Navigation and guidance systems Navigation systems Major Dr
- Slides: 24
ﻣﻨﻈﻮﻣﺎﺕ ﺍﻟﻤﻼﺣﺔ ﻭﺍﻟﺘﻮﺟﻴﻪ Navigation and guidance systems Navigation systems Major Dr. Eng. Elkhidir T. Y. 2015 Elkhidir - NGS 1
introduction Navigation ( Localisation ) may be defined as the process of determining vehicle pose, that is: • vehicle position • vehicle orientation • vehicle velocity This is distinct from Guidance or Control which is the process of controlling a vehicle to achieve a desired trajectory. An autonomous vehicular system generally must include these two basic competencies in order to perform any useful task. Elkhidir - NGS 2
An Historical Perspective The first navigation techniques were used to estimate the position of a ship through dead reckoning, using observations of the ships speed and heading. Absolute information was used to provide a position fix. These fixes were obtained when well known natural or artificial landmarks were recognised. In the open sea, natural landmarks are scarcely available, making an accurate position update not possible. Techniques to determine Latitude were developed in the early 1550's by the Portuguese. Elkhidir - NGS 3
An Historical Perspective The determination of Longitude took another 300 years to be solved. The approaches were based on accurate prediction and observation of the moon and by knowing the time with enough accuracy to evaluate the Longitude. Captain Cook tested one of Harrison's chronometers (the Mark IV), on his last journey. Elkhidir - NGS 4
A Modern Perspective The previous slide introduced the essential elements of navigation, Prediction and Correction. Prediction can be considered to be the use of a model or some description to provide dead reckoning information. Correction is the process whereby the observation of landmarks (either natural or artificial) can reduce the location uncertainty inherent in dead reckoning. It is essential to understand not only the sensors used for navigation, but also the model used for prediction, as they both contribute to the accuracy of the position solution. Elkhidir - NGS 5
A Modern Perspective As both prediction and correction steps contain uncertainty, it is useful to pose navigation as an Estimation problem. If the error in prediction, and the error in correction can be modelled as probability distributions then the Kalman filter can be used to fuse all available information into a common estimate that may then be used for guidance. Elkhidir - NGS 6
Vehicle Modelling The vehicle model can be a very important component of a navigation system. One of the most important issues with modelling is knowing the limitation of the model selected. For example, in the case of a pure kinematic model it is important to know the operational range where the model is valid. A simple kinematics model can be very accurate to predict the trajectory of a vehicle while moving in straight direction. Elkhidir - NGS 7
Vehicle Modelling There are different type of models that can be used for a particular application: • Kinematics models • Dynamics models • Lumped parameter models One of the simplest method of vehicle modelling is simply to exploit the vehicle's kinematic constraints. These constraints are known as the rigid body and rolling motion constraints. Elkhidir - NGS 8
Vehicle Modelling The rigid body constraint makes the assumption that the vehicle frame is rigid, whereas the rolling motion constraint assumes that all points on the vehicle rotate about the Instantaneous Centre of Rotation with the same angular velocity. Elkhidir - NGS 9
Beacon Based Navigation The generally accepted definition of a `beacon', is a target whose position (and perhaps other parameters) is known to the navigation system. By observing a beacon whose absolute position is known, the position of the vehicle with respect to the beacon may be easily computed. Therefore, beacon based navigation systems are perhaps the easiest to implement. The drawback, of course, is that infrastructure is usually needed to implement a navigation system of this type. Elkhidir - NGS 10
Beacon Based Navigation The sensors used in beacon based navigation systems typically fall into two distinct categories: 1. bearing only sensors: return the bearing and/or azimuth to a given beacon. Some laser systems employ this principle. Single cameras also fall into this category. 2. range and bearing sensors: return Range and bearing. Most common type include sonar, laser, radar, and stereo vision. The system will have a list with the location of all the beacons will determine which is the feature the sensor has detected. This process is called data association and will be obviously more difficult and less reliable with bearing only sensors. Elkhidir - NGS 11
Simplified Navigation Examples In this section three simplified navigation-system examples are presented. The examples are simplified with the assumptions that the world is two dimensional, flat, and non -accelerating. Navigation-system equations applicable under more realistic conditions are derived later. In each of the examples considered in the remainder of this section, only two coordinate frames are involved body frame and navigation frame. The body-frame coordinate system, denoted as (u, v, w), is rigidly attached to the vehicle at the center of gravity with the u axis pointing forward, the w axis pointing down, and the v axis completing a right-hand coordinate system. Elkhidir - NGS 12
Simplified Navigation Examples The navigation-frame coordinate system, denoted as (n, e, d), has axes pointing north, east, and down. For these simplified examples (in this introductory), the navigation frame is considered to be non-accelerating. Also, by the twodimensional assumption, altitude, pitch, and roll are also assumed to be zero. The navigation- and the body-frame coordinate systems can be aligned by rotation of the navigation frame by an angle y about its w axis. Elkhidir - NGS 13
Simplified Navigation Examples Elkhidir - NGS 14
Simplified Navigation Examples Dead-Reckoning: Dead-reckoning navigation has been used for centuries in marine applications and is the method many early aviators used to complete early record-setting long-distance flights. The minimum sensing requirements are a direction indicator (usually a compass) and a speed indicator. The navigator multiplies average speed along a given heading by the time of travel to determine distance of travel. This distance is plotted from an initial location along the measured (possibly corrected for expected magnetic variation) heading to determine the expected new location. Elkhidir - NGS 15
Simplified Navigation Examples Dead-Reckoning: In a modern approach to dead reckoning, body-frame velocity and heading are measured electronically. Instantaneous navigation-frame velocities are computed at a high rate based on the measured heading and the bodyframe velocity. The navigation-frame velocities are then integrated to determine the navigation-frame positions. The differential equations describing the ideal mechanization of this approach are Elkhidir - NGS 16
Simplified Navigation Examples Dead-Reckoning: where y is the angle from the navigation north axis to body u axis measured positively in the right-hand sense around the navigation-frame down axis (i. e. , the true heading), (n, e) are the north and the east position components, (u, v) are the components of vehicle velocity in the body frame, and is the matrix that transforms a vector represented in body coordinates to a vector represented in navigation coordinates. Elkhidir - NGS 17
Simplified Navigation Examples Dead-Reckoning: Realizing that the sensors and computation are not perfectly accurate, the system designer is usually interested in determining the expected (typical and worst-case) navigation-system accuracy and the effects of various system errors. For such an analysis, a set of differential equations describing the navigation-system error is useful. The definition of such a set of equations requires assumptions regarding the sensors to be used and the nature of the errors to be analyzed. Elkhidir - NGS 18
Simplified Navigation Examples Dead-Reckoning: If a magnetic compass is used, then the measured heading contains a time-varying bias due to local magnetic fields (earth or current induced) and the presence of nearby magnetically permeable objects. Therefore the measured magnetic heading is modeled a: Elkhidir - NGS 19
Simplified Navigation Examples Inertial Navigation: Inertial navigation is based on application of Newton's laws of motion. In particular, Newton's first law states that a body in motion tends to maintain its motion unless acted on by a force. If a force sensing device is in motion, it maintains its motion until acted on by a force, which the device senses. Since the measuring device (i. e. , an accelerometer) is designed with a known mass, Newton's second law can be applied to determine the acceleration as. F = ma a = F/m Elkhidir - NGS 20
Simplified Navigation Examples Inertial Navigation: If appropriate transformations are applied, then a single integration yields navigation-frame velocity and a second integration provides navigation-frame position. Various issues of the approach are illustrated in the following simplified example. three sensors are used. Two accelerometers are rigidly attached to the vehicle and aligned with the body-frame u and v axes. These accelerometers measure inertial acceleration resolved in the longitudinal and the lateral directions. A single gyro, also rigidly mounted to the vehicle, measures the rotation rate of the vehicle about the down axis relative to the navigation (inertial) frame. Elkhidir - NGS 21
Simplified Navigation Examples Inertial Navigation: This system is illustrated in Fig. below. The differential equations describing the ideal mechanization of the navigation state are Elkhidir - NGS 22
Simplified Navigation Examples Positioning: Measurements from various positioning systems yield equations that for a two-dimensional example have the form where r is some form of distance measurement, [n(t), e(t)] are the unknown coordinates of a receiver-equipped user, [n(i), e(i)] are the known coordinates of one of the positioning-system transmitters, i is the transmitter identifier, and h is a nonlinear function of the user and the transmitter coordinates. Given at least two simultaneous measurements p(i)(t) from suitably situated transmitters, the set of equations can be solved to determine user position. Elkhidir - NGS 23
Thank you Elkhidir - NGS 24
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