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3.3. TIME SYNCHRONIZATION 15
3.3 Time Synchronization
State of the art service robots have normally more than just one PC on board. Thus the clock of the
different PCs have to be synchronized if data from two or more PCs have to be handled according to
time. For coordinate frame transformation this is the case where transformations can be published by
different computers and have to be matched according to their time stamp.
The general problem with multiple computers as described in [31, p. 239] is, that the clock of each
PC has a drift. The drift is produced by production tolerances of the oscillators and by environmental
influences such as different temperatures. Thus clocks on different PCs will always drift apart.
If t is the reference time and C p (t) is the value of the clock on machine p, the equation C p (t) = t
would be true for all p and all t if there would be no drift. Further C p(t) ′ = dC
dt
ideally should be 1.
The frequency of a clock p at time t is C p(t), ′ the skew of a clock is defined as C p(t) ′ − 1 and donates
how much the frequency differs from the perfect clock. C p (t) − t simply defines the offset between
the clock p and the reference clock. The maximum drift rate ρ is specified by the manufacturer and
the timer works in its specification if
1 − ρ ≤ dC
dt ≤ 1 + ρ
If two equal clocks are compared to the reference clock at time ∆t after they were synchronized, they
can not be more than 2ρ · ∆t time units apart. To guarantee that no two clocks ever differ more than
δ, they must be synchronized at least every δ
2ρ
time units. The relationship of a slow, a perfect and a
fast clock is shown in Figure 3.5.
clock time, C
fast clock
dC
dt >1 dC
perfect clock
slow clock
dt =1 dC
dt