Two-stage algorithm for path planning problem with obstacle avoidance

The path-planning problem is considered for mobile robot inside environment with motionless circular obstacles in different sizes. The robot is expected to reach a given target by following the shortest path and avoiding the obstacles. The two-stage algorithm is proposed to solve the problem numerically. In the first stage a line-arc based path is found by using geometric techniques. This path cannot be minimal. However, its length can be used to restrict search space to an ellipse, which contains the minimal path. Thus, the reduced search space makes the next stage more efficient and endurable for real-time applications. In the second stage of the algorithm, by discretization of the restricted elliptic region the problem results in finding the shortest path in a graph and is solved by using the Dijkstra's algorithm. The proposed two-stage algorithm is verified with numerical simulations. The results show that the proposed algorithm is successful for obtaining an optimal solution. The applicability of the proposed algorithm is validated by practical experiment.