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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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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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Related Experiment Video

Updated: Sep 16, 2025

Trajectory Data Analyses for Pedestrian Space-time Activity Study
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Trajectory tracking and obstacle avoidance in dynamic environments using an improved artificial potential field

Long Di1, Naiwei Huang1, Jiaqi He1

  • 1Zhaoqing Power Supply Bureau, Guangdong Power Grid Co., Ltd., Zhaoqing, Guangdong, China.

Plos One
|July 10, 2025
PubMed
Summary

This study introduces a novel real-time trajectory planning framework for robots. It enhances artificial potential fields (APF) to improve path tracking and obstacle avoidance in dynamic environments.

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Area of Science:

  • Robotics
  • Artificial Intelligence
  • Control Systems

Background:

  • Robots require precise trajectory tracking and obstacle avoidance in dynamic environments.
  • Existing methods struggle to balance path-following accuracy with real-time obstacle avoidance.

Purpose of the Study:

  • To propose a real-time trajectory planning framework for robots.
  • To address the challenge of simultaneous accurate trajectory tracking and dynamic obstacle avoidance.
  • To enhance robot safety and performance in unstructured environments.

Main Methods:

  • An enhanced artificial potential field (APF) approach with virtual target points for path precision.
  • A dynamic obstacle repulsion model incorporating velocity and acceleration for proactive avoidance.
  • A probabilistic obstacle motion prediction framework using motion pattern analysis.

Main Results:

  • Achieved a 55.8% reduction in trajectory tracking error compared to improved APF methods.
  • Demonstrated a 41.5% decrease in tracking error relative to Dynamic Movement Primitives (DMP) baselines.
  • Validated superior robustness and safety performance in complex, simulated dynamic obstacle scenarios.

Conclusions:

  • The proposed framework effectively balances trajectory tracking and obstacle avoidance.
  • The integration of predictive motion analysis enhances robot adaptability and safety.
  • The method shows significant improvements over existing APF and DMP approaches.