  In this paper, a modification of A* algorithm is considered for the shortest
path problem. A weightage is introduced in the heuristic part of the A*
algorithm to improve its efficiency. An application of the algorithm is
considered for UAV path planning wherein velocity is taken as the weigtage to
the heuristic. At the outset, calculus of variations based Lagrange's equation
was used to identify velocity as the decisive factor for the dynamical system.
This approach would be useful for other problems as well to improve the
efficiency of algorithms in those areas.
