12.4 A mobile robot moves in the x-y plane among obstacles. All the obstacles are rectangles aligned with the x and y axes. The robot can only move in the directions x and y, and is so small that it can be approximated by a point. The robot has to plan collision-free paths between its current position to some given goal position. The robot aims at minimizing the path length and the changes of the direction of movement (let the cost of one change of direction be equal to one unit of length travelled). The robot uses the A* algorithm to find optimal paths. Define the predicates s( State, NewState, Cost) and h( State,H) (preferably admissible) to be used by the A* program for this search problem. Assume that the goal position for the robot is defined by the predicate goal( Xg/Yg) where Xg and Yg are the x and y coordinates of the goal point. The obstacles are represented by the predicate obstacle(Xmin/Ymin, Xmax/Ymax) where Xmin/Ymin is the bottom left corner of the obstacle, and Xmax/Ymax is its top right corner.