Time-of-flight is in the order 2 ns per foot of range (reach the target and return). This translates into

10.56 ms per mile of range. Measuring short ranges may pose a problem. For 1 in. resolution, the circuit

must resolve 167 ps. An alternate method more suitable to measure short distances is based on a frequency

sweep of the signal generator. In this case, the return signal remains at the initial frequency (usually

10.525 GHz), and it is compared with the current frequency changed by a sweep rate. For example, to

measure a range of 3 ft, one may sweep at 5 MHz/ms. After 6 ns, the frequency changes by 30 Hz (6 ns ×

5 MHz/0.001 s). In this case, 0.0256 mm (0.001 in.) may be resolved easily. When using this method, a

signal amplifier that increases gain with frequency is necessary. See section “Frequency Modulation” for

more details on frequency modulation methods.

Phase Measurement

Time-of-flight (TOF) is defined as a phase shift between emitted and received signals when the dis-

tance is less than one wavelength (Figure 20.69). Given a phase shift f, the distance is calculated as

FIGURE 20.68 The microwave sensor, unlike the motion detector, requires a separate transmitter and receiver.

(Adapted from Williams, 1989.)

FIGURE 20.69 Range from phase measurement.

Locked

Output

Receiver

Transmitter

Filter

Preamp

Modulator

Phase locked

loop

2345

Emitted signal

Return signal

Phase

Amplitude

Time

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Sensors 20-95

if the emitter and receiver are at the same location, or if

the receiver is attached to the target, where c is the speed of travel,

is the measured phase, and f is the

modulation frequency.

The phase shift between outgoing and reflected sine waves can be measured by multiplying the two

signals together in an electronic mixer, then averaging the product over many modulation cycles

(Woodbury et al., 1993). This integrating process can be relatively time consuming, making it difficult to

achieve extremely rapid update rates. The result can be expressed mathematically as follows (Woodbury

et al., 1993):

(20.70)

which reduces to

(20.71)

where t is the time, T is the averaging interval, and A is the amplitude factor from gain of integrating

amplifier.

From the earlier expression for

, it can be seen that the quantity actually measured is in fact the cosine

of the phase shift and not the phase shift itself (Woodbury et al., 1993). This situation introduces a so-

called ambiguity interval for scenarios where the round-trip distance exceeds the modulation wavelength

(i.e., the phase measurement becomes ambiguous once

exceeds 360°). Conrad and Sampson (1990)

define this ambiguity interval as the maximum range that allows the phase difference to go through one

complete cycle of 360°:

(20.72)

where R

is the ambiguity range interval.

Referring to Equation 20.73, it can be seen that the total round-trip distance 2d is equal to some integer

number of wavelengths n

plus the fractional wavelength distance x associated with the phase shift. Since

the cosine relationship is not single-valued for all of

, there will be more than one distance d corre-

sponding to any given phase-shift measurement (Woodbury et al., 1993):

(20.73)

where

d = (x + n

)/2 = true distance to target,

x = distance corresponding to differential phase

n = number of complete modulation cycles.

Careful re-examination of Equation 20.73, in fact, shows that the cosine function is not single-valued

even within a solitary wavelength interval of 360

. Accordingly, if only the cosine of the phase angle is

measured, the ambiguity interval must be further reduced to half the modulation wavelength, or 180

(Scott,

1990). In addition, the slope of the curve is such that the rate of change of the nonlinear cosine function is

not constant over the range of 0

≤

180

, and is in fact zero at either extreme. The achievable accuracy

of the phase-shift measurement technique thus varies as a function of target distance, from best-case

φλ

πφ

c/4

f== d

φλ

πφ

c/2

f==

---

T→∞

lim

---------

----------

---------

sinsin dt

----------

cos

----

---------

cos

+()

---------------------------

cos==cos

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20-96 Mechatronic Systems, Sensors, and Actuators

performance for a phase angle of 90

to worst case at 0 and 180

. For this reason, the useable measurement

range is typically even further limited to 90% of the 180

ambiguity interval (Chen et al., 1993).

A common solution to this problem involves taking a second measurement of the same scene but with

a 90° phase shift introduced into the reference waveform, the net effect being the sine of the phase angle

is then measured instead of the cosine. This additional information (i.e., both sine and cosine measure-

ments) can be used to expand the phase angle ambiguity interval to the full 360° limit previously discussed

(Scott, 1990). Furthermore, an overall improvement in system accuracy is achieved, as for every region

where the cosine measurement is insensitive (i.e., zero slope), the complementary sine measurement will

be at peak sensitivity (Woodbury et al., 1993).

Nevertheless, the unavoidable potential for erroneous information as a result of the ambiguity interval

is a detracting factor in the case of phase-detection schemes. Some applications simply avoid such

problems by arranging the optical path in such a fashion as to ensure the maximum possible range is

always less than the ambiguity interval (Figure 20.70). Alternatively, successive measurements of the same

target using two different modulation frequencies can be performed, resulting in two equations with two

unknowns, allowing both x and n (in the previous equation) to be uniquely determined. Kerr (1988)

describes such an implementation using modulation frequencies of 6 and 32 MHz.

For square-wave modulation at the relatively low frequencies typical of ultrasonic systems (20–

200 kHz), the phase difference between incoming and outgoing waveforms can be measured with the

simple linear circuit shown in Figure 20.71 (Figueroa & Barbieri, 1991a). The output of the exclusive-or

gate goes high whenever its inputs are at opposite logic levels, generating a voltage across capacitor C

that is proportional to the phase shift. For example, when the two signals are in phase (i.e.,

= 0), the

gate output stays low and V is zero; maximum output voltage occurs when

reaches 180°. While easy

to implement, this simplistic approach is limited to very low frequencies and may require frequent

calibration to compensate for drifts and offsets due to component aging or changes in ambient conditions

(Figueroa & Lamancusa, 1992).

Extended Range Phase Measurement Systems

Figueroa and Barbieri (1991a; 1991b) report an interesting method for extending the ambiguity interval

in ultrasonic phase-detection systems through frequency division of the received and reference signals.

Since the span of meaningful comparison is limited (best case) to one wavelength,

, it stands to reason

that decreasing the frequency of the phase detector inputs by some common factor will increase

by a

similar amount. The concept is illustrated in Figure 20.72. Due to the very short wavelength of ultrasonic

energy (i.e., about 0.25 in. for the Polaroid system at 49.1 kHz), the total effective range is still only 4 in.

FIGURE 20.70 By limiting the maximum distance measured to be less than the range ambiguity interval R

erroneous distance measurements can be avoided.

FIGURE 20.7 At low frequencies typical of ultrasonic systems, a simple phase-detection circuit based on an exclusive-

or gate will generate an analog output voltage proportional to the phase difference seen by the inputs. (Adapted from

Figueroa & Barbieri, 1991a.)

MDARS

security

Maximum range

Reference

Phase difference

Signal

XOR Gate

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Sensors 20-97

after dividing the detector inputs by a factor of 16. Due to this inherent range limitation, ultrasonic phase-

detection ranging systems are not extensively applied in mobile robotic applications, although Figueroa

and Lamancusa (1992) describe a hybrid approach used to improve the accuracy of TOF ranging for

three-dimensional position location.

An ingenious method to measure range using phase information was developed by Young and Li (1992).

The method reconstructs the total range by piecing together multiple consecutive phase chunks that reset

every 2

radians of phase difference between emitted and received signals. This is another method that

overcomes the limitation of phase-based systems to ranges shorter than one acoustic wavelength. The

discontinuities at every 2

radians are eliminated by first taking the derivative of the phase, resulting in a

smooth signal with sharp pulses (impulses) at the location of each discontinuity. Subsequently, the pulses

are ignored and the result is integrated and multiplied by a constant to reconstruct the overall range. The

method was tested with an experiment that employed 40 kHz transducers. Distances from 40 to 400 mm

were measured with errors from ±0.1629 to ±0.4283 mm.

Laser-based continuous-wave ranging originated out of work performed at the Stanford Research

Institute in the 1970s (Nitzan et al., 1977). Range accuracies approach those achievable by pulsed laser

TOF methods. Only a slight advantage is gained over pulsed TOF rangefinding, however, since the difficult

time-measurement problem is replaced by the need for fairly sophisticated phase-measurement electron-

ics (Depkovich & Wolfe, 1984). In addition, problems with the phase-shift measurement approach are

routinely encountered in situations where the outgoing energy is simultaneously reflected from two target

surfaces at different distances from the sensor, as for example when scanning past a prominent vertical

edge (Hebert & Krotkov, 1991).

The system electronics are set up to compare the phase of a single incoming wave with that of the

reference signal and are not able to cope with two superimposed reflected waveforms. Adams (1993)

describes a technique for recognizing the occurrence of this situation in order to discount the resulting

erroneous data.

Frequency Modulation

This is a method devised to improve the accuracy in detecting the time-of-arrival of the wave to the

receiver. Instead of a single frequency wave, a frequency modulated wave of the form f = f

+ kt is emitted.

The difference between the emitted and received frequency at any time is ∆f = kt − k(t − t

) = kt

(Figure 20.73). The advantage of this method is that one does not need to know exactly when the wave

arrived to the receiver. However, accurate real-time frequency measurement electronics must be used,

and the transducers must respond within the frequency band sweep. Modulation other than linear is

also possible in order to improve signal-to-noise ratio and hence accuracy.

The signal is reflected from a target and arrives at the receiver at time t + T:

where T is the round-trip propagation time, d is the distance to target, and c is the speed of travel.

FIGURE 20.72 Dividing the input frequencies to the phase comparator by some common integer value will extend

the ambiguity interval by the same factor, at the expense of resolution. (Adapted from Figueroa & Barbieri, 1991a.)

Transmiitted

TTL sinc

Received

TTL wave

Phase

Receiver

to TTL

Transmitter

Function

generator

Frequency

divider

Frequency

divider

Phase

detection

Volts

------

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20-98 Mechatronic Systems, Sensors, and Actuators

The received signal is compared with a reference signal taken directly from the transmitter. The received

frequency curve (Figure 20.74) will be displaced along the time axis relative to the reference frequency

curve by an amount equal to the time required for wave propagation to the target and back. (There might

also be a vertical displacement of the received waveform along the frequency axis, due to the Doppler

effect.) These two frequencies when combined in the mixer produce a beat frequency F

where k is a constant.

This beat frequency is measured and used to calculate the distance to the object:

where

d = range to target,

c = speed of light,

= beat frequency,

= repetition (modulation) frequency,

= total FM frequency deviation.

Distance measurement is therefore directly proportional to the difference or beat frequency and is as

accurate as the linearity of the frequency variation over the counting interval.

Advances in wavelength control of laser diodes now permit this ultrasonic and radar ranging technique

to be used with lasers. The frequency or wavelength of a laser diode can be shifted by varying its

temperature. Consider an example where the wavelength of an 850-nm laser diode is shifted by 0.05 nm

in 4

s: the corresponding frequency shift is 5.17 MHz/ns. This laser beam, when reflected from a surface

FIGURE 20.73 The frequency difference between the emitted signal and received signal is proportional to the time-

of-flight at any given time.

FIGURE 20.74 The received frequency curve is shifted along the time axis relative to the reference frequency.

–2 3 8 13 18

Time

Amplitude

Emitted signal

Return signal

Time-of-flight

Frequency f = f

+ kt

Frequency f = f

+ k (t -t

)

2d/c

ft()= fT t+()– kT=

-------------

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Sensors 20-99

1 m away, would produce a beat frequency of 34.5 MHz. The linearity of the frequency shift controls the

accuracy of the system.

The frequency-modulation approach has an advantage over the phase-shift measurement technique

in which a single distance measurement is not ambiguous. (Recall that phase-shift systems must perform

two or more measurements at different modulation frequencies to be unambiguous.) However, frequency

modulation has several disadvantages associated with the required linearity and repeatability of the

frequency ramp, as well as the coherence of the laser beam in optical systems. As a consequence, most

commercially available FMCW ranging systems are radar based, while laser devices tend to favor TOF

and phase-detection methods.

Triangulation Ranging

Triangulation ranging is based upon an important premise of plane trigonometry, which states that given

the length of a side and two angles of a triangle, it is possible to determine the length of the other sides

and the remaining angle. The basic Law of Sines can be rearranged as shown below to represent the length

of side B as a function of side A and the angles

and

In ranging applications, length B would be the desired distance to the object of interest at point P

(Figure 20.75) for known sensor separation baseline A.

Triangulation ranging systems are classified as either passive (use only the ambient light of the scene)

or active (use an energy source to illuminate the target). Passive stereoscopic ranging systems position

directional detectors (video cameras, solid-state imaging arrays, or position sensitive detectors) at posi-

tions corresponding to locations P

and P

(Figure 20.76). Both imaging sensors are arranged to view

the same object point, P

, forming an imaginary triangle. The measurement of angles

and

conjunction with the known orientation and lateral separation of the cameras allows the calculation of

range to the object of interest.

Active triangulation systems, on the other hand, position a controlled light source (such as a laser) at

either point P

or P

, directed at the observed point P

. A directional imaging sensor is placed at the

remaining triangle vertex and is also aimed at P

. Illumination from the source will be reflected by the

FIGURE 20.75 Triangulation ranging systems determine range B to target point P

by measuring angles f and q at

points P

and P

FIGURE 20.76 Passive stereoscopic ranging system configuration.

Camera 2

Camera 1

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target, with a portion of the returned energy falling on the detector. The lateral position of the spot as

seen by the detector provides a quantitative measure of the unknown angle

, permitting range deter-

mination by the Law of Sines.

The performance characteristics of triangulation systems are to some extent dependent on whether

the system is active or passive. Passive triangulation systems using conventional video cameras require

special ambient lighting conditions that must be artificially provided if the environment is too dark.

Furthermore, these systems suffer from a correspondence problem resulting from the difficulty in match-

ing points viewed by one image sensor with those viewed by the other. On the other hand, active

triangulation techniques employing only a single detector do not require special ambient lighting, nor

do they suffer from the correspondence problem. Active systems, however, can encounter instances of

no recorded strike because of specular reflectance or surface absorption of the light.

Limiting factors common to all triangulation sensors include reduced accuracy with increasing range,

angular measurement errors, and a missing parts (also known as shadowing) problem. Missing parts refers

to the scenario where particular portions of a scene can be observed by only one viewing location (P

). This situation arises because of the offset distance between P

and P

, causing partial occlusion of the

target (i.e., a point of interest is seen in one view but otherwise occluded or not present in the other). The

design of triangulation systems must include a tradeoff analysis of the offset: as this baseline measurement

increases, the range accuracy increases, but problems due to directional occlusion worsen.

Stereo Disparity

The first of the triangulation schemes to be discussed, stereo disparity (also called stereo vision, binocular

vision, and stereopsis) is a passive ranging technique modeled after the biological counterpart. When a

three-dimensional object is viewed from two locations on a plane normal to the direction of vision, the

image as observed from one position is shifted laterally when viewed from the other. This displacement

of the image, known as disparity, is inversely proportional to the distance to the object. Humans sub-

consciously verge their eyes to bring objects of interest into rough registration (Burt et al., 1992). Hold

up a finger a few inches away from your face while focusing on a distant object and you can simultaneously

observe two displaced images in the near field. In refocusing on the finger, your eyes actually turn inward

slightly to where their respective optical axes converge at the finger instead of infinity.

Most implementations use a pair of identical video cameras (or a single camera with the ability to

move laterally) to generate the two disparity images required for stereoscopic ranging. The cameras are

typically aimed straight ahead viewing approximately the same scene, but (in simplistic cases anyway)

do not possess the capability to verge their center of vision on an observed point, as can human eyes.

This limitation makes placement of the cameras somewhat critical because stereo ranging can take place

only in the region where the fields of view overlap. In practice, analysis is performed over a selected range

of disparities along the Z axis on either side of a perpendicular plane of zero disparity called the horopter

(Figure 20.77). The selected image region in conjunction with this disparity range defines a three-dimen-

sional volume known as the stereo observation window (Burt et al., 1993).

More recently there has evolved a strong interest within the research community for dynamically

reconfigurable camera orientation (Figure 20.78), often termed active vision in the literature (Aloimonos

et al., 1987; Swain & Stricker, 1991; Wavering et al., 1993). The widespread acceptance of this terminology

is perhaps somewhat unfortunate in view of potential confusion with stereoscopic systems employing

an active illumination source (see section 4.1.3). Verging ste reo, another term in use, is perhaps a more

appropriate choice. Mechanical verging is defined as the process of rotating one or both cameras about

the vertical axis in order to achieve zero disparity at some selected point in the scene (Burt et al., 1992).

There are four basic steps involved in the stereo ranging process (Poggio, 1984):

•

A point in the image of one camera must be identified (Figure 20.79, left).

•

The same point must be located in the image of the other camera (Figure 20.79, right).

•

The lateral positions of both points must be measured with respect to a common reference.

•

Range Z is then calculated from the disparity in the lateral measurements.

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Sensors 20-101

On the surface this procedure appears rather straightforward, but difficulties arise in practice when

attempting to locate the specified point in the second image (Figure 20.79). The usual approach is to

match “interest points” characterized by large intensity discontinuities (Conrad & Sampson, 1990). Match-

ing is complicated in regions where the intensity and/or color are uniform (Jarvis, 1983b). Additional

factors include the presence of shadows in only one image (due to occlusion) and the variation in image

characteristics that can arise from viewing environmental lighting effects from different angles. The

effort to match the two images of the point is called

correspondence

, and methods for minimizing this

FIGURE 20.77 The stereo observation window is that volume of interest on either side of the plane of zero disparity

known as the horopter. (Courtesy David Sarnoff Research Center.)

FIGURE 20.78 This stereoscopic camera mount uses a pair of lead-screw actuators to provide reconfigurable

baseline separation and vergence as required. (Courtesy Robotic Systems Technology, Inc.)

Resolution

cell

Stereo

observation

window

Camera

field of

view

Horopter

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computationally expensive procedure are widely discussed in the literature (Nitzan, 1981; Jarvis, 1983a;

Poggio, 1984; Loewenstein, 1984; Vuylsteke et al., 1990; Wildes, 1991).

Probably the most basic simplification employed in addressing the otherwise overwhelming correspon-

dence problem is seen in the epipolar restriction that reduces the two-dimensional search domain to a

single dimension (Vuylsteke et al., 1990). The epipolar surface is a plane defined by the point of interest

P and the positions of the left and right camera lenses at L and R, as shown in Figure 20.80. The

intersection of this plane with the left image plane defines the left epipolar line as shown. As can be seen

from the diagram, since the point of interest P lies in the epipolar plane, its imaged point P

must lie

somewhere along the left epipolar line. The same logic dictates that the imaged point P

must lie along a

similar right epipolar line within the right image plane. By carefully aligning the camera image planes

such that the epipolar lines coincide with identical scan lines in their respective video images, the

correspondence search in the second image is constrained to the same horizontal scan line containing

the point of interest in the first image. This effect can also be achieved with nonaligned cameras by careful

calibration and rectification (resampling).

To reduce the image processing burden, most correspondence schemes monitor the overall scene at

relatively low resolution and examine only selected areas in greater detail. A foveal representation analo-

gous to the acuity distribution in human vision is generally employed as illustrated in Figure 20.81,

allowing an extended field-of-view without loss of resolution or increased computational costs (Burt

et al., 1993). The high-resolution fovea must be shifted from frame to frame in order to examine different

regions of interest individually. Depth acuity is greatest for small disparities near the horopter and falls

off rapidly with increasing disparities (Burt et al., 1992).

Active Triangulation

Rangefinding by active triangulation is a variation on the stereo disparity method of distance measure-

ment. In place of one camera is a laser (or LED) light source aimed at the surface of the object of interest.

FIGURE 20.79 Range Z is derived from the measured disparity between interest points in the left and right camera

images. (Courtesy David Sarnoff Research Center.)

FIGURE 20.80 The epipolar surface is a plane defined by the lens centerpoints L and R and the object of interest

at P. (Adapted from Vuylsteke et al., 1990.)

δθ

local

pattern

Range (Z )

Camera

field of

view

Step ( z)

Analysis

window

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Sensors 20-103

The remaining camera is offset from this source by a known distance A and configured to hold the

illuminated spot within its field of view (Figure 20.82).

For one- or two-dimensional array detectors such as vidicon or CCD cameras, the range can be

determined from the known baseline distance A and the relative position of the laser-spot image on the

image plane. For mechanically scanned single-element detectors such as photodiodes or phototransistors,

the rotational angles of the detector and/or source are measured at the exact instant the detector observes

the illuminated spot. The trigonometric relationships between these angles and the baseline separation

are used (in theory) to compute the distance. To obtain three-dimensional information for a volumetric

region of interest, laser triangulators can be scanned in both azimuth and elevation. In systems where

the source and detector are self-contained components, the entire configuration can be moved mechan-

ically. In systems with movable optics, the mirrors and lenses are generally scanned in synchronization

while the laser and detector remain stationary.

Drawbacks to active triangulation include the missing parts situation, where points illuminated by the

light source cannot be seen by the camera and vice versa (Jarvis, 1983b), as well as surface absorption

or specular reflection of the irradiating energy (see Chapter 9). On the positive side, however, point-

source illumination of the image effectively eliminates the correspondence problem encountered in stereo

disparity rangefinders. There is also no dependence on scene contrast, and reduced influence from

ambient lighting effects. (Background lighting is effectively a noise source that can limit range resolution.)

FIGURE 20.81 The foveal stereo representation provides high acuity near the center of the observation window,

with decreasing resolution towards the periphery. (Courtesy David Sarnoff Research Center.)

FIGURE 20.82 An active triangulation-ranging configuration employing a conventional CCD array as the detector.

Foveal

observation

window

Footprint

Laser

Camera

Target object

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