ADP-Based Decentralized Adaptive Optimal Control for Two Cooperating Robots

This paper proposes a decentralized adaptive optimal control algorithm for two cooperating robots (2CR) to transport bulky loads in the form of beams based on adaptive dynamic programming (ADP). First, the cooperative model of 2CR is derived in the form of a strict-feedback nonlinear system, where Lagrange equations are used to present the dynamics. The Lagrange multipliers are relaxed by an appropriate projection method. In addition, disturbances of unknown dry friction forces of wheels on the ground are completely rejected. Second, an augmented decentralized feedforward controller is designed to decompose the centralized dynamics into decentralized dynamics. It is shown that if the decentralized closed-loop dynamics are stable, the originally centralized dynamics are also stable. Third, the ADP principle is used to design a decentralized adaptive optimal control law for the affine system. The Hamilton-Jacobi-Isaac (HJI) equation is established, and its nonanalytic solution is approximated by adaptive critic structures using only simple single-neural networks. It is shown that errors of function approximation and closed-loop signals are uniformly ultimately bounded. Finally, a numerical simulation is conducted to validate the effectiveness of the designed control algorithm.