Exponential and robust position-constrained control of robot manipulators via diffeomorphisms

Area of Science:

• Robotics
• Control Engineering
• Nonlinear System Dynamics

Background:

• Mechanical systems with constraints are crucial in control engineering.
• Stabilizing nonlinear systems under constraints requires advanced control strategies.
• Existing methods often involve complex computations for constraint satisfaction.

Purpose of the Study:

• To propose a design procedure for position-constrained controllers in robot manipulators.
• To develop a control strategy that simplifies handling system constraints.
• To achieve stable control for robotic systems without violating position constraints.

Main Methods:

• Constructing a diffeomorphism to map constrained dynamics to unconstrained dynamics.
• Designing the controller in the transformed unconstrained space.
• Employing an explicit control law to avoid extra computations.
• Augmenting with sliding modes for uncertain cases to ensure finite-time convergence.

Main Results:

• Achieved exponential stability in both constrained and unconstrained states for the certain case.
• Guaranteed finite-time convergence and exponential convergence within the manifold for the uncertain case.
• Validated the approach through experimental results on a 2 DOF lightweight robot manipulator.

Conclusions:

• The proposed controller design effectively handles position constraints in robot manipulators.
• The diffeomorphism-based approach simplifies controller design and computation.
• The method offers robust stability guarantees even in the presence of system uncertainties.