Page 131 - Introduction to Autonomous Mobile Robots

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a) b) Chapter 4
Transmitter/
Receiver
Transmitter
v Receiver v Object

Figure 4.16
Doppler effect between two moving objects (a) or a moving and a stationary object (b).

of view, his or her motion triggers a change in heat in the sensor’s reference frame. In the
next section, we describe an important type of motion detector based on the Doppler effect.
These sensors represent a well-known technology with decades of general applications
behind them. For fast-moving mobile robots such as autonomous highway vehicles and
unmanned flying vehicles, Doppler-based motion detectors are the obstacle detection
sensor of choice.

4.1.7.1 Doppler effect-based sensing (radar or sound)
Anyone who has noticed the change in siren pitch that occurs when an approaching fire
engine passes by and recedes is familiar with the Doppler effect.
f
A transmitter emits an electromagnetic or sound wave with a frequency . It is either
t
received by a receiver (figure 4.16a) or reflected from an object (figure 4.16b). The mea-
f
sured frequency at the receiver is a function of the relative speed between transmitter
v
r
and receiver according to
1
f = f ------------------ (4.15)
⁄
t
r
1 + vc
if the transmitter is moving and
⁄
(
f = f 1 + vc) (4.16)
r
t
if the receiver is moving.
In the case of a reflected wave (figure 4.16b) there is a factor of 2 introduced, since any
change x in relative separation affects the round-trip path length by 2x . Furthermore, in
such situations it is generally more convenient to consider the change in frequency ∆f ,
known as the Doppler shift, as opposed to the Doppler frequency notation above.