Path planning with the Leapfrog method in the presence of obstacles

Abstract

In this work, the Leapfrog algorithm from optimal control is presented as a method for optimal path planning for a mobile robot in the presence of obstacles. The proposed algorithm allows the robot to plan a collision-free path through static obstacles by minimizing a cost functional that includes energy terms and the Gaussian potential function. The Leapfrog path is initialized using the RRT planning algorithm and refines the RRT result to produce an optimal path. Comparison is made with the BVP4C optimization algorithm showing that similar path cost can be obtained with the Leapfrog approach. The Leapfrog algorithm shows value for continued development as an optimal path planning method since it initializes easily, creates a feasible path on each iteration, and can find solutions where other solvers may fail.