2.3.2.2 Hybrid A-Star Algorithm

combination of the cost function of the Greedy Best Search ℎ(��) which manages to minimize the total cost to reach a goal greatly with disregard to optimality or completeness, the greedy cost function is added with the cost function of the uniform-cost search ��(��) which is optimal and complete but inefficient in most cases. From this combination the A* cost function is ��(��)= ��(��)+ℎ(��), where ��(��) returns the cost from the starting node to the node n, where the ℎ(��) function estimates the cost of the lowest-cost path from the node n to the goal node. As stated by (32), the A* algorithm is complete which means it will return a solution if there is any. Also, it returns an optimal solution, in case there are multiple solution it will return the path with the lowest cost of all.

2.3.2.2 Hybrid A-Star Algorithm

Hybrid A* based upon the standard A* algorithm. it is mostly used when a path planning algorithm for non-holonomic robots is needed (mostly cars), that is why it is implemented in autonomous vehicles. As thoroughly described in (33) the key difference between Hybrid A* and A* is the heuristic functions. Hybrid A* when calculating the cost of the path take into consideration factors such as the dimensions of the robot, its kinematic model including steering angle and the speed of the robot. This allows it to generate paths that are short but is the same time smooth and drivable for a car.

Heuristics guiding hybrid A* is divided into two heuristics. The first heuristic as named in (33) is called non-holonomic-without-obstacles, this functions as its name suggests, it does not into account the obstacles in the environment but it focuses on the non-holonomic nature of the car

when calculating the heuristic. The second heuristic function calculates the shortest distance to the goal while ignoring the non-holonomic nature of the car, this function is really useful in detecting all U-shaped obstacles and dead ends.

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