Inertial guidance system
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An inertial guidance system consists of an Inertial Measurement Unit (IMU) combined with control mechanisms, allowing the path of a vehicle to be controlled according to the position determined by the inertial navigation system. These systems are also referred to as an inertial platform.
An inertial navigation system (INS) provides the position, velocities and attitude of a vehicle by measuring the accelerations and rotations applied to the system's inertial frame. It is widely used because it refers to no real-world item beyond itself. It is therefore immune to jamming and deception. (See relativity and Mach's principle for some background in the physics involved).
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Overview
Inertial guidance systems were originally developed for navigating rockets. American rocket pioneer Robert Goddard experimented with rudimentary gyroscopic systems. Dr. Goddard's systems were of great interest to contemporary German pioneers including Wernher von Braun.
A typical inertial navigation system uses a combination of roll, pitch and azimuth gyroscopes, to stabilize the x, y and z accelerometers to solve a large set of differential equations to convert these readings into estimates of velocities, position and attitude, starting off from a known initial position of latitude and longitude.
All inertial navigation systems suffer from integration drift, as small errors in measurement are integrated into progressively larger errors in velocity and especially position. This is a problem that is inherent in every open loop control system. The inaccuracy of a good-quality navigational system is normally less than 0.6 nautical miles per hour.
Inertial navigation may also be used to supplement other navigation systems, providing a higher degree of accuracy than is possible with the use of any single navigation system. For example, if, in terrestrial use, the inertially tracked velocity is intermittently updated to zero by stopping, the position will remain precise for a much longer time, a so-called zero velocity update.
Control theory in general and Kalman filtering in particular, provide a theoretical framework for combining of the information from various sensors. One of the most common alternative sensors is a satellite navigation radio such as GPS.
Inertial navigation systems in detail
INSs have angular and linear accelerometers (for changes in position); some include a gyroscopic element (for maintaining an absolute positional reference).
Angular accelerometers measure how the vehicle is rotating in space. Generally, there's at least one sensor for each of the three axes: pitch (nose up and down), yaw (nose left and right) and roll (clockwise or counterclockwise from the cockpit).
Linear accelerometers measure how the vehicle is moving in space. Since it can move in three axes (up & down, left & right, forward & back), there is a linear accelerometer for each axis.
A computer continually calculates the vehicle's current position. First, for each of the six degrees of freedom (x,y,z and theta x, theta y and theta z), it integrates the sensed amount of acceleration over time to figure the current velocity. Then it integrates the velocity to figure the current position.
Inertial guidance is impossible without computers. The desire to use inertial guidance in the Minuteman missile and Project Apollo drove early attempts to miniaturize computers.
Inertial guidance systems are now usually combined with satellite navigation systems through a digital filtering system. The inertial system provides short term data, while the satellite system corrects accumulated errors of the inertial system.
An inertial guidance system that will operate near the surface of the earth must incorporate Schuler tuning so that its platform will continue pointing towards the center of the earth as a vehicle moves from place to place.
Basic schemes
Gimbaled Gyrostabilized platforms
Some systems place the linear accelerometers on a gimballed gyrostabilized platform. The gimbals are a set of three rings, each with a pair of bearings initially at right angles. They let the platform twist about any rotational axis. There are two gyroscopes (usually) on the platform.
Two gyroscopes are used to cancel gyroscopic precession, the tendency of a gyroscope to twist at right angles to an input force. By mounting a pair of gyroscopes (of the same rotational inertia and spinning at the same speed) at right angles the precessions are cancelled, and the platform will resist twisting.
This system allows a vehicle's roll, pitch and yaw angles to be measured directly at the bearings of the gimbals. Relatively simple electronic circuits can be used to add up the linear accelerations, because the directions of the linear accelerometers do not change.
The big disadvantage of this scheme is that it uses many expensive precision mechanical parts. It also has moving parts that can wear out or jam, and is vulnerable to gimbal lock. The primary guidance system of the Apollo spacecraft used a 3-axis gyrostabilized platform, feeding data to the Apollo Guidance Computer. Maneuvers had to be carefully planned to avoid gimbal lock.
Fluidically Suspended Gyrostabilized Platforms
Gimbal lock constrains maneuvering, and it would be nice to eliminate the slip rings and bearings of the gimbals. Therefore, some systems use fluid bearings or a flotation chamber to mount a gyrostabilized platform. These systems can have very high precisions. Like all gyrostabilized platforms, this system runs well with relatively slow, low-power computers.
The fluid bearings are pads with holes through which pressurized inert gas (such as Helium) or oil press against the spherical shell of the platform. The fluid bearings are very slippery, and the spherical platform can turn freely. There are usually four bearing pads, mounted in a tetrahedral arrangement to support the platform.
In premium systems, the angular sensors are usually specialized transformer coils made in a strip on a flexible printed circuit board. Several coil strips are mounted on great circles around the spherical shell of the gyrostabilized platform. Electronics outside the platform uses similar strip-shaped transformers to read the varying magnetic fields produced by the transformers wrapped around the spherical platform. Whenever a magnetic field changes shape, or moves, it will cut the wires of the coils on the external transformer strips. The cutting generates an electric current in the external strip-shaped coils, and electronics can measure that current to derive angles.
Cheap systems sometimes use bar codes to sense orientations, and use solar cells or a single transformer to power the platform. Some small missiles have powered the platform with light from a window or optic fibers to the motor. A research topic is to suspend the platform with pressure from exhaust gases. Data is returned to the outside world via the transformers, or sometimes LEDs communicating with external photodiodes.
Strapdown systems
Lightweight digital computers permit the system to eliminate the gimbals, creating "strapdown" systems, so called because their sensors are simply strapped to the vehicle. This reduces the cost, eliminates gimbal lock, removes the need for some calibrations, and increases the reliability by eliminating some of the moving parts. Angular accelerometers called "rate gyros" measure how the angular velocity of the vehicle changes.
A strapdown system has a dynamic measurement range several hundred times that required by a gimbaled system. That is, it must integrate the vehicle's attitude changes in pitch, roll and yaw, as well as gross movements. Gimballed systems could usually do well with update rates of 50 to 60 updates per second. However, strapdown systems normally update about 2000 times per second. The higher rate is needed to keep the maximum angular measurement within a practical range for real rate gyros: about 4 milliradians. Most rate gyros are now laser interferometers.
The trigonometry involved is too complex to be accurately performed except by digital electronics. However, digital computers are now so inexpensive and fast that rate gyro systems can now be practically used and mass-produced. The Apollo lunar module used a strapdown system in its backup Abort Guidance System (AGS).
Types of sensors
Laser gyros
Laser gyroscopes were supposed to eliminate the bearings in the gyroscopes, and thus the last bastion of precision machining and moving parts.
A laser gyro splits a beam of laser light into two beams in opposite directions around a circular path. When the gyro is rotating at some anglular rate, the distance traveled by each beam becomes different - the shorter path being opposite to the rotation. The phase-shift between the two beams can be measured by an interferometer, and is proportional to the rate of rotation (Sagnac effect).
In practice, at low rotation rates the electromagnetic peaks and valleys of the light lock together. The result is that there is no change in the interference pattern, and therefore no measurement change.
To unlock the counter-rotating light beams, laser gyros either have independent light paths for the two directions (usually in fiber optic gyros), or the laser gyro is mounted on a piezo-electric crystal that rapidly rotates the gyro back and forth through a small angle to decouple the light waves.
Alas, the shaker is the most accurate, because both light beams use exactly the same path. Thus laser gyros retain moving parts, but they do not move as far.
Vibrating gyros
Less expensive navigation systems intended for use in automobiles, may use a Vibrating structure gyroscope to detect changes in heading, and the odometer pickup to measure distance covered along the vehicle's track. This type of system is much less accurate than a higher-end INS, but is adequate for the typical automobile application where GPS is the primary navigation system, and dead reckoning is only needed to fill gaps in GPS coverage when buildings or terrain block the satellite signals.
Hemispherical Resonator Gyros ("Brandy Snifter Gyros")
If a standing wave is induced in a globular brandy snifter, and then the snifter is tilted, the waves continue in the same plane of movement. They don't tilt with the snifter. This trick is used to measure angles. Instead of brandy snifters, the system uses hollow globes machined from piezoelectric materials such as quartz. The electrodes to start and sense the waves are evaporated directly onto the quartz.
This system has almost no moving parts, and is very accurate. However it is still relatively expensive due to the cost of the precision ground and polished hollow quartz spheres.
Although successful systems were constructed, and an HRG's kinematics appear capable of greater accuracy, they never really caught on. Laser gyros were just more popular.
The classic system is the Delco 130Y Hemispherical Resonator Gyro, developed about 1986. See also [1] for a picture of an HRG resonator.
Quartz rate sensors
This system is usually integrated on a silicon chip. It has two mass-balanced quartz tuning forks, arranged "handle-to-handle" so forces cancel. Aluminum electrodes evaporated onto the forks and the underlying chip both drive and sense the motion. The system is both manufacturable and inexpensive. Since quartz is dimensionally stable, the system can be accurate.
As the forks are twisted about the axis of the handle, the vibration of the tines tends to continue in the same plane of motion. This motion has to be resisted by electrostatic forces from the electrodes under the tines. By measuring the difference in capacitance between the two tines of a fork, the system can determine the rate of angular motion.
Current state of the art non-military technology (2005) can build small solid state sensors that can measure human body movements. These devices have no moving parts, and weigh about 50 grams.
Solid state devices using the same physical principles are used to stabilize images taken with small cameras or camcorders. These can be extremely small (≈5mm) and are built with MEMS (Microelectromechanical Systems) technologies.
MHD sensor
Sensors based on magnetohydromagnetic principles can be used to measure angular velocities and are described in "MHD sensor".
Pendular accelerometers
The basic accelerometer is just a mass on a spring with a ruler attached. The ruler may be an exotic electromagnetic sensor, but it still senses distance. When the vehicle accelerates, the mass moves, and ruler measures the movement. The bad thing about this scheme is that it needs calibrated springs, and springs are nearly impossible to make consistent.
A trickier system is to measure the force needed to keep the mass from moving. In this scheme, there's still a ruler, but whenever the mass moves, an electric coil pulls on the mass, cancelling the motion. The stronger the pull, the more acceleration there is. The bad thing about this is that very high accelerations, say from explosions, impacts or gunfire, can exceed the capacity of the electronics to cancel. The sensor then loses track of where the vehicle is.
Both sorts of accelerometers have been manufactured as integrated micromachinery on silicon chips.
Accelerometer-only systems
Some systems use four pendular accelerometers to measure all the possible movements and rotations. Usually, these are mounted with the weights in the corners of a tetrahedron. Thus, these are called "tetrahedral inertial platforms", or TIPs.
When the vehicle rolls, the masses on opposite sides will be accelerated in opposite directions. When the vehicle has linear acceleration, the masses are accelerated in the same direction. The computer keeps track.
TIPs are cheap, lightweight and small, especially when they use micromachined integrated accelerometers. However, as of 2002 they are not very accurate. When they are used, they are often used in small missiles.
See also
inertial measurement unit, aircraft, spacecraft, attitude control, Kalman filter, Schuler tuning
External links
- Inertial Instruments- Where to Now? a survey from MIT's Draper Lab; describes the precision needed for various applications, as well as common technologies. (.pdf format)
- A history of inertial navigation systems (.pdf format)
External links
Examples of manufacturers:
Northrop Grumman, USA, see especially [2]
Lital, Italy (a division of Northrop Grumman, USA)
Xsens, Nederlands miniature solid state sensors
Kearfott Guidance & Navigation Corporation, USAde:Inertiales Navigationssystem es:Sistema de guía inercial ja:慣性誘導装置 no:Treghetsnavigasjon fi:Inertianavigointi sv:Tröghetsnavigering zh:惯性导航系统