Optimal motion planning of a multiple-robot system based on decomposition coordination

The problem of the optimal control of multiple-robot systems in the presence of obstacles is solved. All the robots are subject to state and control constraints. The method is based on nonlinear programming and decomposition coordination. The problem is solved by satisfying the constraints on the states and the controls as well as those on the obstacles. To generalize the problem, N_R robots with N_O obstacles are considered. No distinction is made between the different types of robots, allowing the generalization of this problem to the case of mobile robots with a known work space. In order to generate an optimal control that accounts for the presence of obstacles, all robot segments and obstacles are considered as convex and compact sets in R³. An additional property is used to obtain a distance function C¹. The proposed method is programmed on a VAX station and is used as a CACSD tool for the path planning of two modular assembly robots