Symmetry Error Cost Function-Based Modular Robot Tracking Control: An Approximate Dynamic Programming Cooperative Game Approach

To address the issue the that traditional positive definite quadratic cost function, which incorporates both state and control variables, tends to approach infinity over an infinite time horizon in tracking problems—thus rendering optimization infeasible—this paper proposes a symmetric error cost function-based approach for the tracking control of modular robots. The dynamic model of the modular robot system is constructed using joint torque feedback technology. By adopting the concept of approximate dynamic programming, each module of the system is treated as a participant in a cooperative game, transforming the trajectory tracking problem into an optimal control formulation. A critic fuzzy network is employed to approximate the system’s cost function, thereby deriving the optimal tracking control policy. The stability of the closed-loop system is demonstrated through the stability theorem, and the effectiveness of the proposed algorithm is verified via an experimental platform.