Global Positioning System Reference
In-Depth Information
2.4 RISS mechanization
2.4.1 Attitude equations
The equations for calculating pitch and roll from accelerometers are based on the idea
presented in (Noureldin et al., 2002)(Noureldin et al., 2004). The robot acceleration derived
from wheel encoder measurements is removed from the forward accelerometer measurement
before computing the pitch angle. The equation for pitch
and neglecting acceleration in the
forward direction since the robot travels at very low speeds is as follows:
ρ
sin
−
1
f
y
−
sin
−
1
f
y
g
a
f
ρ
=
≈
(6)
g
Where:
f
y
is the forward accelerometer reading;
g
is the acceleration due to gravity; and
a
f
is the forward acceleration and is derived from the forward velocity of the robot
calculated from the average velocity measured by the wheel encoders from Equation 2.
The transverse accelerometer has to be compensated for the normal acceleration of the vehicle
and then it is used to calculate the roll angle. The equation for roll
θ
:
sin
−
1
f
x
+
V
f
ω
z
g
cos
θ
=
−
(7)
ρ
Where:
f
x
is the transversal accelerometer reading; and
ω
z
is the vertical gyroscope reading.
The equation for the time-rate-of-change of yaw according to (Iqbal et al., 2009) using the
previous value for
V
e
from RISS mechanization:
tan
φ
˙
ψ
=
ω
z
−
ω
e
sin
φ
−
V
e
(8)
R
+
h
Integrating in discrete time gives us:
˙
ψ
(
) =
ψ
(
−
) +
ψ
(
)
Δ
k
k
1
k
t
(9)
2.4.2 Velocity equations
There are three accelerometers that can be used to measure acceleration in the body frame
of the mobile robot. Use these acceleration values to compute a velocity increment in the
current time-step in order to compute an estimate for velocities. Use roll, pitch and yaw to
calculate a rotation matrix
l
b
from the body frame to the local frame in Equation 1. Calculate
R
ie
for the earth's rotation rate since the last velocity calculation. In
addition, calculate the skew-symmetric matrix
a skew-symmetric matrix
ω
el
for the LLF change-of-orientation since last
ω
calculation.
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