Inertial Navigation:
Inertial navigation is a
self-contained navigation technique in which measurements provided by accelerometers
and gyroscopes are used to track the position and orientation of an object
relative to a known starting point, orientation and velocity. Inertial
measurement units (IMUs) typically contain three orthogonal rate gyroscopes and
three orthogonal accelerometers, measuring angular velocity and linear
acceleration respectively. By processing signals from these devices it is
possible to track the position and orientation of a device.
Inertial navigation is
used in a wide range of applications including the navigation of aircraft,
tactical and strategic missiles,
spacecraft, submarines and ships. Recent advances in the construction of MEMS devices have made it
possible to manufacture small and light inertial navigation systems. These Advances
have widened the range of possible applications to include areas such as human
and animal motion capture.
Inertial System Configurations:
Nearly all IMUs fall into one of the two categories outlined
below. The difference between the two catagories is the frame of reference in
which the rate-gyroscopes and accelerometers operate. Throughoutthis report we
will refer to the navigation system’s frame of reference as the body frame and
to the frame of reference in which we are navigating as the global frame, as
shown in Figure 1.
Figure 1: The body and global frames of reference.
Inertial System Configurations:
Stable Platform Systems:
In stable platform type systems the inertial sensors are mounted
on a platform which is isolated from any external rotational motion. In other
words the platform is held in alignment with the global frame. This is achieved
by mounting the platform using gimbals (frames) which allow the platform
freedom in all three axes, as shown in Figure 2. The platform mounted
gyroscopes detect any platform rotations. These signals are fed back to torque
motors which rotate the gimbals in order to cancel out such rotations, hence
keeping the platform aligned with the global frame. To track the orientation of
the device the angles between adjacent gimbals can be read using angle pick-offs.
To calculate the position of the device the signals from the platform mounted
accelerometers are double integrated. Note that it is necessary to subtract
acceleration due to gravity from the vertical channel before performing the
integration. The stable platform inertial navigation algorithm is shown in Figure
3.
Figure 2: A stable platform IMU.
Figure 3: Stable platform inertial navigation algorithm..
Strap down Systems:
In strap down systems the inertial sensors are mounted rigidly
onto the device, and therefore output quantities measured in the body frame
rather than the global frame. To keep track of orientation the signals from the
rate gyroscopes are ‘integrated’. To track position the three accelerometer
signals are resolved into global coordinates using the known orientation, as
determined by the integration of the gyro signals. The global acceleration
signals are then integrated as in the stable platform algorithm. This procedure
is shown in Figure 4.
Figure 4: Strapdown inertial navigation algorithm.
Stable platform and strap down systems are both based on the
same underlying principles. Strapdown systems have reduced mechanical
complexity and tend to be physically smaller than stable platform systems.
These benefits are achieved at the cost of increased computational complexity.
As the cost of computation has decreased strapdown systems have become the
dominant type of INS.
Gyroscopes:
Types of Gyroscope:
In this section the main types of gyroscope are presented. Note
that this is far from an exhaustive list. In particular there are many
different varieties of mechanical gyroscope which are not described.
Mechanical:
A conventional gyroscope consists of a spinning wheel mounted
on two gimbals which allow it to rotate in all three axes, as show in Figure 5.
An effect of the conservation of angular momentum is that the spinning wheel
will resist changes in orientation. Hence when a mechanical gyroscope is subjected
to a rotation the wheel will remain at a constant global orientation and the
angles between adjacent gimbals will change. To measure the orientation of the
device the angles between adjacent gimbals can be read using angle pick-offs.
Note that a conventional gyroscope measures orientation. In contrast nearly all
modern gyroscopes are rate-gyros, which measure angular velocity.
The main disadvantage of mechanical gyroscopes is that they
contain moving parts. Moving parts cause friction, which in turn causes the
output to drift over time. To minimize friction high-precision bearings and
special lubricants are used, adding to the cost of the device. Mechanical
gyroscopes also require a few minutes to warm up, which is not ideal in many
situations.
Figure 5: A conventional mechanical gyroscope
Optical:
A fibre optic gyroscope (FOG) uses the interference of light to
measure angular velocity. A FOG consists of a large coil of optical fibre. To
measure rotation two light beams are fired into the coil in opposite directions.
If the sensor is undergoing a rotation then the beam travelling in the
direction of rotation will experience a longer path to the other end of the
fibre than the beam travelling against the rotation, as illustrated in Figure
6. This is known as the Sagnac effect. When the beams exit the fibre they are combined.
The phase shift introduced due to the Sagnac effect causes the beams to
interfere, resulting in a combined beam whose intensity depends on the angular
velocity. It is therefore possible to measure the angular velocity by measuring
the intensity of the combined beam.
Ring laser gyroscopes (RLGs) are also based on the Sagnac
effect. The difference between a FOG and RLG is that in a RLG laser beams are
directed around a closed path using mirrors rather than optical fibre. Unlike mechanical gyroscopes, optical gyros
contain no moving parts and require only a few seconds to start-up. The accuracy of an optical gyro is
largely dependent on the length of the light transmission path (larger is better), which is constrained by the size of device.
Figure 6: The Sagnac effect.
MEMS Gyroscopes:
Despite years of development, mechanical and optical gyroscopes
still have high part counts and a requirement for parts with high-precision
tolerances and intricate assembly techniques. As a result they remain expensive.
In contrast MEMS sensors built using silicon micro-machining techniques have
low part counts (a MEMS gyroscope can consist of as few as three parts) and are
relatively cheap to manufacture. MEMS gyroscopes make use of the Coriolis
effect, which states that in a frame of reference rotating at angular velocity !,
a mass m moving with velocity v experiences a force:
Fc = −2m(w×
v)
MEMS gyroscopes contain vibrating elements to measure the
Coriolis effect. Many vibrating element geometries exist, such as vibrating
wheel and tuning fork gyroscopes. The simplest geometry consists of a single
mass which is driven to vibrate along a drive axis, as shown in Figure 7. When
the gyroscope is rotated a secondary vibration is induced along the
perpendicular sense axis due to the Coriolis force. The angular velocity can be
calculated by measuring this secondary rotation.
At present MEMS sensors cannot match the accuracy of optical
devices, however they are expected to do so in the future. Below is a list of
the advantageous properties of MEMS sensors.
Ø small
size;
Ø low
weight;
Ø rugged
construction;
Ø low
power consumption;
Ø short
start-up time;
Ø inexpensive
to produce (in high volume)
Figure 7: A vibrating mass gyroscope
Accelerometers:
Types of Accelerometer:
An accelerometer can be broadly classified as either a
mechanical or solid state device. In this section these three types of
accelerometer are described,
Mechanical
A mechanical accelerometer consists of a mass suspended by
springs, as shown in Figure 8. The displacement of the mass is measured using a
displacement pick-off, giving a signal that is proportional to the force F acting
on the mass in the direction of the input axis. Newton’s second law F = ma is
then used to calculate the acceleration acting on the device.
Figure 8: A mechanical accelerometer
Solid State:
Solid-state accelerometers can be broken into various
sub-groups, including surface acoustic wave, vibratory, silicon and quartz
devices. Solid state accelerometers are small, reliable and rugged. An example
of a solid-state accelerometer is the surface acoustic wave (SAW)
accelerometer. A SAW accelerometer consists of a cantilever beam which is
resonated at a particular frequency, as shown in Figure 9. A mass is attached
to one end of the beam which is free to move. The other end is rigidly attached
to the case. When an acceleration is applied along the input axis the beam
bends. This causes the frequency of the surface acoustic wave to change proportionally
to the applied strain. By measuring this change in frequency the acceleration
can be determined.
Figure 9: A surface acoustic wave accelerometer
MEMS Accelerometers:
Micro-machined silicon accelerometers use the same principles
as mechanical and solid state sensors. There are two main classes of MEMS
accelerometer. The first class consists of mechanical accelerometers (i.e:
devices which measure the displacement of a supported mass) manufactured using
MEMS techniques. The second class consists of devices which measure the change
in frequency of a vibrating element caused by a change of tension, as in SAW
accelerometers.
