Initialization of the leapfrog algorithm for mobile robot path planning

Abstract

This work deals with formulating an optimal motion planning problem for a mobile robot in the presence of obstacles using optimal control. For obstacle avoidance, a repulsive potential function defined as a Gaussian function is applied in the cost functional which minimizes the energy control effort. The Leapfrog method numerically solves the formulated optimal control problem. With Leapfrog one has only to choose the initial and final states. An initial feasible path is prescribed and subdivided into path segments. In this work, the trajectories produced by A* and RRT algorithms are used as initial feasible paths for Leapfrog. Simulations are performed to evaluate the effectiveness of the Leapfrog method. It is observed that the optimal path that Leapfrog produces does not depend on the initial path, nor on the method by which the initial path is formed.