Path planning algorithms have evolved during decades to become computationally less expensive and optimal. In this paper a deterministic approach is used to find a path near to the shortest path using motion primitives. The motion primitives are constructed using a non-holonomic vehicle model. The physical model enables the algorithm to use a friction map and calculate paths with lower lateral slip forces. Furthermore the algorithm takes into account the steer rate using steer angles assigned for motion primitives. The algorithm is an A* based search method along with a heuristic to find a near optimal solution. The performance and calculation time of the algorithm is tunable by adjusting motion primitive size and discretization steps. In order to compare the algorithm output to optimal solution a direct multiple shooting method is used. The algorithm is simulated in different scenarios that shows the properties of the algorithm. The results attained from search method is compared with optimal solution in two different test scenarios and the comparison shows consistency of search method to the optimal solution.