Min-Max Optimal Control of Robot Manipulators Affected by Sensor Faults

Area of Science:

• Robotics
• Control Systems Engineering
• Fault-Tolerant Control

Background:

• Robot manipulator control is critical for operational reliability.
• Sensor faults can compromise system stability and performance.
• Existing methods may not adequately address fault tolerance and stability simultaneously.

Purpose of the Study:

• To synthesize a control law for robot manipulators that guarantees sensor fault effects remain within acceptable limits.
• To ensure the stability of the closed-loop system under fault conditions.
• To develop an efficient optimization procedure for control law synthesis.

Main Methods:

• Lyapunov stability analysis to derive conditions for optimization.
• Design of a control law simplifying Lyapunov function construction.
• Formulation of the optimization problem as a zero-sum differential game.
• Application of Newton's method with hyper-dual numbers for derivative calculation.

Main Results:

• Conditions for applying the bisection method in optimization were established.
• A control law was designed to facilitate stability analysis.
• The proposed algorithm effectively solved the zero-sum differential game.
• Simulations on a three-degree-of-freedom robot manipulator validated the approach.

Conclusions:

• The developed control law synthesis effectively manages sensor fault impacts.
• The closed-loop system stability is guaranteed under fault conditions.
• The optimization method provides an efficient approach for robust control design.