Collision free trajectory planning for multiple mobile robots in environment with periodic motion obstacle

In this paper, we study the collision free trajectory planning problem of multiple mobile robots in the environment with the periodic motion obstacle. We formulate this problem as an optimal control problem. We find the solution using the penalty function method and the conjugate gradient algorithm. The numerical examples show that the penalty function method is useful for the problem with moving obstacles in some cases. It is interesting to notice that considerably different trajectories are obtained according to the period of the motion of the moving obstacle, even though formulation is the usual simple optimal control one