Fictitious play based Markov game control for robotic arm manipulator

Abstract

Markov games can be used as a platform to deal with exogenous disturbances and parametric variations. In this work an attempt has been made to achieve a superior performance with fuzzy Markov game based control by hybridizing two game theory based approaches of `fictitious play' and `minimax'. The work attempts a `safe yet consistent' Markov game controller which advocates a minimax policy during the startup control stages and later moves to a more enterprising policy based on stochastic fictitious play. The proposed controller addresses continuous state action space problems wherein we use fuzzy inference system as a universal approximator for generalization with a proportional derivative control in the nested position tracking loop. The proposed controller is simulated on a two link robot and its performance compared against fuzzy Markov game control and fuzzy Q control. Simulation results elucidate the fact that proposed control scheme leads to an improved controller with lower tracking error and torque requirements.