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In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
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A three-dimensional force system refers to a scenario in which three forces act simultaneously in three different directions. This type of problem is commonly encountered in physics and engineering, where it is necessary to calculate the resultant force on the system, which can then be used to predict or analyze the behavior of the object or structure under consideration.
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Research on Path Planning Method for Mobile Platforms Based on Hybrid Swarm Intelligence Algorithms in

Shuai Wang1, Yifan Zhu2, Yuhong Du3,4

  • 1School of Mechanical and Automotive Engineering, Liaocheng University, Liaocheng 252000, China.

Biomimetics (Basel, Switzerland)
|August 27, 2025
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Summary

An improved Artificial Bee Colony-Beetle Antennae Search (IABCBAS) algorithm enhances path planning by incorporating chaos theory and reverse learning. This novel approach significantly reduces path distance and planning time in complex environments.

Keywords:
adaptive balanceoptimized search algorithmpath planning applicationssearch performance evaluation

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Area of Science:

  • Robotics and Artificial Intelligence
  • Computational Intelligence
  • Optimization Algorithms

Background:

  • Traditional path planning algorithms like Dijkstra and APF require complete environmental data, leading to complexity and reduced efficiency.
  • Swarm intelligence algorithms offer robust data processing for path planning but suffer from premature convergence and local optima issues.
  • Existing swarm intelligence methods need enhancements for improved diversity and searchability in complex environments.

Purpose of the Study:

  • To propose an improved Artificial Bee Colony-Beetle Antennae Search (IABCBAS) algorithm for efficient and reliable path planning.
  • To address the limitations of traditional and existing swarm intelligence algorithms in path planning.
  • To enhance population diversity, spatial searchability, and the ability to escape local optima in path planning algorithms.

Main Methods:

  • Introduced Tent chaos and non-uniform variation into the Artificial Bee Colony algorithm to improve population diversity and searchability.
  • Incorporated stochastic reverse learning and a greedy strategy into the Beetle Antennae Search algorithm to enhance direction-finding and local optima escape.
  • Implemented adaptive weight adjustment to balance global search and local refinement between the two integrated algorithms.

Main Results:

  • The IABCBAS algorithm demonstrated superior path point search performance and high stability across various dimensional and environmental complexities.
  • Ablation experiments confirmed that the introduced optimization strategies significantly improved convergence accuracy and speed in path planning.
  • Compared to other algorithms, IABCBAS reduced average path planning distance by 23.83% in 2D and planning time by 27.97% in 3D environments.

Conclusions:

  • The improved IABCBAS algorithm offers enhanced efficiency and reliability for path planning compared to traditional and existing swarm intelligence methods.
  • The integration of chaos theory, reverse learning, and adaptive strategies effectively overcomes limitations of individual algorithms.
  • The algorithm's performance improvements suggest significant potential for practical engineering applications in path planning.