An interesting problem in the control of mobile robots is the steering. In this paper a mobile robot with front-wheel
steering is treated. A third-order kinematic model is developed. The problem of optimally steering the robot from an
initial position and heading to a final position and heading is addressed. The performance measure is taken to be elapsed
time. Assuming a fixed speed, this corresponds to a path of minimum distance. It is found that the trajectory consists of
segments of maximum-curvature turns and segments of straight lines. The straight-line segments are singular arcs. The
problem is shown to simplify when final heading is free. Four examples are solved.
In remote sensing, one is often interested in not only ascertaining the presence of certain resources or objects of interest, but also in determining their locations. Ground registration involves locating the target in sensor coordinates and performing a series of coordinate transformations to convert this location to earth coordinates. One application of this would be in preparing a scaled map showing the precise locations of the resources/objects of interest. To improve ground registration accuracy one can combine multiple looks from a single sensor and/or looks from multiple sensors. One advantage in utilizing multiple sensors is that one can fuse the measurements in such a way as to exploit the best characteristics of each sensor. This paper is applied to vehicular mounted remote sensing and presents the benefits obtained when combining radar and IR as a means of determining ground coordinates of the objects of interest.
When performing remote sensing, one often uses vehicular mounted sensors. This provides the flexibility of moving around and searching over a large area and can be done via airborne vehicles, ground vehicles or marine vehicles. For this type of sensing, one needs to know the position and orientation of the sensor platform in order to ground register the location of detected objects. The research reported herein is concerned with the use of a ground vehicle as a sensor platform. Digital camera-type sensors such as infra-red are considered. The focus is on requirements for accurate ground registration of detected objects of interest. A four-antenna GPS array has been chosen for vehicle attitude measurement. Relationships between positions of the array elements and vehicle attitude are derived. It is seen that the attitude computations depend on differences in the various measurements. Thus common-mode errors in the measured position of the array elements cancel, enabling quite accurate attitude measurement even when utilizing somewhat imprecise units in the GPS array. A more precise single differential GPS (DGPS) has been chosen for vehicle position measurements. Relationships between pixel coordinates in the image frame and the angle of the corresponding ray from the camera to the object of interest are derived. A series of transformations are used to convert this ray to ground coordinates. Finally the intersection of the ray with the ground is computed based on the assumption that the ground in the field-of-view is flat and at a known elevation. In this manner an object of interest in the image frame may be ground registered. Sensitivity of the ground registration with respect to vehicle attitude measurement errors is developed. It is seen that small errors in pitch, roll or yaw can cause quite large errors in the computed ground coordinates. In the case of multiple looks at the same object of interest, the geo-registration process involves target tracking and data association. This process is facilitated by combining the single-look measurements in an optimal fashion via a Kalman Filter. In fact the accuracy obtained via multiple looks can be significantly greater than for a single look. The results obtained indicate that accurate geo-registration of remotely sensed objects is possible when using vehicular mounted sensors in conjunction with DGPS and that such a scheme is feasible with commercially available GPS and IR cameras. Geo-registration accuracy within a fraction of a meter is attainable for near objects.
When searching for land mines using vehicular mounted sensors, it is important that the ground locations of the detected mines be accurately determined. This is useful for data association when one has multiple looks at a mine by a single sensor or if one uses multiple sensors. It is of ultimate importance for the primary mission, which is to neutralize the detected mines or at least to mark them for avoidance. Factors that contribute to errors in geo-location include inaccurate knowledge of the vehicle position and/or attitude, and also incomplete knowledge about the terrain being searched. This paper addresses the problem of incomplete terrain knowledge and presents relationships between terrain unevenness and the resulting geo-location errors. The results of this analysis indicate that there may be significant geo-location errors for situations where the terrain is not so smooth, e.g., off road searches. The problem can be alleviated via better knowledge of the terrain. Such knowledge could be acquired via scanning the field of view with a ranging device, recording range as a function of azimuth and elevation. A variety of uneven surfaces have been simulated. Two types of sensors are considered, Linear-Array Radar and Camera Type Sensors. Geo-location is then computed based on: a) no range measurements, b) four range measurements (to the four vertices of the sensor field of view), and c) nine range measurements (to the four vertices and intermediate points at the top and bottom row, as well as three measurements across the center row). The geo-location errors are much worse for the Camera Type Sensor, but they can be significant for the Linear-Array Radar also. If the field of view is planar or almost planar, even coarse range scanning can improve geo-location accuracy. For more complex surfaces fine scanning may be required. The computed geo-location errors, and the conclusions drawn as to the effectiveness of the different models are presented in the paper.
This paper is concerned with the problem of target geo- location when using forward-looking vehicular-mounted sensors for landmine detection. Intermediate and downward- looking sensor may also be used, but the geo-location problem is most complex for the forward-looking sensor. A nonlinear states model for the vehicle position and attitude. Knowledge of these sensors specifications along with information as to the location and orientation of the sensor on the vehicle combined with knowledge of the vehicle position and attitude make it possible for one to compte the sensor field-of-view or footprint. Given this, one can then analyze sensor frames and for any detected mines, convert their locations from sensor-frame coordinates to ground coordinates.
This paper builds on the method of Principal Components Analysis and its use for obtaining from a set of training image vectors a basis in which the members are rank ordered in terms of importance. The particular focus of this research is situations where the training vectors arise from images acquired at one range, call it the base range, and the image under question has been acquired at a different range. A natural question is whether one must train for all possible ranges. It is shown that, under certain assumptions, the eigenvectors for the data corresponding to ranges other than the base range may be approximated by performing a simple transformation on the eigenvectors derived from the training set at the base range. This is an important result, tending to obviate the need for acquisition of additional training patterns or for additional complex computations. It is also shown that under these assumptions the eigenvalues remain approximately constant over the different ranges even though pixel size is changed. Bounds for the errors of approximation introduced by the method are derived.
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