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

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.