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In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
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Collision-free formation trajectory tracking control for second-order multi-agent systems by PPC method.

Liqiu Zhu1, Yining Qian2, An-Yang Lu3

  • 1College of Information Science and Engineering, Northeastern University, Shenyang 110819, China.

ISA Transactions
|July 17, 2025
PubMed
Summary
This summary is machine-generated.

This study ensures multi-agent systems safely track formation trajectories and maintain communication. It prevents collisions between agents and with obstacles using prescribed performance control and potential functions.

Keywords:
Collision avoidanceFormation trajectory trackingMulti-agent systemsPrescribed performance control

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Area of Science:

  • Robotics
  • Control Systems
  • Artificial Intelligence

Background:

  • Multi-agent systems require precise formation control and continuous communication.
  • Ensuring safety necessitates preventing collisions among agents and with environmental obstacles.

Purpose of the Study:

  • To develop a control strategy for multi-agent systems that achieves accurate formation trajectory tracking.
  • To maintain reliable communication links between agents.
  • To guarantee collision avoidance for both inter-agent and agent-obstacle scenarios.

Main Methods:

  • Prescribed Performance Control (PPC) method to design expected velocities for trajectory tracking and collision avoidance.
  • Introduction of a continuous potential function to generate an obstacle avoidance term within the expected velocity.
  • Development of a control algorithm for individual agents to adjust their velocities according to the designed expected velocity.

Main Results:

  • The proposed method enables agents to accurately follow a designated formation trajectory.
  • Effective prevention of collisions between agents.
  • Successful avoidance of obstacles in the operational environment.
  • Sustained communication links among the agents throughout the operation.

Conclusions:

  • The developed control strategy effectively addresses formation trajectory tracking and communication maintenance in multi-agent systems.
  • The integration of PPC and potential functions ensures comprehensive safety by mitigating collision risks.
  • Simulation results validate the robustness and efficacy of the proposed approach for practical applications.