Distributed algorithms of stochastic games for robot systems in smart manufacturing.

Area of Science:

• Robotics
• Control Theory
• Optimization

Background:

• Distributed systems require robust equilibrium-seeking algorithms.
• Uncertainty in cost functions poses challenges for robot system coordination.
• Inequality constraints define operational boundaries for robotic agents.

Purpose of the Study:

• To develop a distributed algorithm for generalized stochastic Nash equilibrium seeking in robot systems.
• To handle cost functions with uncertainty and inequality constraints.
• To ensure stable and efficient coordination of multiple robots.

Main Methods:

• Utilizing Tikhonov regularization to manage cost function uncertainty.
• Introducing auxiliary parameters in control laws for equilibrium seeking.
• Employing the operator splitting method for convergence analysis.

Main Results:

• Successfully relaxed the strongly monotone condition to strictly monotone.
• Demonstrated convergence of the proposed control laws.
• Validated the algorithm's effectiveness in a multi-robot communication network example.

Conclusions:

• The proposed method effectively achieves distributed generalized stochastic Nash equilibrium seeking for robots.
• Tikhonov regularization and auxiliary parameters are key to handling uncertainty and constraints.
• The operator splitting method provides a rigorous framework for convergence analysis.