Optimal collision-free path planning of two mobile robots

An offline discrete-time collision-free path-planning scheme to allow two mobile robots to work in a common space is described. The problem is formalized as a minimax time collision-free path search problem. The degree of freedom of the problem is first reduced by applying the collision-free constraint. Subsequently, the solution is found by three levels of search. The golden-section search method is applied to reduce the amount of search required