GEOMETRIC MODELS OF THE CHASE METHOD ON THE PLANE AND ON THE SURFACE DELIVERY

2021 ◽  
pp. 18-25
Author(s):  
A. A. Dubanov
Keyword(s):  
Surface Modifications ◽  
Unmanned Vehicles ◽  
Line Of Sight ◽  
Displacement Method ◽  
Horizontal Projection ◽  
Pursuit Problem ◽  
Parallel Displacement ◽  
Straight Line ◽  
Direction Of Movement ◽  
Made In

In this article models of the pursuit method in the pursuit problem. The considered models are based on the correction of the vector of the direction of motion. Suppose, on a plane, the intended direction is the line of sight of the pursuer and the target. Correction of the direction of movement consists in the rotation of the velocity vector until it coincides with the line of sight. When constructing trajectories on the surface, a line of sight is built on the horizontal projection plane. After calculating horizontal projections, all points are projected back onto the surface. Have been developed models for calculating the trajectories of the pursuer and the target in the problem of studying the plane and on the surface. Modifications of the mathematical models of the methods of parallel dropping and chasing were made in relation to the plane and the surface. In our models and algorithms, the speed of the pursuer can be directed arbitrarily. With the modification of the parallel displacement method, the straight line of this movement was replaced by a predicted trajectory of movement at a point in time, which moves to itself. When modifying the chase method, the line of sight was also replaced with a compound curve, taking into account the restrictions on the curvature of the pursuer trajectory. These models can be in demand by developers of autonomous unmanned vehicles equipped with artificial intelligence systems.

scholarly journals Geometric models of the run method

2021 ◽  
Vol 2131 (3) ◽  
pp. 032044
Author(s):  
A Dubanov
Keyword(s):  
Artificial Intelligence ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Velocity Vector ◽  
Unmanned Vehicles ◽  
Line Of Sight ◽  
Direction Vector ◽  
Horizontal Projection ◽  
Pursuit Problem ◽  
Artificial Intelligence Systems

Abstract This article discusses models of the run method in the pursuit problem. The considered models are based on the correction of the direction vector. Let’s assume that the intended direction on a plane is the line of sight between the pursuer and the target. The direction correction consists in the rotation of the velocity vector until it coincides with the line of sight. When constructing trajectories on the surface, a line of sight is built on the horizontal projection plane. After calculating horizontal projections, all points are projected back onto the surface. On the basis of the research carried out proposed a mathematical model, proposed mathematical models of the method of pursuit on a plane and on a surface given in an explicit form. Mathematical models are the development of chase and parallel approach methods. A modification of these methods is that the speed of the pursuer and the target are directed at random. These models can be in demand by developers of autonomous unmanned vehicles equipped with artificial intelligence systems.

scholarly journals Using Sequential Photography to Estimate Ice Velocity at the Terminus of Columbia Glacier, Alaska

1986 ◽  
Vol 8 ◽  
pp. 117-123 ◽  
Author(s):  
R.M. Krimmel ◽  
L.A. Rasmussen
Keyword(s):  
Time Resolution ◽  
Principal Direction ◽  
Film Plane ◽  
Time Sequence ◽  
Line Of Sight ◽  
Glacier Surface ◽  
Ice Flow ◽  
Straight Line ◽  
Camera Orientation ◽  
Ice Velocity

The terminus of Columbia Glacier, Alaska, was observed with a single automatic 35 mm camera to determine velocity with a time resolution in the order of a day. The photographic coordinates of the image of a target were then transformed linearly into the direction numbers of the line of sight from the camera to the target. The camera orientation was determined from the film-plane locations of known landmark points by using an adaption of vertical photogrammetry techniques. The line of sight, when intersected with some mathematically-defined glacier surface, defines the true space coordinates of a target, The time sequence of a target’s position was smoothed, first in horizontal x, y space to a straight line, then in y (the principal direction of ice flow) and time with a smoothing cubic spline, and then the x-component was computed from the y-component by considering the inclination of the straight line. This allows daily velocities (about 8 m/day) to be measured at a distance of 5 km, using a 105 mm lens. Errors in daily displacements were estimated to be 1 m. The terminus configuration was also measured using the same photo set.

scholarly journals Pupillary axis of a heterocentric astigmatic eye

2013 ◽  
Vol 72 (1) ◽  
Author(s):  
W. F. Harris
Keyword(s):  
Anterior Chamber ◽  
Contact Lens ◽  
Line Of Sight ◽  
Compound System ◽  
Linear Optics ◽  
Optical Instrument ◽  
Entrance Pupil ◽  
Naked Eye ◽  
Straight Line

The pupillary axis of the eye is a clinically useful concept usually defined as the line through the centre of the entrance pupil that is perpendicular to the cornea. However if the cornea is astigmaticthen, strictly speaking, the entrance pupil is blurred and the pupillary axis is not well defined.  A modified definition is offered in this paper: the pupillary axis is the infinite straight line containing the incident segment of the ray that passes through the centre of the (actual) pupil and is perpendicular to the first surface of the eye.  The definition holds for the naked eye and for an eye with an implant in the anterior chamber.  It also holds for the com-pound system of eye and optical instrument such as a contact lens in front of it if the first surface is interpreted as the first surface of the compound system and the pupil as the limiting aperture of the compound system.  Linear optics is applied to obtain a formula for the position and inclination of the pupillary axis at incidence onto the system; the refracting surfaces may be heterocentric and astigmatic.  The formula allows one to examine the sensitivity of the pupillary axis to displacement of the pupil and any other changes in the anterior eye.  Strictly the pupillary axis depends on the frequency of light but examples show that the dependence is probably negligible.  The vectorized generalization of what is sometimes called angle lambda is easily calculated from the inclination of the pupillary axis and the line of sight. (S Afr Optom 2013 72(1) 3-10)

scholarly journals Motion of Multiple Robot in a Curved Boundary & Obstacles

2019 ◽  
Vol 9 (1) ◽  
pp. 6011-6014
Keyword(s):  
Curve Fitting ◽  
The Other ◽  
Multiple Robots ◽  
Curved Boundary ◽  
Medical Supplies ◽  
Straight Line ◽  
Multiple Robot ◽  
Assembly Operations ◽  
Curve Equation ◽  
Made In

An attempt is made in this paper to gain the flexibility of movement of robots around the boundary of the workspace, where in many robots are moving at a time in the presence of the static curved obstacles. The boundary of the workspace may be a straight line or curve shaped. The obstacle may be polygonal or curved shaped. A program is developed for the motion of the multiple robots to move from its origin location to the desired location without colliding with the boundary, the other moving robots and the static obstacles. The program is based on the curve fitting technique. As and when the robot comes close to the curved boundary or curved barrier, it will trace the path formed by the curve equation using the technique of curve fitting. Since there are multiple robots, the path planning ensures the robots to reach their targets in minimum time. During tracing the path, if more than one robot is following the same path, priority is assigned to such robots. Multiple robots finds application in assembly operations, medical supplies and meals to patients, disinfecting the rooms for patients etc.

scholarly journals Optimal synthesis of a four-bar linkage by method of controlled deviation

2004 ◽  
Vol 31 (3-4) ◽  
pp. 265-280 ◽  
Author(s):  
Radovan Bulatovic ◽  
Stevan Djordjevic
Keyword(s):  
Objective Function ◽  
Optimal Synthesis ◽  
Straight Line ◽  
Individual Comparison ◽  
Four Bar Linkage ◽  
The Given ◽  
Initial Selection ◽  
Selection Of ◽  
Process Calculation ◽  
Made In

This paper considers optimal synthesis of a four-bar linkage by method of controlled deviations. The advantage of this approximate method is that it allows control of motion of the coupler in the four-bar linkage so that the path of the coupler is in the prescribed environment around the given path on the segment observed. The Hooke-Jeeves?s optimization algorithm has been used in the optimization process. Calculation expressions are not used as the method of direct searching, i.e. individual comparison of the calculated value of the objective function is made in each iteration and the moving is done in the direction of decreasing the value of the objective function. This algorithm does not depend on the initial selection of the projected variables. All this is illustrated on an example of synthesis of a four-bar linkage whose coupler point traces a straight line, i.e. passes through sixteen prescribed points lying on one straight line. .

RADISHCHEV PLOT IN MULTIVARIATE ANALYSIS OF THE PROBLEM OF MULTIPLE TARGETS GROUP PURSUIT

2021 ◽  
pp. 22-31
Author(s):  
A. A. Dubanov
Keyword(s):  
Multivariate Analysis ◽  
Line Segment ◽  
Iterative Process ◽  
Straight Line Segment ◽  
Line Of Sight ◽  
Radius Of Curvature ◽  
Time Step ◽  
Minimum Radius ◽  
Group Pursuit ◽  
Straight Line

This article discusses a kinematic model of the problem of group pursuit of a set of goals. The article discusses a variant of the model when all goals are achieved simultaneously. And also the possibility is considered when the achievement of goals occurs at the appointed time. In this model, the direction of the speeds by the pursuer can be arbitrary, in contrast to the method of parallel approach. In the method of parallel approach, the velocity vectors of the pursuer and the target are directed to a point on the Apollonius circle. The proposed pursuit model is based on the fact that the pursuer tries to follow the predicted trajectory of movement. The predicted trajectory of movement is built at each moment of time. This path is a compound curve that respects curvature constraints. A compound curve consists of a circular arc and a straight line segment. The pursuer's velocity vector applied to the point where the pursuer is located touches the given circle. The straight line segment passes through the target point and touches the specified circle. The radius of the circle in the model is taken equal to the minimum radius of curvature of the trajectory. The resulting compound line serves as an analogue of the line of sight in the parallel approach method. The iterative process of calculating the points of the pursuer’s trajectory is that the next point of position is the point of intersection of the circle centered at the current point of the pursuer’s position, with the line of sight corresponding to the point of the next position of the target. The radius of such a circle is equal to the product of the speed of the pursuer and the time interval corresponding to the time step of the iterative process. The time to reach the goal of each pursuer is a dependence on the speed of movement and the minimum radius of curvature of the trajectory. Multivariate analysis of the moduli of velocities and minimum radii of curvature of the trajectories of each of the pursuers for the simultaneous achievement of their goals i based on the methods of multidimensional descriptive geometry. To do this, the projection planes are entered on the Radishchev diagram: the radius of curvature of the trajectory and speed, the radius of curvature of the trajectory and the time to reach the goal. On the first plane, the projection builds a one-parameter set of level lines corresponding to the range of velocities. In the second graph, corresponding to a given range of speeds, functions of the dependence of the time to reach the target on the radius of curvature. The preset time for reaching the target and the preset value of the speed of the pursuer are the optimizing factors. This method of constructing the trajectories of pursuers to achieve a variety of goals at given time values may be in demand by the developers of autonomous unmanned aerial vehicles.

Tracing Small-Scale Fluctuations in the Soft X-ray Background

1997 ◽  
Vol 166 ◽  
pp. 321-324
Author(s):  
R. Warwick ◽  
I. Hutchinson ◽  
R. Willingale ◽  
K. Kuntz ◽  
S. Snowden
Keyword(s):  
Column Density ◽  
Galactic Halo ◽  
Inverse Correlation ◽  
Line Of Sight ◽  
Small Scale ◽  
X Ray ◽  
Hydrogen Column Density ◽  
X Ray Background ◽  
Counting Statistics ◽  
Made In

AbstractAn overlapping set of ROSAT PSPC observations made in a region of very low Galactic foreground column density, has been used to investigate variations in the soft X-ray background on angular scales of 15′ – 5°. In the ¼ keV band there is a clear inverse correlation of the count-rate with the line-of-sight hydrogen column density. However, after correcting for this absorption effect, strong residual fluctuations remain in the data, with an amplitude which is significantly larger than that due to the counting statistics or the confusion of unresolved discrete sources. In contrast a similar analysis for the ¾ and 1.5 keV ROSAT bands shows no evidence for an excess signal. The most likely origin of the ¼ keV fluctuations would seem to be in a patchy distribution of ~ 106 K gas in the Galactic halo.

Steady State Eeg as a Measure of Peripheral Light Loss

1986 ◽  
Vol 30 (13) ◽  
pp. 1249-1253
Author(s):  
Richard T. Gill ◽  
Kevin M. Kenner ◽  
Andrew M. Junker
Keyword(s):  
Steady State ◽  
Stimulus Intensity ◽  
Line Of Sight ◽  
Strong Response ◽  
Experimental Conditions ◽  
Pilot Studies ◽  
Sensitive Measure ◽  
Stimulus Parameters ◽  
Light Loss ◽  
Made In

The objective of this research was to assess the feasability of using ElectroEncephaloGrams (EEG) to measure the extent of acceleration induced Peripheral Light Loss (PLL). Two pilot studies were conducted to determine if an EEG response to peripherally localized stimuli could be detected and to establish the stimulus parameters that would yield a strong response. Results revealed: (1) identifiable EEG responses to stimuli located as far as ± 60 degrees from the foveal line-of-sight; (2) higher stimulus intensity and, in particular, higher depth of modulation yielded stronger EEG responses; and (3) coherence was found to be a more sensitive measure than RMS Power or Gain. These findings were used to establish the experimental conditions that were used in a study whose objective was to estimate the minimum time necessary to detect the presence, or absence, of an EEG response to peripherally localized stimuli. Results revealed a reliabe determination for stimuli located at ± 45 degrees could be made in 20 seconds or less.

Sign in / Sign up

Export Citation Format

Share Document