A Generalized Reduced Gradient Method for the Optimal Control of Very-Large-Scale Robotic Systems

Abstract

This paper develops a new indirect method for distributed optimal control (DOC) that is applicable to optimal planning for very-large-scale robotic (VLSR) systems in complex environments. The method is inspired by the nested analysis and design method known as generalized reduced gradient (GRG). The computational complexity analysis presented in this paper shows that the GRG method is significantly more efficient than classical optimal control or direct DOC methods. The GRG method is demonstrated for VLSR path planning in obstacle-populated environments in which robots are subject to external forces and disturbances. The results show that the method significantly improves performance compared to the existing direct DOC and stochastic gradient methods.