The first modification is that the map V in FMT consists of three-number lists, each of which contains q 1 , q 2 , F(q), which is the value of q 1 , the value of q 2 , and the corresponding free energy value F(q) instead of x and y in a 'normal' path planning problem. The second is that in the collision check process, the term 'collision' is confirmed by finding that the straight line that connects two sets of q 1 , q 2 passes through a pair of q 1 , q 2 whose energy is infinite or undefined. Additionally, the search radius, r, is defined as the set of points that have the distance ∆q 1 2 + ∆q 2 2 + ∆F(q) 2 less than r away from a specific point in V.