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Relative Motion Analysis using Rotating Axes

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Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame.
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Consider a crane whose telescopic boom rotates with an angular velocity of 0.04 rad/s and angular acceleration of 0.02 rad/s2. Along with the rotation, the boom also extends linearly with a uniform speed of 5 m/s. The extension of the boom is measured at point D, which is measured with respect to the fixed point C on the other end of the boom. For the given instant, the distance between points C and D is 60 meters.
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Curvilinear Motion: Rectangular Components

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Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
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Absolute Motion Analysis- General Plane Motion01:24

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Updated: Jul 9, 2025

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A visual positioning model for UAV's patrolling video sequence images based on DOM rectification.

Haojie Liu1, Wei Fan2, Di Wu1

  • 1Yellow River Engineering Consulting Co., LTD., Zhengzhou, 450003, China.

Scientific Reports
|December 8, 2023
PubMed
Summary

This study introduces a new visual positioning model for unmanned aerial vehicles (UAVs) using Digital Orthophoto Maps (DOMs). The model achieves precise, real-time positioning of UAV video, even with varying conditions.

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Area of Science:

  • Geospatial Information Science
  • Computer Vision
  • Robotics

Background:

  • Precise positioning of aerial images from unmanned aerial vehicles (UAVs) is crucial for monitoring and disaster assessment.
  • Real-time, robust, and accurate positioning of UAV video sequences remains a significant challenge.

Purpose of the Study:

  • To develop a visual positioning model for UAV patrolling video sequences based on Digital Orthophoto Map (DOM) rectification.
  • To enable precise, robust, and dynamic real-time positioning of UAV video data.

Main Methods:

  • A robust block-matching algorithm to find the best matching area between UAV video frames and a pre-acquired DOM.
  • A precise polynomial-rectifying algorithm to calculate accurate mapping parameters for real-time positioning.

Main Results:

  • The proposed algorithms achieved stable positioning with approximately 2.5m accuracy within 1 second.
  • Effective positioning was demonstrated despite significant differences in spatial resolution, features, illumination, and topography between DOM and UAV imagery.

Conclusions:

  • The developed model significantly improves the real-time precise positioning of UAV patrolling video sequences.
  • The mathematical model can be integrated into existing UAV systems without requiring additional hardware.