Time-scale separation of a class of robust PD-type tracking controllers for robot manipulators

Area of Science:

• Robotics
• Control Systems Engineering
• Applied Mathematics

Background:

• Trajectory tracking is crucial for robot manipulator performance.
• Existing control methods may lack robustness or require precise parameter tuning.
• Singularly perturbed systems offer a theoretical framework for robust control design.

Purpose of the Study:

• To develop and analyze a class of PD-type robust controllers for robot manipulator trajectory tracking.
• To investigate the impact of parameterization on tracking error bounds.
• To explore extensions of the proposed controller for enhanced performance and reduced sensor requirements.

Main Methods:

• Application of singularly perturbed systems theory to design PD-type controllers.
• Parameterization of proportional and derivative gains using a perturbing parameter.
• Theoretical analysis to establish the relationship between the perturbing parameter and tracking error.
• Experimental validation on a planar two degrees-of-freedom direct-drive robot.

Main Results:

• A smaller perturbing parameter leads to a smaller ultimate bound of the joint position tracking error.
• Two controller extensions were proposed: one with error-varying gains and another with dynamic extension to eliminate joint velocity measurements.
• Experimental results demonstrated superior performance of a nonlinear PD controller derived from the proposed class.

Conclusions:

• The proposed PD-type robust controllers effectively improve robot manipulator trajectory tracking.
• The perturbing parameter offers a systematic way to tune controller gains for reduced tracking error.
• The nonlinear PD controller extension shows significant promise for practical robotic applications.