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Related Concept Videos

Rigid Body Equilibrium Problems - II01:21

Rigid Body Equilibrium Problems - II

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Virtual Work for a System of Connected Rigid Bodies

Virtual work is a powerful method used to solve problems involving several connected rigid bodies. When the system is in equilibrium, virtual work is zero. This allows the calculation of the resulting forces when a system undergoes a virtual displacement. When attempting to analyze such a system, first, use a free-body diagram, where an independent coordinate represents the configuration of the links, and mark its deflected position resulting from the positive virtual displacement.
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Rigid Body Equilibrium Problems - I00:49

Rigid Body Equilibrium Problems - I

A rigid body is said to be in static equilibrium when the net force and the net torque acting on the system is equal to zero. To solve for rigid body equilibrium problems, do the following steps.
Planar Rigid-Body Motion01:22

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Related Experiment Videos

Event-triggered adaptive formation control for multi-agent systems using ratio-of-distance rigidity.

Armin Sheikh Sofla1, Khalil Alipour2, Bahram Tarvirdizadeh1

  • 1Advanced Service Robots (ASR) Laboratory, Department of Mechatronics Engineering, School of Intelligent Systems Engineering, College of Interdisciplinary Science and Technology, University of Tehran, Tehran, Iran.

Scientific Reports
|June 25, 2026
PubMed
Summary

This study presents adaptive formation control for multi-agent systems using relative distance ratios. An event-triggered strategy reduces control updates while ensuring stable, coordinated maneuvers despite system uncertainties.

Keywords:
Adaptive formation controlEvent-triggered controlMulti-agent systemsNonsmooth controlRatio-of-distance (RoD) rigidityTime-varying formation maneuvering

Related Experiment Videos

Area of Science:

  • Robotics
  • Control Theory
  • Multi-Agent Systems

Background:

  • Coordinated control of multi-agent systems is crucial for complex tasks.
  • Maintaining rigid formations under dynamic conditions presents significant challenges.
  • Existing methods often require continuous communication and control updates.

Purpose of the Study:

  • To develop an adaptive formation control strategy for multi-agent systems.
  • To achieve and maintain rigid formations while tracking maneuvering velocities.
  • To enhance practical efficiency through an event-triggered control approach.

Main Methods:

  • Utilized a ratio-of-distance (RoD) rigidity framework for scalable formation description.
  • Developed distributed adaptive control laws with event-triggered updates.
  • Employed Lyapunov-based stability analysis for system verification.
  • Incorporated nonsmooth control terms for time-varying velocity tracking.

Main Results:

  • Formation errors asymptotically converge to zero.
  • Adaptive signals remain bounded, ensuring system stability.
  • Event-triggered control significantly reduces control updates compared to continuous methods.
  • Velocity consensus is achieved for maneuvering tasks.

Conclusions:

  • The proposed adaptive event-triggered formation control is effective for uncertain multi-agent systems.
  • The RoD framework facilitates scalable and stable rigid formation control.
  • The method offers practical advantages in terms of reduced communication and computation.