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Safe Tracking Control of an Uncertain Euler-Lagrange System with Full-State Constraints using Barrier Functions.

Iman Salehi1, Ghananeel Rotithor1, Daniel Trombetta1

  • 1Department of Electrical and Computer Engineering at University of Connecticut, Storrs, CT 06269.

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Summary
This summary is machine-generated.

This study introduces a new safe tracking control method for uncertain Euler-Lagrange systems. It uses adaptive learning and barrier functions to ensure system states remain bounded during trajectory tracking.

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Area of Science:

  • Robotics
  • Control Systems Engineering
  • Applied Mathematics

Background:

  • Euler-Lagrange (EL) systems are widely used to model mechanical systems.
  • Controlling EL systems with uncertainties and state constraints is challenging.
  • Existing methods may not guarantee safety or handle parameter uncertainties effectively.

Purpose of the Study:

  • To develop a novel, safe tracking control design for uncertain Euler-Lagrange systems.
  • To ensure system states remain within prescribed bounds during operation.
  • To achieve accurate trajectory tracking despite unknown system parameters.

Main Methods:

  • Utilizing a barrier function (BF) to transform constrained dynamics into unconstrained ones.
  • Designing an adaptive tracking controller with online parameter learning laws.
  • Conducting stability analysis to guarantee semi-globally uniformly ultimately bounded (SGUUB) errors.

Main Results:

  • The proposed method successfully learns system parameters online.
  • Simulations with a two-link planar manipulator demonstrate effective trajectory tracking.
  • The controller ensures that system states remain within predefined bounds.

Conclusions:

  • The developed adaptive control method offers a safe and effective solution for uncertain EL systems.
  • Barrier functions are crucial for handling state constraints in adaptive control.
  • The approach guarantees bounded tracking and parameter estimation errors, validated through simulation.